The flight of the ball, and particularly of the golf ball, exercises a strange fascination for many people to whom the phenomena of flight exhibited by a spinning ball travelling through the air, are not of the slightest practical importance. That is to say, there is an immense number of people who take merely a scientific, and one might almost say an artistic interest in the effects produced by the combined influence of spin and propulsion. Scientific men have been for many years well aware of the causes which produce the swerve of a ball in the air. By swerve I mean, of course, a curve in the flight of the ball which is due to other causes than gravitation, and in the word swerve I do not include the drift of a ball which has been perfectly cleanly hit, but which, in the course of its carry, has been influenced by a cross wind. This does not legitimately come under the heading of swerve. It is more correctly described as drift, and will be dealt with in due course.

In the Badminton Magazine of March 1896, the late Professor Tait published an article on "Long Driving." Professor Tait was a practical golfer and a very learned and scientific man. He proved most clearly that a golf ball could not be driven beyond a certain distance. He proved this absolutely and conclusively by mathematics, but, so the story runs, his son, the famous Freddie Tait, proved next day with his driver, that his father's calculations were entirely wrong, for he is alleged to have driven a golf ball over thirty yards farther than the limit which his learned parent had shown to be obtainable. Naturally, Professor Tait had to reconsider his statements, and he then arrived at the conclusion that there must have been in the drive of his son, which had upset his calculations, some force which he had not taken into consideration. He soon came to the conclusion that this was back-spin, and he dealt with this matter of back-spin, which is a matter of extreme importance to golf, in a most erudite article, which is much too advanced for the ordinary golfer, so I shall content myself here with referring to just a few of the most important points in connection with it. It is necessary that I should, in dealing with the flight of the ball, give those of my readers who are not already acquainted with the simple principles of swerve, some idea of what it is which causes the spinning ball to leave the line of flight that it would have taken if it had been driven practically without spin.

The explanation is very simple. If a ball is proceeding through the air, and spinning, the side which is spinning towards the hole gets more friction than the other side which is spinning away from the hole. It is well known that a projectile seeks the line of least resistance in its passage through the air. It follows that the greater friction on the forward spinning half causes the ball to edge over towards the side which is spinning away from the hole. This, in a very few words, is the whole secret of swerve.

Professor Tait stated in his article that Newton was well aware of this fact some 230 years before the publication of the professor's article, and that he remarked when speaking of a spinning tennis ball with a circular as well as a progressive motion communicated to it by the stroke, "that the parts on that side where the motions conspire must press and beat the contiguous air more violently, and there excite a reluctancy and reaction of the air proportionately greater."

This really is an extremely simple matter and a very simple explanation. I have taken care to explain it so simply, for swerve is, by a very great number of people, looked upon as an abstruse problem—in fact, my book on Swerve, or the Flight of the Ball, is catalogued as a treatise on applied mathematics, instead of, as I intended it to be, simply a practical application of the ascertained facts to the behaviour of the ball in the air.

Professor Tait's article has enjoyed a wonderful vogue. Although it was published nearly twenty years ago it is quite frequently quoted at the present time. There are, however, in it some errors which one would not have expected to have found in such a scientific article. Speaking of the golf ball shortly after it has left the club, Professor Tait said:

It has a definite speed, in a definite direction, and it may have also a definite amount of rotation about some definite axis. The existence of rotation is manifested at once by the strange effects it produces on the curvature of the path so that the ball may skew to right or left; soar upwards as if in defiance of gravity, or plunge headlong downwards instead of slowly and reluctantly yielding to that steady and persistent pull.

There is, in this statement of Professor Tait's, a fundamental error in so far as regards the flight of the ball. He said: "The existence of rotation is manifested at once by the strange effects it produces on the curvature of the path." This is incorrect from a scientific point of view, and it is also badly stated. The existence of rotation is not manifested "at once"; in very many cases, practically in all, the ball proceeds for quite a long distance before the effect of rotation is seen. This is more particularly so when it is a matter of back-spin, but it is equally true of the pulled ball or the sliced ball. Both of these proceed for a considerable distance before the effect of spin is noticeable. In fact it is well known to all golfers that the spin begins to get to work as the velocity of the ball decreases. Also it seems as though it is incorrect to refer to the strange effects it (rotation) produces on the curvature of the path, for it is the rotation itself which produces the curvature.

Professor Tait then said:

The most cursory observation shows that a ball is hardly ever sent on its course without some spin, so that we may take the fact for granted, even if we cannot fully explain the mode of its production. And the main object of this article is to show that long carry essentially involves under-spin.

I shall deal with these two statements later on.

Professor Tait said:

To find that his magnificent carry was due merely to what is virtually a toeing operation—performed no doubt in a vertical and not in a horizontal plane, is too much for the self-exalting golfer!

The fact, however, is indisputable. When we fasten one end of a long untwisted tape to the ball and the other to the ground and then induce a good player to drive the ball (perpendicularly to the tape) into a stiff clay face a yard or two off, we find that the tape is always twisted in such a way as to show under-spin; no doubt to different amounts by different players, but proving that the ball makes usually from about one to three turns in six feet, say from forty to a hundred and twenty turns per second, this is clearly a circumstance not to be overlooked.

It is wonderful how easily a scientific man, as Professor Tait was, can be led astray when he sets out to find the thing he has imagined. Professor Tait, by a footnote to his article in the Badminton Magazine, to my mind entirely discounts the value of his experiments. His footnote is so important that I must quote it fully. He says:

In my laboratory experiments, players could not be expected to do full justice to their powers. They had to strike as nearly as possible in the centre, a ten-inch disc of clay, the ball being teed about six feet in front of it. Besides this pre-occupation, there was always more or less concern about the possible consequence of rebound, should the small target be altogether missed.

It will be apparent even to anyone who is not possessed of a scientific or analytical mind that Professor Tait compelled his players to endeavour to play their strokes in such a manner that the ball had to travel down a line decided on by Professor Tait. I do not know at what height Professor Tait placed his clay disc from the earth, but it is evident that if he put it very low down it would involve the playing by the golfer of a stroke which would naturally produce back-spin, and in any case the trajectory was arbitrarily fixed. In experimenting with such a stroke as this, and in such a manner as this, it should be evident that there should have been no restriction whatever as to the player's trajectory. If it was decided that it was necessary to catch the ball in a clay disc, that disc should have been so large that it was impossible for the golfer's ball to escape it. It should not have been necessary for the golfer to aim at the disc. The mere fact of his aiming at the disc and the ball being teed so near as six feet to the disc, all tended to produce the shot which would give the results which Professor Tait was looking for, but that does not prove that the ordinary stroke at golf is produced in a similar manner, and I do not for one moment believe that it is.

In speaking of the stroke proper Professor Tait said:

The club and the ball practically share this scene between them; but the player's right hand, and the resistance of the air, take some little part in it. It is a very brief one, lasting for an instant only, in the sense of something like one ten-thousandth of a second.

We may note here that Professor Tait said: "The right hand and the resistance of the air take some little part in it." One would be inclined to think from this that Professor Tait was, as indeed was probably the case, an adherent of the fetich of the left, for there can be no doubt that in "the stroke proper" the right hand does much more than take "some" little part in it.

I think that Professor Tait is wrong in his idea that under-spin, or, as I prefer to call it, back-spin, is essential to a long carry. I firmly believe that a ball which is hit with practically no spin whatever, can have a very long carry. However, as the paper which I am now about to consider follows in many ways very closely on the lines of Professor Tait's article, I shall leave this matter for consideration when I am dealing with that paper.

The paper which I am now referring to is one which was read at the weekly evening meeting of the Royal Institution of Great Britain on Friday, 18th March 1910, by Professor Sir J. J. Thomson, M.A., LL.D., D.S.C., F.R.S., M.R.I., O.M.; Cavendish Professor of Experimental Physics, Cambridge; Professor of Physics, Royal Institution, London; Professor of Natural Philosophy, Royal Institution, and winner of the Nobel Prize for Physics, 1906. The title of this paper was "The Dynamics of a Golf Ball." It will be observed that neither the Institution under the auspices of which this lecture was delivered, nor the lecturer, is inconsiderable. Professor Thomson is, without doubt, a very distinguished physicist, and we must therefore receive anything he writes with a certain amount of respect. There are, however, in this paper, so many remarkable statements that it is necessary for me to deal with it quite fully.

Professor Thomson tells us very early in the lecture that Newton was well aware of the cause of swerve which I have already set out, some 250 years ago, and that he remarked that in a spinning tennis ball the "parts on that side where the motions conspire, must press and beat the contiguous air more violently, and there excite a reluctancy and reaction of the air proportionately greater."

Professor Thomson says at the beginning of his lecture:

There are so many dynamical problems connected with golf that a discussion of the whole of them would occupy far more time than is at my disposal this evening. I shall not attempt to deal with the many important questions which arise when we consider the impact of the club with the ball, but shall confine myself to the consideration of the flight of the ball after it has left the club.

I may say here that Professor Thomson, although he announces his intention of doing this, is later on in his paper, as we shall see, tempted into considering the questions of impact, and, in my opinion, making several grave errors therein. We may, however, in the meantime, pass this by.

Professor Thomson continues:

This problem is in any case a very interesting one, which would be even more interesting if we could accept the explanations of the behaviour of the ball given by some contributors to the very voluminous literature which has collected around the game. If this were correct, I should have to bring before you this evening a new dynamics and announce that matter when made up into golf balls obeys laws of an entirely different character from those governing its action when in any other condition.

This, at the outset, is an extremely remarkable statement to come from so eminent a physicist, for I may say that Professor Thomson, after making a remark of this nature, proceeds to explain the phenomena of swerve on exactly the same links which I have set out fully and explicitly in my book Swerve, or the Flight of the Ball. That, however, is a matter of small importance. It may be that Professor Thomson has not had the opportunity of perusing this book. It may indeed be that Professor Thomson has been unfortunate enough only to have read articles wherein an erroneous explanation of the well-known phenomena of the flight of the ball is given. Be that as it may, there can be no doubt that the explanation which has been given of the causes of swerve has been adequate and accurate, and there would not have been any necessity whatever for Professor Thomson to bring before the learned Institution whose fellows listened to his address "a new dynamics." It would have been sufficient if he had correctly explained the phenomena of the flight and run of a golf ball according to the well-recognised laws which govern the flight and run of all balls. This, however, he quite failed to do.

Professor Thomson says: "If we could send off the ball from the club as we might from a catapult, without spin, its behaviour would be regular, but uninteresting." It is quite possible to send a golf ball off a club without spin. It is just as possible, from a practical point of view, to send a golf ball away without spin from the face of a driver as it is from the pouch of a catapult. The catapult is a machine, and it is a certainty that it can be made to propel a golf ball without any initial spin whatever. A machine can be made to drive a golf ball with just as little spin, and as a matter of practical golf, by far the greater number of golf balls are driven without appreciable spin—that is to say, without spin which has any definite action on the flight of the ball.

The learned lecturer says: "A golf ball when it leaves a club is only in rare cases devoid of spin." It is impossible to prove or disprove this statement, for practically no ball goes through the air with the same point always in front. We may see this quite clearly if we care to mark a lawn-tennis ball, and to hit it perfectly truly, and slowly, so that it goes almost as a lob across the net. We shall see even then that the marked part of the ball moves from one place to another. In fact, even if a golf ball were driven by a machine which did not impart to it any initial spin, it is almost a certainty that that ball would not have proceeded far before it had acquired sufficient motion to justify one in technically calling it spin. Spin, however, is a delightfully indefinite word, but this much one may at least say, and it is, in effect, a contradiction of Sir J. J. Thomson's assertion, namely that in the vast majority of balls hit with golf clubs, especially by skilled players, the effect of spin on the stroke unless designedly applied, which is comparatively rare, is practically negligible.

Professor Thomson says that

... a golf ball, when it leaves the club, is only in rare cases devoid of spin, and it is spin which gives the interest, variety, and vivacity to the flight of the ball; it is spin which accounts for the behaviour of a sliced or pulled ball; it is spin which makes the ball soar or "douk," or execute those wild flourishes which give the impression that the ball is endowed with an artistic temperament and performs these eccentricities, as an acrobat might throw in an extra somersault or two for the fun of the thing. This view, however, gives an entirely wrong impression of the temperament of a golf ball, which is, in reality, the most prosaic of things, knowing while in the air only one rule of conduct which it obeys with an intelligent conscientiousness, that of always following its nose. This rule is the key to the behaviour of all balls when in the air, whether they are golf balls, base-balls, cricket balls, or tennis balls.

The idea of a spherical object having a nose is so unscientific and so inexact that it is not necessary for me to dwell very strongly on it here, and I should not do so were it not that this looseness of description is of considerable importance in dealing with Professor Thomson's ideas. He continues:

Let us, before entering into the reasons for this rule, trace out some of its consequences. By the nose on the ball we mean the point on the ball furthest in front.

It will be obvious to my readers that this description is scientifically extremely inaccurate, for if we take a line through the ball from the point of contact with the club to the point on the ball farthest in front, which Professor Thomson calls its nose, we shall find that the flight of that ball will always be in that same line produced, whereas in the spinning ball it is nothing of the sort. The whole trouble here is that Professor Thomson wants to have the "nose," as he calls it, of the ball, both a fixed and a moving point. This, obviously, is most unscientific. If the nose of the ball is the point that is farthest in front, I cannot say too emphatically that it stands to reason that the ball in flight will go straight out after that point, but the fact is that the point in front is continually changing; moreover, the fact that the ball goes the way it is spinning is not explained by any tendency of the ball to wander that way on account of the spin irrespective of the friction of the air.

It will thus be seen that Professor Thomson's explanation in this matter is incorrect and misleading. This is about the most unscientific explanation which could be given of this matter, and it is one which is calculated to mislead people who would otherwise understand the matter quite clearly, so we shall drop Professor Thomson's idea of giving the ball a "nose" which is always in the front of it, but which is also supposed to be continually travelling sideways. It is obvious that Professor Thomson cannot have it both ways.

It is very clear indeed that Professor Thomson is not well acquainted with the method of applying spin to balls which are used in playing games. He says:

A lawn-tennis player avails himself of the effect of spin when he puts "top-spin" on his drives, i.e. hits the ball on the top so as to make it spin about a horizontal axis, the nose of the ball travelling downwards as in figure 4; this makes the ball fall more quickly than it otherwise would, and thus tends to prevent it going out of the court.

I have played lawn-tennis for more than twenty years, and I am the author of three books on the game, one of which is supposed to be the standard work on the subject, and I can assure Professor Thomson that no lawn-tennis player would dream of doing anything so silly as to hit a lawn-tennis ball "on the top" in an attempt to obtain "top-spin."

The scientific method of obtaining top-spin is to hit the lawn-tennis ball on what Professor Thomson, if he were driving the ball over the net to me, would call its nose—that is to say, I should hit the ball on the spot which was farthest from Professor Thomson. I should hit it there with a racket whose face was practically vertical, but I should hit it an upward, forwardly glancing blow which would impart, as Professor Thomson expresses it, "spin about a horizontal axis to the ball."

Professor Thomson goes so far as to show by diagram the travel of a ball which has been hit so as to impart top-spin to it, but even in this diagram he is absolutely wrong, for he shows that immediately the ball has been hit with top-spin it begins to fall, but this is not so. In lawn-tennis the ball travels for a long distance before the spin begins to assert itself, and to overcome the force of the blow which set up the spin.

Professor Tait makes this same error in his article on "Long Driving," and it is quite evident to me that Professor Thomson is following, in many respects, the errors of his eminent predecessor.

Professor Thomson also says:

Excellent examples of the effect of spin on the flight of a ball in the air are afforded in the game of base-ball. An expert pitcher, by putting on the proper spin, can make the ball curve either to the right or the left, upwards or downwards; for the side-way curves the spin must be about a vertical axis; for the upward or downward ones, about a horizontal axis.

There are no particular laws with regard to the curves of a base-ball. The same laws regulate the curves in the air of every ball from a ping-pong ball to a cricket ball, and Professor Thomson, in saying that "for the side-way curves the spin must be about a vertical axis," is absolutely wrong. Every lawn-tennis player who knows anything whatever about the American service, will know that Professor Thomson is utterly wrong in this respect, for the whole essence of the swerve and break of the American service, which has a large amount of side-swerve, is that the axis of rotation shall be approximately at an angle of fifty degrees, and any expert base-ball pitcher will know quite well that he can get his side-curve much better if he will, instead of keeping his axis of rotation perfectly vertical, tilt it a little so that it will have the assistance of gravitation at the end of its flight instead of fighting gravitation, as it must do if he trusts entirely to horizontal spin about a vertical axis for his swerve.

Professor Thomson says:

If the ball were spinning about an axis along the line of flight, the axis of spin would pass through the nose of the ball, and the spin would not affect the motion of the nose; the ball, following its nose, would thus move on without deviation.

The spin which Professor Thomson is describing here is that which a rifle bullet has during its flight, for it is obvious that the rifle bullet is spinning "about an axis along the line of flight," and that the axis of spin does pass through the nose of the bullet, but we know quite well that in the flight of a rifle bullet there is a very considerable amount of what is called drift. It is, of course, an impossibility to impart to a golf ball during the drive any such spin as that of the rifle bullet, although in cut mashie strokes, and in cutting round a stymie, we do produce a spin which is, in effect, the same spin, but this is the question which Professor Thomson should set himself to answer. He states distinctly that a ball with this spin would not swerve. If this is so, can Professor Thomson explain to us why the rifle bullet drifts? As a matter of fact, a ball with this spin would swerve, but not to anything like the same extent as would a ball with one of the well-recognised spins which are used for the purpose of obtaining swerve.

PLATE XI.

Professor Thomson proceeded to prove by the most elaborate experiments the truth of those matters stated by Newton centuries ago, but it will not be necessary for me to follow him in these, because these principles have been recognised for ages past.

It is curious to note that in the reference to Newton, who was aware of this principle of swerve so long ago, we are shown that Newton himself did not quite grasp the method of production of the stroke, although he analysed the result in a perfectly sound manner. Writing to Oldenburg in 1671 about the Dispersion of Light, he said in the course of his letter: "I remembered that I had often seen a tennis ball struck with an oblique racket describe such a curved line." The effect of striking a tennis ball with an oblique racket is, generally speaking, to push it away to one side. The curve, to be of a sufficiently pronounced nature to be visible, must be produced by the passage of the racket across the intended line of flight of the ball.

This matter of the different pressure on one side of the ball from that on the other is very simple when one thoroughly grasps it. Professor Thomson gives in his paper an illustration which may perhaps make the matter clearer to some people than the explanation which is generally given. He says:

It may perhaps make the explanation of this difference of pressure easier if we take a somewhat commonplace example of a similar fact. Instead of a golf ball let us consider the case of an Atlantic liner, and, to imitate the rotation of the ball, let us suppose that the passengers are taking their morning walk on the promenade deck, all circulating round the same way. When they are on one side of the boat they have to face the wind, on the other side they have the wind at their backs. Now, when they face the wind, the pressure of the wind against them is greater than if they were at rest, and this increased pressure is exerted in all directions and so acts against the part of the ship adjacent to the deck; when they are moving with their backs to the wind, the pressure against their backs is not so great as when they were still, so the pressure acting against this side of the ship will not be so great. Thus the rotation of the passengers will increase the pressure on the side of the ship when they are facing the wind, and diminish it on the other side. This case is quite analogous to that of the golf ball.

Even in this simple illustration it seems to me that Professor Thomson is wrong, for he is pre-supposing that which he does not state—a head wind. It is quite obvious that these passengers might have to face a wind coming from the stern of the ship, and in this case the analogy between the passengers circulating round the deck of a ship, and his golf ball would receive a serious blow. In stating a matter which is of sufficient importance to be dealt with before such a learned body as the Royal Institution of Great Britain, it is well to be accurate. If Professor Thomson had stated that his Atlantic liner was going into a head wind, or, for the matter of that, even proceeding in a dead calm, his analogy might have been correct, but it is obvious that he has left out of consideration a following wind of greater speed than that at which the liner is travelling.

Professor Thomson has not added anything to the information which we already possessed with regard to the effect of back-spin on a ball; rather has he, as I shall show when dealing with the question of impact with the ball, clouded the issue. At page 12 of his remarkable lecture he says: "So far I have been considering under-spin. Let us now illustrate slicing and pulling; in these cases the ball is spinning about a vertical axis." We here have a very definite statement that in slicing and pulling the ball is spinning about a vertical axis, but it is not doing so.

Professor Thomson has "an electromagnet and a red hot piece of platinum with a spot of barium oxide upon it. The platinum is connected with an electric battery which causes negatively electrified particles to fly off the barium and travel down the glass tube in which the platinum strip is contained; nearly all the air has been exhausted from this tube. These particles are luminous, so that the path they take is very easily observed."

These particles, I may explain, take, in Professor Thomson's mind, the place of golf balls, and by an electromagnet he shows us exactly what golf balls do, but it seems to me that if Professor Thomson is not absolutely clear what is happening to the sliced ball and the pulled ball, there is a very great chance that, like Professor Tait, he may induce his particles to do the thing that he wishes them to do, and not the thing that a real golf ball with a real pull or a real slice would do. This, as a matter of fact, is exactly what Professor Thomson does, for, as I shall show quite simply and in such a manner as absolutely to convince the merest tyro at golf, Professor Thomson is utterly wrong when he states that in the slice and the pull the ball is spinning about a vertical axis.

I shall not need any diagrams or figures to bring this home to anyone who is possessed of the most rudimentary knowledge of mechanics. It should be quite evident to anyone that to produce spin about a vertical axis it would be necessary to have a club with a vertical face, or to strike a blow with the face of the club so held that at the moment of impact the face of the club was vertical. Now this does not happen with the slice at golf, for the very good reason that if one so applied one's club, the ball would not rise from the earth. The club which produces the slice is always lofted in a greater or less degree, and quite often the natural loft is increased by the player designedly laying the face back during the stroke. It is evident that in the impact with the driver or brassy, the ball, especially the modern rubber-cored ball, flattens on to the face of the club and remains there whilst the club is travelling across the line of flight. This naturally imparts to the ball a roll—in other words, as the club cuts across the ball it rolls it for a short distance on its face.

It is obvious that this rolling process will, to a greater or less extent, give to the ball a spin about an axis which is approximately the same as that of the loft on the face of the club. Therefore, it is clear that in all sliced balls the axis of spin will be inclined backward. It seems likely, also, that as the axis of spin is inclined backward and the ball is rising, there will be some additional friction at the bottom of it which would not be there in the case of a ball without spin. This probably helps to produce the sudden rise of the slice. In all good cut shots with lofted clubs, the angle of the axis of spin is to a very great extent regulated by the amount of loft on the face of the club.

Professor Thomson's error with regard to the slice being about a vertical axis is beyond question, but his error in saying that the axis of rotation of the pull and the slice is identical, is, from a golfing point of view, simply irretrievable. Print is a very awkward thing—it stays. The merest tyro at golf knows quite well that the pulled ball and the sliced ball behave during flight and after landing on the ground in a totally different manner from each other. If Professor Thomson knows so much, it should unquestionably be evident to so distinguished a scientist that there must be a very considerable difference in the rotation of these balls. The slice, as is well known, rises quickly from the ground, flies high, and is not, generally speaking, a good runner. The pull, on the other hand, flies low and runs well on landing.

It is not merely sufficient to contradict Professor Sir J. J. Thomson in these matters, so I shall explain fully the reason for the difference in the flight and run of the slice and the pull. The slice is played as the club head is returning across the line of flight, and therefore is more in the nature of a chop than is the pull. Frequently the spin that is imparted to the ball is the resultant of the downward and inwardly glancing blow. This not only leaves the axis of rotation inclined backward, but sometimes inclined also slightly away from the player, but it is obvious that even if the ball had, as Professor Thomson thinks it has, rotation about a vertical axis, which is the rotation of a top, such rotation would, on landing, tend to prevent the ball running, for, as is well known, every spinning thing strives hard to remain in the plane of its rotation, but the slice is more obstinate still than this, for the axis of rotation being inclined backward, frequently at the end of the flight, coincides with the line of flight of the ball, so that the ball is spinning about an axis which, to adopt Professor Thomson's term, runs through its "nose." This means that the slice frequently pitches in the same manner as might a rifle bullet if falling on its "nose," and the effect is, to a very great extent, the same. The ball tries to stay where it lands.

Let us now consider the flight and run of the pull. The pull is played by an upward, outward, glancing blow. The ball is hit by the club as it is going across the line of flight away from the player and this imparts to the ball a spin around an axis which lies inward towards the player. This means that the pull goes away to the right, and then swerves back again towards the middle of the course if properly played, and upon landing runs very freely. The reason for this run has not been clearly understood by many, and it is quite evident that Professor Thomson does not know of it, so I shall give an extremely plain illustration.

Nearly every boy has at some time played with a chameleon top, or some other top of the same species, that is to say, a disc top. Every boy who has played with such a top will be familiar with the fact that when the spin is dying away from the top, it rolls about until one edge of it touches the earth or whatever it is spinning on. Immediately this happens the top runs away as carried by the spin.

That is about the simplest illustration which it is possible to give of the plane of spin of the pulled ball during its flight and of its run after it has touched the earth, but from this very simple explanation it will be perfectly obvious to anyone who gives the matter the least consideration that not only is the axis of rotation of the pull and the slice dissimilar, but as a matter of fact the rotation of the pull and the slice is almost diametrically opposed the one to the other.

Professor Thomson says:

Let us now consider the effect of a cross wind. Suppose the wind is blowing from left to right, then, if the ball is pulled, it will be rotating in the direction shown in figure 26 (from right to left); the rules we found for the effect of rotation on the difference of pressure on the two sides of a ball in a blast of air show that in this case the pressure on the front half of the ball will be greater than that on the rear half, and thus tend to stop the flight of the ball. If, however, the spin was that for a slice, the pressure on the rear half would be greater than the pressure in front, so that the difference in pressure would tend to push on the ball and make it travel further than it otherwise would.

I have not given this aspect of the question a great amount of thought, but it seems obvious that in playing for a slice in the circumstances mentioned by Professor Thomson, it is extremely unlikely that the greater pressure would be, as he says, on the rear half. If, indeed, this were so the slice would, in my opinion, not take effect; also on account of the tremendous speed of the golf ball it seems to me utterly improbable that in any ordinary wind which one encounters on a golf links it would be possible to obtain on the rear half of a golf ball a greater pressure than that on the forward spinning half, or, to be more accurate, quarter of the ball. I cannot help thinking that Professor Thomson in saying that in such a case as this the greater pressure would be on the rear half of the ball is falling into an error, for it seems to me that he is overlooking the tendency of the ball to set up for itself something in the nature of a vacuum which will undoubtedly tend to protect the rear portion of the ball from the force which must assail it in front during its passage through the air.

Professor Thomson says that "the moral of this is that if the wind is coming from the left we should play up into the wind and slice the ball, while if it is coming from the right we should play up into it and pull the ball."

That is Professor Thomson's theory. I shall give my readers the benefit of my practice, which is that whenever there is a cross wind of any description whatever, hit the ball as straight as it is possible for you to do it, right down the middle of the course from the tee to the hole, and forget all about pulls or slices. On a windy day avoid anything whatever in the nature of side-spin because once you have applied it to a ball you never know where that ball is going to end, and if you want any confirmation for this practice you may get it from Harry Vardon in The Complete Golfer, for there can be very little doubt that a side wind has nothing like the effect on the ball that golfers seem to imagine, provided always, of course, that the ball be hit cleanly and without appreciable spin. It is not given to one golfer in a thousand to know how to use the pull and slice to obtain assistance from the wind and also to be capable of executing the strokes. As a matter of practical golf these strokes should, for at least ninety-five per cent of golfers, be rigidly eschewed.

At the beginning of Professor Thomson's article he said:

I shall not attempt to deal with the many important questions which arise when we consider the impact of the club with the ball, but confine myself to the consideration of the flight of the ball after it has left the club.

It would, indeed, have been well if Professor Thomson had carried out his expressed intention of leaving this matter alone, for in dealing with it he has shown most conclusively that he has no practical grip of the question which he has attempted to deal with. At page 15 of his article he says:

I have not time for more than a few words as to how the ball acquires the spin from the club, but if you grasp the principle that the action between the club and the ball depends only on their relative motion, and that it is the same whether we have the ball fixed and move the club, or have the club fixed and project the ball against it, the main features are very easily understood.

I can readily believe that this statement of Professor Thomson's is absolutely accurate. The only thing which troubles me about it is that I think the person of ordinary intellect will find it absolutely impossible to "grasp the principle" which Professor Thomson lays down. If we have the club fixed and project the ball against it, we know quite well that the ball will rebound from the club, but if we are to have the ball fixed and move the club against it, nothing will happen unless we move the club fast enough, in which case we should simply smash the club.

This is a most amazing illustration of looseness of thought—such an astonishing illustration that I should not have believed Professor Thomson capable of it if it had not been published broadcast to the world with his authority. Of course, I know perfectly well what Professor Thomson means to say, but I have not to deal with that, and as a matter of fact what he means to say is quite wrong, but it will be sufficient for me to show that what he does say is wrong.

Professor Thomson then goes on to say:

Suppose Fig. 27 represents the section of the head of a lofted club moving horizontally forward from right to left, the effect of the impact will be the same as if the club were at rest and the ball were shot against it horizontally from left to right.

Here Professor Thomson shows that he is quite under a misapprehension as to the production of the golf stroke. He pre-supposes that the club is moving in a horizontal direction at the moment it hits the ball. In a vast majority of instances, probably in about ninety per cent of cases, the club is not moving in a horizontal direction—in fact, it would be hardly too much to say that it never moves in a horizontal direction. It is nearly always moving either upwards or downwards in a curve at the moment it strikes the ball, so that it stands to reason, especially when the club face is travelling upwards, which is what it does in the great majority of cases, that the blow is never delivered horizontally, but is always struck more or less upward through the ball's centre of mass.

Practical teachers of golf know how extremely hard it is to induce the beginner, and for the matter of that many people who are far beyond beginners, to trust the loft of the club to raise the ball from the earth; so many players never get out of the habit of attempting to hit upwards.

It stands to reason that if the blow in golf were delivered as with a billiard cue, any blow struck in that manner, provided the face of the club had sufficient loft, would tend to produce back-spin, but practically no blow in golf is struck in the manner described by Professor Thomson; nor is the beneficial back-spin of golf obtained in this manner, in fact the loft of the club has comparatively little to do with producing the back-spin which so materially assists the length of the carry. There can, of course, be no doubt that loft does assist a person in producing this back-spin, or, as Professor Thomson calls it, under-spin, but to nothing like the extent which is imagined by the worthy Professor. The beneficial back-spin of golf is obtained by striking the golf ball before the head of the club has reached the lowest point in its swing; in other words, the back-spin is put on a golf ball by downward cut—by the very reverse to that cut which is put on a ball when a man tops it badly. In the one case it is up cut, or, as it is called in lawn-tennis, top, which is a misleading term which has led many people, besides Sir J. J. Thomson, astray, and in the other case it is downward cut, which is exactly similar in its effect to the chop at lawn-tennis.

Professor Thomson, for the purpose of illustrating the fact that the golf ball obtains the beneficial spin, which influences its carry so materially, from the loft of the club, shows us a club face with a loft much greater than that of a niblick, and proceeds to demonstrate from this loft, which it is unnecessary to tell a golfer does not exist on any club which is used for driving, that the ball acquires its back-spin from the loft of the face of the club.

I have already referred to the Professor's fundamental fallacy that the golf stroke is delivered in a horizontal line—in effect that the force of the blow proceeds horizontally, but he is guilty of another very great error from the point of view of practical golf when he shows a club such as he has done, in order to explain how the beneficial back-spin of golf is obtained. Such a club as he shows might be useful for getting out of a bunker, but it certainly would be of no use whatever in practical golf for driving. As every golfer knows, the face of the driver is, comparatively speaking, very upright, and firing a ball at a wall built at the same angle as the loft of a driver would certainly not produce on that ball much in the way of back-spin. The idea of a modern golf ball which flattens very considerably on the face of the club, rolling up the face of a driver on account of its loft, is too ridiculous to be considered seriously by a practical golfer.

The trouble is that Professor Thomson always takes for his hypothesis something which does not exist in golf, so that in the great majority of cases it does not really matter to us what he proves. As a matter of fact, there is in golf only one horizontal stroke, and that is the stymie stroke introduced into the game by me, and which I have hereinbefore fully described. This stroke shows us conclusively how the power goes mostly into elevation instead of into propulsion. It is an absolute answer, if one were required, to Professor Thomson's theories. Professor Thomson's error is of such a fundamental nature that I must quote his sentence again in giving my readers the full paragraph wherein he exposes the delusion under which he is suffering. He says:

Suppose Fig. 27 represents the section of the head of a lofted club moving horizontally forward from right to left, the effect of the impact will be the same as if the club were at rest and the ball were shot against it horizontally from left to right. Evidently, however, in this case the ball would tend to roll up the face, and would thus get spin about a horizontal axis in the direction shown in the figure; this is under-spin and produces the upward force which tends to increase the carry of the ball.

This is the rock upon which Professor Thomson has split. He is under the impression that the beneficial back-spin of golf is obtained by loft, whereas it is perfectly possible to obtain the beneficial back-spin of golf with a club having a vertical face, and being at the moment of impact in a vertical plane, but in order to do this it would be necessary that the ball should be teed very high, as indeed one of the most famous professionals in the world is in the habit of doing when he is playing for a low ball against the wind.

When in Modern Golf I stated that a high tee for a low ball was practical golf, it was considered revolutionary, if not incorrect, doctrine, but players now understand that by using the high tee for a low ball they are enabled to cut down beyond the ball more than they could do if the ball were lying on the earth, and that they are, in this manner, enabled to obtain much more of the back-spin which gives the ball its extra carry, and also to play it with less loft.

This is a very serious error for a man of Professor Thomson's attainments to make, and indeed it is to me a wonder how he could possibly make the mistake of thinking that the force in the blow at golf is administered horizontally. This is one of the worst errors which he has made, but the idea that the back-spin of golf is obtained mainly by the loft of the club is utterly unsound and pernicious. It is so unsound, and the correct understanding of the method of producing this stroke is so important to golf, especially to the golf of the future, that I must explain fully how this stroke is obtained.

I have already shown that it is played by a downward glancing blow which hits the ball before the club reaches the lowest point in its swing, and I have already shown the delusion under which many players labour, even including so eminent a player as Harry Vardon, that the ball is struck down on to the earth. Although the ball is struck a descending blow, there is in the blow much more of the forward motion than the downward, so that all the ordinary principles with regard to getting the ball up into the air, apply with equal force to this stroke as to any other, and it is a matter of prime importance that the ball must be struck below the centre of its mass—that the loft of the club must get in underneath what is popularly called the middle of the ball. If this does not take place the ball will not rise from the earth, and to show as Harry Vardon does, at page 170 of The Complete Golfer, that the ball must be struck at or above the centre of its mass, and with, as he indicates at page 106, a vertical face, is utterly unsound golf.

I cannot emphasise too strongly that in this miscalled push shot, which is answerable for all back-spin, the loft must be allowed to do its work in the ordinary manner, otherwise the stroke will be a failure.

Having now made it perfectly clear how this stroke is obtained, I must explain a little more clearly the wonderful character of this ball which is without any doubt whatever, in my mind, the king of golf strokes in so far as regards obtaining distance and accuracy and direction. On account of the downward glancing blow the ball has been struck, it leaves the club with a very great amount of back-spin. The hands are always forward of the ball at the moment of impact in this stroke when it is properly played. It stands to reason that this, to a certain extent, decreases the loft of the club with which the stroke is played. The result is that the ball goes away on the first portion of its journey with a very low flight, keeping very close indeed to the earth. All the time it is doing this, however, the ball, as we know, is spinning backwards, which means that the lower portion of the ball is spinning towards the hole, and that it is on the lower portion of the ball that the motions of progression and revolution conspire.

It is equally obvious that on the upper portion of the ball the progression through the air is at the same rate, but in so far as regards its frictional-producing result on the air, it is lessened by the fact that the upper portion of the ball is revolving or spinning backwardly towards the player. The result of this is that the ball is getting much more friction on the lower portion than it is on the top, but as speed can always dominate spin, this is not very apparent until about two-thirds of the carry.

As the speed of the ball begins to decrease, the friction of the spin gets a better grip on the air, and the result is that with the continual rubbing of the air on the lower portion of the ball, it is forced upward and so it continues until the lifting power of the combined propulsion and revolution is exhausted. By this time the ball has arrived at the highest point of its trajectory and it then begins in the natural order of things to fall towards the earth.

It is obvious that by this time much of the back-spin will have been exhausted, but there still remains a considerable amount of rotation, and as the ball begins to fall towards the earth this back-spin which has hitherto been used for forcing the ball upwards into the air, still exerts its influence, and as it is travelling towards the earth the remnant of the back-spin exerts its influence to extend the carry of the ball, because the main frictional portion of the ball has, to a certain extent, on account of the dropping of the ball, been altered and shifted probably a little more towards the lower side of the ball.

The result of all this is that by the time this ball, in a well played drive, comes to earth, most of the beneficial back-spin which obtained for it its long flight, will have been exhausted, and that portion which remains and has not been exhausted will, in all probability, be killed on impact, for the ball pitches on one point, and naturally the top portion tends to throw forward so that the ball will run along the course. It stands to reason that it would require an enormous amount of back-spin to stay with the ball during the period of its low flight, to lift the ball then to the highest point in its trajectory near the end of its carry, to stay with it still in its descent, and then to be strong enough to resist the shock of landing so as to check the run of the ball. The result is that on account of the low trajectory of this ball and of the phenomena explained by me, it is frequently, when well played, and particularly in dry weather, a good runner, so that we see that in this ball we have practically the ideal golf drive; a drive with which no other can compare; a drive which is as good, although it is called the wind-cheater, for a still day as in a gale.

From this explanation it will be seen what a poor chance anyone would have who follows Professor Thomson's ideas of obtaining the beneficial back-spin of golf from the loft of the club and a horizontal blow.

Professor Thomson gives some illustrations of the pull and the slice. In two of his figures he shows horizontal blows being produced in a straight line with the line of flight. Both of these, I may say, are absolutely impossible in golf. He shows a slice in Fig. 29 which would be much more likely to result in a pull, and he shows a pull in Fig. 31 which would almost certainly result in a slice even if the shots were possible, which, as he shows them, they are not.

Professor Thomson shows by diagram an ordinary slice which he says is produced by "such a motion as would be produced if the arms were pulled in at the end of the stroke." This in itself is an utterly loose definition. What Professor Thomson evidently means is if the arms were pulled in during the stroke or at the moment of impact, but as I have shown the slice is not produced by the arms being pulled in at the moment of impact. It is produced by the club head travelling across the ball at an angle to the intended line of flight of the ball. Professor Thomson shows the slice in this case by diagram, and correctly, but he says that if the club were fixed rigidly and the ball were fired at the club down the same line as the club made in its previous stroke, the ball would come off the club in exactly the same manner as when it was hit by the club, but in this he is making a very grave error, as I think I shall be able to show.

I shall quote Professor Thomson with regard to this matter. His proposition is so simple that although I give his indicating letters it will not be necessary for me to reproduce his diagram. He says:

Suppose, now, the face of the club is not square to its direction of motion, but that looking down on the club its line of motion when it strikes the ball is along P Q (Fig. 28), such a motion as would be produced if the arms were pulled in at the end of the stroke, the effect of the impact now will be the same as if the club were at rest and the ball projected along R S, the ball will endeavour to roll along the face away from the striker; it will spin in the direction shown in the figure about a vertical axis. This, as we have seen, is the spin which produces a slice.

This, as we have already seen, is not the spin which produces a slice, but we need not waste any further time going into that matter. We can, however, deal with what Professor Thomson meant to say when he wrote

... but if you grasp the principle that the action between the club and the ball depends only on their relative motion, and that it is the same whether we have the ball fixed and move the club or have the club fixed and project the ball against it, the main features are very easily understood.

For the purpose of analysing what Professor Thomson evidently meant when he wrote this, let us take the ordinary case of a slice. We all know now quite well that a slice is produced by a glancing blow coming inwardly across the intended line of flight, and Professor Thomson tells us it is exactly the same thing whether we hit the ball with the club or fire the ball against the club. Let us see how this works out in the slice.

We will consider, for the sake of argument, that the slice has been produced by a stroke which has come across the intended line of flight at an angle of 30 degrees. We shall now fasten our club rigidly and fire the golf ball out of a catapult against its face so that it hits it dead in the centre, and so that it travels down a line at an angle of 30 degrees to the face. Now most of us know enough elementary mechanics to know that in hitting a still object such as the face of the golf club, the ball will come off it at the same angle at which it hit it—in other words that the angle of reflection is the same as the angle of incidence, allowing always, of course, for the slight alteration which will be made by the loft of the club. In this case, of course, we have one object which is absolutely still, and all the motion during impact is confined to the ball.

Now let us consider the impact in the slice. In this case the club strikes the ball a violent blow. The ball, to a very great extent, flattens on the face of the club, and both the ball and the club travel together for a certain distance across the direct line of flight to the hole, and during the time that they are thus travelling together the club is imparting spin to the ball and influencing its direction, so that instead of the ball doing anything whatever in the nature of spinning off the face of the club at a natural angle, it is driving, during its initial stages, very straightly for a long distance before the spin begins to take effect.

It seems to me that the slice may be taken as a very good illustration showing that what Professor Thomson meant to explain is quite incorrect from a golfing point of view. It is quite evident that before we could accept as authoritative the explanations which have been given by Professor Thomson of these somewhat abstruse problems, it would be necessary for us to have, as he puts it, "a new dynamics."

I have already dealt very fully both in England and America with this remarkable lecture by Professor Thomson. I have criticised it in the leading reviews and magazines of the world, and the authoritative golfing paper of England—Golf Illustrated—in a leader, invited Professor Thomson to make good his assertions, but he has not been able to do so. One can understand fallacious matter being published under the names of professional golfers when one knows quite well that the majority of the work is done by journalists hired for the purpose, but it is almost impossible to understand how such utterly false doctrine could be put out by so eminent a man, and under the auspices of the Royal Institution of Great Britain.

The flight of the ball has always been a fascinating and for most people a very mysterious subject, but except in one or two matters there is no mystery whatever about the flight of the golf ball, but even amongst practical golfers there is an amazing lack of accurate information. For instance, we find Mr. Walter J. Travis, in Practical Golf at page 139, saying:

With a very rapid swing, the force or energy stored up in the gutta ball is greater than in the Haskell. The latter, by reason of its greater comparative resiliency does not remain in contact with the club head quite so long, and therefore does not receive the full benefit of the greater velocity of the stroke in the same proportion as the less resilient gutta. It flies off the face too quickly to get the full measure of energy imparted by a very swift stroke. This responsiveness or resiliency, however, asserts itself in a greater and more compensating degree in the case of the shorter driver. It makes up, in his case, for the lack of speed, and he finds his distance very sensibly increased.

This is a remarkable error for a golfer like Mr. Travis to make. It is abundantly plain that the rubber-cored ball stays on the face of the club much longer than the old gutta-percha ball did. Provided that there were such things in the world as incompressible balls, the impact in the drive would be of the least possible duration with them, but the more compressible the ball becomes the longer it will dwell on the face of the golf club.

That the rubber-cored ball does dwell for a greater period on the face of the club is responsible, to a great extent, for the fact that the modern ball swerves much more when sliced or pulled than did the old guttie in similar circumstances, and the reason seems to be that on account of the fact that the ball stays longer on the face of the club during the time that the club is going across the intended line of flight, it is able to impart to the ball a much greater spin. This spin, as we know, exerts its influence principally towards the end of the ball's flight, and in all probability it gets to work now approximately at the same place where the spin in the old gutta-percha ball began to assert itself, but probably a little further in the carry.

We all know that once the spin has begun to assert itself so as to make the ball swerve, its deflection from the line, particularly with a suitable wind, is extremely rapid, and we all know equally well that the carry of the rubber-cored ball is much longer than that of the old gutta-percha. It stands to reason that the ball having a much greater distance wherein to swerve will execute a correspondingly larger swerve than it would if its carry were shorter.

We find some amazing statements made by authors who profess to deal with golf. For instance at page 167 of The Mystery of Golf, we are informed that

... another important thing about the follow-through, surely, is this. As Mr. Travis has pointed out, such is the resiliency of the rubber ball that club and ball are in contact for an appreciable period of time—the impact, that is, is not instantaneous. It is highly probable that the trajectory of the ball is largely influenced by this period of contact. If you follow through your club head travels in precisely the same line as the ball, and the flight of the ball is by this rendered straighter, steadier, and longer.

This, truly, is a wonderful instance of analytical thought by one who is attempting to explain the mystery of golf. He has come to the conclusion that "it is highly probable that the trajectory of the ball is largely influenced by this period of contact."

I have seen many goals kicked at Rugby football, and have kicked a few myself, and I am almost sure that in every case when a goal was scored the boot had a good deal to do with the direction. Marvellous analysis this!

We may, however, discard these wonderful efforts of analysis and deal with the remark made by the author that "if you follow through, your club head travels in precisely the same line as the ball," for this is absolutely incorrect in the case of many strokes wherein one desires to influence the flight of the ball by applying spin. For instance, at practically no time of its travel, no matter how good the stroke is and how perfect one's follow-through, is the club head in the slice or the pull "in precisely the same line as the ball." This is merely one of hundreds of instances of confused thought for which the poor golfer has to suffer.

I have before referred to the idea of pulling and slicing to counteract wind. It is astonishing how deeply rooted this idea is. At page 53 of Concerning Golf Mr. John L. Low says: "There is no shot which produces such straight results as the sliced shot against a right hand breeze," to which I reply that there is no shot which gives such straight results as the straight shot in itself without slice or pull of any description whatever, and that as a matter of fact it is practically impossible to calculate within twenty yards, and that means double the distance, where one will land if one starts pulling and slicing in a cross wind.

PLATE XII.

This is a matter of such importance that I must quote Harry Vardon in support of my statement. He says at page 92 of The Complete Golfer:

Now, however, that this question is raised, I feel it desirable to say, without any hesitation, that the majority of golfers possess vastly exaggerated notions of the effect of strong cross winds on the flight of their ball. They greatly over-estimate the capabilities of a breeze. To judge by their observations on the tee, one concludes that a wind from the left is often sufficient to carry the ball away at an angle of 45 degrees, and indeed sometimes when it does take such an exasperating course and finishes on the journey some fifty yards away from the point from which it was desired to despatch it, there is an impatient exclamation from the disappointed golfer, "Confound this wind! Who on earth can play in a hurricane!" or words to that effect. Now I have quite satisfied myself that only a very strong wind indeed will carry a properly driven ball more than a very few yards out of its course, and in proof of this I may say that it is very seldom when I have to deal with a cross wind that I do anything but play straight at the hole without any pulling or slicing or making allowances in any way.

If golfers will only bring themselves to ignore the wind, then it, in turn, will almost entirely ignore their straight ball. When you find your ball at rest the afore-mentioned forty or fifty yards from the point which you desired to send it, make up your mind, however unpleasant it may be to do so, that the trouble is due to an unintentional pull or slice, and you may get what consolation you can from the fact that the slightest of these variations from the ordinary drive is seized upon with delight by any wind, and its features exaggerated to an enormous extent. It is quite possible therefore that a slice which would have taken the ball only twenty yards from the line when there was no wind, will take it forty yards away with the kind assistance of its friend and ally.

These are, unquestionably, words of wisdom. There can be no doubt whatever that the straight ball is the ball all the time in golf, and it is absolutely certain that what Vardon says about the effect of the wind on the golf ball is true. Wind has remarkably little effect on the golf ball which is driven without spin. I have had no doubt on this subject for at least seventeen years. I had my lesson in one ball during the course of a match played over my home links in New Zealand. One of the holes was on top of a volcanic mountain at a place where New Zealand is only a few miles wide, and there was a howling gale raging from ocean to ocean right across the island. I can remember as if it were yesterday, the champion of New Zealand, as he was then, playing this hole. He drove a very high and perfectly straight ball from tee to green, and the ball travelled to all appearances as directly as if there had been no wind whatever, whereas had there been the least slice on the ball it would have been picked up by the wind and carried away into the crater which lay sixty or a hundred yards off the course.

Speaking of Mr. Low reminds me that he makes some extraordinary statements with regard to spin. At page 35 of Concerning Golf he says: "I have said that a ball with left to right spin swings in the air towards the left in exactly the opposite direction from a sliced ball and from contrary causes." It is obvious that this is wrong, for the spin of the slice is from left to right, and of course, as every one knows, that spin makes the ball swerve towards the right, which is the swerve of the slice.

At page 32 Mr. Low makes the same error. He says there: "Now a pulled ball comes round to the left because the sphere is rotating from left to right, or in the direction contrary to the hands of a watch." This, of course, is a contradiction, for the hands of a watch as we look at them do rotate from left to right, but in any case Mr. Low's explanation is quite incorrect, because the spin of the ball is not in a direction contrary to the hands of a watch laid face upwards on the ground, as Mr. Low affirms.

Mr. Low says at page 31:

Every child nowadays seems to know how to slice a ball; you have only to ask the question and the answer will come quickly enough, "Oh, draw the hands in when you are hitting," or, in other words, spin the ball in the direction of the hands of a watch laid face upwards on the ground. The ball advancing with this spin finds it is resisted most strongly by the atmosphere on its left side, and therefore goes towards the right in the direction of least resistance. The converse is the case with a pulled ball in the sense of a ball which curves in the air from right to left.

We have already shown in dealing with Professor Thomson's article that this statement is quite incorrect. In passing I may also refer to the fact that Mr. Low's idea of the production of the slice, viz. by drawing the hands in when one is hitting, is also wrong. There is no drawing in of the hands at the moment of impact in the properly played slice. It is the drawing in, if we may use the term, of the head of the club in its travel across the intended line of flight, but not anything which is done intentionally during impact. However, that is by the way.

Mr. Low is evidently under the impression, as was Professor Thomson, that the spin of the ball in the slice is about a vertical axis. This is an error in itself, as we have shown, but it is not nearly so bad an error as it is to say that the pull is the converse of the slice in this respect, for, as we have seen, if the ball were merely spinning about a vertical axis it could not possibly have the running powers which it possesses, to say nothing of its low flight. Although Mr. Low has got somewhat mixed in describing his rotation, it is evident from his reference to the hands of the clock that his ideas are correct in so far as regards the general direction of spin, but where he is at fault is in stating the axis of rotation of his ball.

If we accept Mr. Low's statement about the axis of rotation we shall have the pulled ball, when it lands, striking the earth with a spin equivalent to a sleeping top, but that is not what we want in the pulled ball, for neither would it give us the low trajectory which we desire so much, nor would it give us, on landing, the running which we desire, if anything, still more. The spin which we desire to produce and which we must have in our minds to produce when we are playing the stroke, is such a spin as will give us, when the ball lands, approximately the spin of a disc top as it falls to earth when its spin is nearly exhausted. I am speaking now, of course, not of the question of degree, but of the plane of spin. We must have our ball spinning in such a plane that when it touches the earth it will behave in the same manner as the disc top does when its side comes into contact with the floor.

In dealing with "The Science of the Stroke," James Braid in Advanced Golf goes into an analysis of the effect of spin on flight. He says early in the chapter:

At the present time most players know how they ought to be standing, and what the exact movements of their arms, wrists, and body should be in order to swing the club in the right way and make the ball travel as far as possible, but they do not all know, and in few cases one suspects have ever troubled to think, what is the process by which these movements, when properly executed, bring about the desired effect.

I do not know how Braid can truthfully say that at the present time most players know how they ought to be standing, when we are confronted with the fact that his own book, Advanced Golf, and practically every book which has been published on the game, tells the unfortunate golfer to stand as he ought not to be standing instead of giving him the simple truth and sound golf, and it is incomprehensible to me how Braid can say that they know "what the exact movements of their arms, wrists, and body should be in order to swing the club in the right way," when he himself has confessed in Advanced Golf that, particularly with regard to the wrists, which unquestionably have a most important function to fulfil in the golf drive, he absolutely does not know where they come in. It is useless in a work on Advanced Golf to assume on the part of one's readers a knowledge superior to that which the author of the book himself has given as his own limitations. Braid says:

They have the cause and also the effect, but they do not often see the connection between the two. Of course, the ball in a ball game moves always according to scientific laws, but it has seemed to those who have studied these matters that the scientific problems involved in the flight of the golf ball are more intricate, but at the same time more interesting, than in many other cases.

Of course this is quite stupid, because, as I have frequently explained, there is no special set of mechanical laws for golf—or the golf ball.

The golf ball follows in all respects exactly the same laws as those which govern the flight and run of any other ball. The only difference in connection with the golf ball is that it is probably the most unscientifically constructed ball in the world of sport. Braid continues:

The chief matter of this kind that it is desirable the golfer should understand is that concerning the character and effect of the spin that is given to the golf ball when it leaves the club. This spin is at the root of all the difficulties and all the delights of the game, and yet there are some players—one might even say many—who do not even know that their ball spins at all as they hit it from the tee.

I may pause here to note that James Braid says that spin is at the root of all the difficulties and all the delights of golf. This is in many respects quite an exaggeration, but I am giving it exactly as he says it, for the simple reason that it emphasises the fact which I have always insisted on, that a proper knowledge of the application of spin to the golf ball is essential for one who would attain to the greatest success or who would obtain the greatest enjoyment from the game.

Braid quotes the work of the late Professor Tait very extensively. Referring to the most important subject of back-spin, he says:

It appears to be the proper regulation of the under-spin given to the ball when applying it from the tee and through the green, at all events when length is what is most required, that makes success, and it is in this way that players of inferior physical power must make up for their deficiency and drive long balls.

I may say at once that any idea whatever of the proper regulation of back-spin in the drive is, from the point of view of practical golf, merely nonsense. In so far as regards obtaining extra distance by driving a low ball with back-spin, whose properties I have already fully described, there is nothing whatever to be done but to get back-spin and as much of it as one possibly can. The golfer has yet to be born who in driving can obtain too much back-spin. Braid says:

It is in the long drive that the principles of spin are most interesting and important, but it must be remembered also that they are very prominent in their action upon the flight of the ball in the case of many other shots, and the peculiarities of different trajectories can generally be traced to this cause after a very little thought by one who has a knowledge of the scientific side of the matter, as explained by Professor Tait. This is particularly the case with high lofted approach shots.

One may remark here, perhaps, that there is no more unsuitable stroke in which to study the peculiarity of the application of back-spin to the trajectory of the ball than in the high lofted approach shots, for it is in such shots as these practically an impossibility, if one may so express it, to locate the influence of the spin on the flight of the ball. It is quite a different thing in the wind-cheater class of stroke where one sees the ball travelling low across the turf and can absolutely mark the place where the back-spin begins to get to work and give the ball its upward tendency towards the end of the drive, and, when the velocity of the ball has become sufficiently reduced, to allow the back-spin to exert its lifting power.

I now come to a matter which is of very great importance in the application of back-spin to the ball. It is quite evident to me that Braid is falling into the same error as that which was originally made by Professor Tait, and followed fifteen years later by Professor Sir J. J. Thomson. On page 226 he says:

Therefore the great authority concluded that good driving lies not merely in powerful hitting, but "in the proper apportionment of quite good hitting with such a knack as gives the right amount of under-spin to the ball"; and one of his calculations was to the effect that, in certain circumstances, a man who imparted under-spin to his ball when driving it might get a carry of about thirty yards more than that obtained by another man who hit as hard but made no under-spin. There would, of course, be a great difference in the comparative trajectories of the two balls. In the case of the short one there is no resistance to gravity, and consequently, in order to get any sort of flight at all, the ball must be directed upwards when it is hit from the tee, or, to use a scientific term, there must be "initial elevation." This may be only very slight, but it is quite distinguishable, and in fact a player, who is only at the beginning of his practice, and has little knowledge of the principles of the game, will generally be found trying to hit his ball in an upward direction, and by that means will make it travel farther than it would have done otherwise. On the other hand, the ball that is properly driven by a good player is not only not consciously aimed upwards, but, according to Professor Tait, is not hit upwards. For some distance after it has left the tee it follows a line nearly parallel with the ground, and eventually rises as the result of the under-spin which is forcing it upwards all the time.

We may pause here to consider a few of the statements in this remarkable passage. I may say again that the idea of driving a ball with the "proper apportionment of quite good hitting with such a knack as gives the right amount of under-spin to the ball" is simply a wild guess at what takes place during the execution of a correct drive with back-spin. The proper playing of this stroke is a matter of very considerable difficulty, and it is practically a certainty that no golfer has ever lived or ever will live who could regulate his back-spin in the drive to any appreciable extent; all that he ever thinks of doing—all that he is ever likely to do—is to obtain his back-spin, and as much of it as he can.

It is, of course, quite wrong to say that in the ball hit without back-spin there is "no resistance to gravity," for if there were no resistance to gravity the ball would be on the earth. However, we know quite well what is meant, although, when we are dealing with a matter which is absolutely a matter of science, we do not expect such loose statements as these. I should probably have passed this remark, but for the fact that it is emphasised by the statement that in order to get any sort of flight at all the ball must be directed upwards when it is hit from the tee, which again, as a matter of practical golf, is what nine of ten golfers do, although we are told that "a player who is only at the beginning of his practice, and has little knowledge of the principles of the game, will generally be found trying to hit his ball in an upward direction."

It is astonishing how few players, even of quite a good class, are content to leave the question of elevation entirely to the club. It probably would be no exaggeration to say that quite ninety per cent of the players make an attempt, however extremely slight it may be, to assist the club in lifting the ball from the earth. According to the best theory in golf, this is quite wrong, for the blow should be at least in a horizontal direction, which practically it never is, and preferably in the line of the arc formed by the club head in its travel through the air on its downward path. The latter case, of course, would produce back-spin, and a considerable amount of it. The former would probably produce slight back-spin, but a very slight amount. However, the very great majority of golfing hits are at the moment of impact proceeding upwardly, and it is this fact which puts any idea whatever of the unconscious application of back-spin by the ordinary golfer quite beyond serious consideration. The amount of back-spin which is unconsciously applied to the golf ball is practically negligible.

We see that, according to Professor Tait, the ball which is properly driven by a good player is not only not consciously aimed upwards, but that it is actually not hit upwards. Indeed we are told that for some distance after it has left the tee it follows a line nearly parallel with the ground and eventually rises as the result of the under-spin that is forcing it upwards all the time. This statement is not in accordance with the experience of practical golfers. It is evident that Professor Tait was under the impression, in which, as I have stated before and now emphasise, he has been followed by Professor Sir J. J. Thomson, that the beneficial back-spin in golf is obtained by the loft of the club. There can be no doubt whatever that if a golf ball were struck a blow by a golf club having any considerable degree of loft and proceeding at the moment of impact in a straight line, the result would be to impart some degree of back-spin, but this is not what happens in practical golf. At no portion of the travel of the head of the club in the golf drive is it proceeding in a horizontal direction, and in the vast majority of cases, at the moment of impact, even with the very best of stroke players, the club is going upward. If this were not so it would be impossible for many of our greatest drivers to get the trajectories they do with the comparatively straight-faced clubs which they use.

Braid quotes an experiment which was made by Professor Tait in the course of his investigations with regard to the qualities of under-spin. It appears that the Professor laid a ball to the string of a crossbow, the string being just below the middle of the ball, so that when it was let go it would impart a certain amount of under-spin to it. When he shot the ball in this way he made it fly straight to a mark that was thirty yards distant; but when he shot it a second time, pulling the string to the same extent and laying it to the middle of the ball so that no under-spin would be given to it, the ball fell eight feet short of the same mark.

It is impossible to accept such a rough and crude experiment as this as evidence in any way whatever of the influence of back-spin in the drive; rather it would seem to show beyond a shadow of doubt that the extra carry was obtained because the power of propulsion was applied to the ball at a lower portion, and therefore tended to give it a greater trajectory. It should be obvious that this result would be obtained even disregarding the question of back-spin, which in such an extremely short flight as thirty yards would certainly not have any opportunity whatever to make such a difference in the length of carry as that suggested.

It is, however, when we come to deal with questions of practical golf that we find that the ideas of the late Professor Tait will not bear looking into.

Braid says:

However, it is well to bear in mind one thing that the Professor said, "The pace which the player can give the club head at the moment of impact depends to a very considerable extent on the relative motion of his two hands (to which is due the 'nip') during the immediately preceding two-hundredth of a second, while the amount of beneficial spin is seriously diminished by even a trifling upward concavity of the path of the head during the ten-thousandth of a second occupied by the blow."

Here we have plain evidence of the fact that Professor Tait is under the impression that there is some particular snap which he calls "nip" imported into the stroke immediately before impact. We have already dealt fully with this matter. We remember what Vardon has said in condemning the idea, and we know that Braid himself has confessed that he knows nothing about the matter, so it will not seem disrespectful if we come to the conclusion that we can disregard this vague statement about the "nip" in the blow. We can then proceed to notice the really important remark made that "the amount of beneficial spin is seriously diminished by even a trifling upward concavity of the path of the head during the ten-thousandth of a second occupied by the blow." It seems to me that this last statement is absolutely accurate, and it is the thing which I have always contended for in dealing with the practical side of golf driving, as contradistinguished from the purely theoretical, which has been put before us by Professor Tait, and following him, by Professor Sir J. J. Thomson. It will be observed that Professor Tait said that the amount of beneficial spin is "seriously diminished by even a trifling upward concavity of the path of the head during the ten-thousandth of a second occupied by the blow."

Some of my readers may remember that when I was dealing with Professor Sir J. J. Thomson's lecture before the Royal Society in an article which appeared in The English Review in February 1911, I stated that what actually did happen was that there took place in practically every drive at golf exactly this "trifling upward concavity of the path of the head during the ten-thousandth of a second occupied by the blow," and that therefore the amount of beneficial back-spin obtained from the loft of the club was practically negligible.

It is quite clear that Professor Tait was under the impression that back-spin was got from the loft of the club proceeding in a horizontal direction, but it is well known now to golfers who give the science of the game any attention whatever, that back-spin is not obtained in this manner, and that back-spin so obtained would be practically ineffectual as an aid to distance, for the loft of the driver and the brassy is not sufficient, even if the golf drive were played in the manner suggested, to produce any considerable amount of back-spin. As we have already seen, the beneficial back-spin in the golf drive is obtained by the club striking the ball long before the beginning of the "upward concavity of the path of the head," that is to say, in its arc as it is proceeding downwards to the lowest point in the swing from which it then starts that "upward concavity."

I have emphasised and re-emphasised this matter, for it is evident that when famous men like Professors Tait and Thomson start out with an absolutely erroneous idea, an idea which is fundamentally wrong, it is quite natural for less gifted men to be led astray. Braid says, and it must be remembered that this is in Advanced Golf (page 229): "So far as I know, it cannot be stated in accurate scientific terms and figures, and by lines drawn on paper, what is the proper scientific swing in order to get the best drive." This seems to me, especially in a book like this, to be a wonderful statement, particularly when we are dealing with the scientific results arrived at by men of the greatest eminence, results which I may say have been known for more than two hundred and fifty years.

There is no doubt whatever which is the best way to swing in order to get the best drive, and it can be explained in scientific language and shown by diagram and by figures, and in fact it has been so shown again and again.

Braid says:

What golfers have done, therefore, in the past has been to find out gradually which is the best way in which to hit the ball in order to make it travel far, and thus they have groped their way to the stances and swings which, if the truth were known, would probably be set out by science as the best possible ones for the purpose.

This very well expresses what has taken place. The golfers have "groped their way" to what they have found out, without a glimmering of the scientific reasons for doing it, and the consequence is that, as they got their practice first, and were not informed of what they were doing by that theory which is the best of all theory, the concentrated essence of the practice of experts, they have signally failed to impart their science to those who have come after them.

At page 229 Braid says:

However, there are certain things that the player should know about his drive when it is right, and which he should aim at producing, and they have been very well set forth by Professor Tait as the result of his investigations into the trajectories of golf balls hit under varying conditions of club-force, wind, and so forth. One of the first things to say, and this is really important in estimating their chances of making certain carries that are constantly set to them in the course of their play, is that some golfers have a delusion to the effect that the ball is at its highest point in the middle of its flight—that is to say, they think that just about half-way between the point from which it was hit and the point at which it will touch the ground again, the ball is at its highest, and after that commences to fall again. In this belief when they have, say, a 140 yards' carry to make, they will reckon that their ball must then be coming down very fast towards the turf, having been at its highest, some 50 or 60 yards before. They may think in such circumstances that they ought to hit up a little more and try to hit harder to make up for doing so. They would be wrong entirely, and that because they did not know what the under-spin was that they gave to the ball, or what effect it had on its flight. Thus in the case just quoted, assuming that the ball had a total carry of from 150 to 160 yards, it would be at its highest point when it had travelled about 130 yards, and there would be no occasion to hit up, unless the object to be carried were very high.

It is obvious that in such a case as that given no practical golfer would in any way whatever consider the question of the amount of back-spin on his ball, for he would know that he has no possibility whatever of gauging its effect in the air in such a shot, and he will leave that to regulate itself and to act when the ball strikes the earth.

It is unquestionable that theoretically this may be done, and it is well known that I am a strong advocate of the use of back-spin, but in the case quoted by Braid there is nothing whatever to show that the ball has been played in such a manner as to produce an appreciable quantity of serviceable back-spin, or that such a method of play is necessary or advisable.

Braid continues:

The fact is that a well-driven ball that has a total carry—that is, from the tee to the point where it touches the turf again, and not the distance of the obstacle that it clears—of about 165 yards, under normal conditions of wind and weather, is at its highest about 135 yards from the point where it was struck, and after that it begins to fall rapidly. This is chiefly the result of the under-spin which is given to it when it is struck by the driver in the proper way, and it shows the importance of under-spin to the golfer, for if there were none, then all our courses would have to be shortened, hazards brought closer to the tee, and the principles upon which the game is played would have to be altered in many respects. If there were no under-spin, then the ball would have no help against the force of gravity, and the result would be that the highest point of its flight would be half-way between the point from which it was driven and that at which it alighted.

We see here again strong evidence of the fact that Braid is under the same impression as Professor Tait, and that is that the back-spin of golf is obtained from the loft of the club, whereas the loft of the club has one function, and that is to raise the ball from the earth, and there will be no particular necessity to alter our courses, for in ordinary every-day golf, back-spin is practically not used, except when it is intentionally applied by the golfer by means of the stroke suitable for its production.

Braid gives a series of diagrams taken from Professor Tait's lecture which illustrate various trajectories of golf balls driven in varying circumstances. Many of these are so entirely theoretical that I need not consider them, but in referring to one of them Braid says:

The ball which has travelled farthest, or rather the one that has been given most carry, is that which has been hit in the right way, and to which has therefore been imparted the right amount of under-spin. This is, in fact, the ideal trajectory of a well-driven ball. It starts low, rises very slowly and gradually, the line of flight bending upwards slightly, and does not come down too quickly after the vertex has been reached.

This is, on the whole, a sound but very general description of an accurately played wind-cheater, but the remarkable thing is that although Braid expresses himself in such terms of admiration for this particular ball he does not anywhere in Advanced Golf show us how to produce the stroke which gives this beneficial back-spin. This surely is a very great oversight. Nor so far as I have been able to see does he explain clearly how the beneficial back-spin of golf is obtained.

Braid shows clearly by his quotation from Professor Tait's article that in the Professor's mind was the deep-rooted idea that it was possible to drive golf balls by a stroke delivered at the moment of impact in the same manner as is a blow from a billiard cue, but, needless to say, this is in the golf drive utterly impracticable. Professor Tait, in his paper, used a considerable number of diagrams to show that too much back-spin is bad in the drive, but as I have already pointed out, although this is very well in mere theory, it does not work out in the slightest degree in golf. It is easy to take light balloons and give them back-spin and show that it influences their trajectories to such an extent that they will go behind the point where they were struck, but a golf ball is a very small, hard, and heavy thing, and by the time that its back-spin begins to exert its influence in a marked manner on its flight it has travelled a considerable distance and the rate of spin will have materially diminished, so that no golfer need ever be afraid of applying too much back-spin to his drive.

Braid proceeds:

Of course, as already indicated, the golfer does not know, and in one sense does not care exactly how much under-spin he gives to his ball when he drives it, only being aware that he has given too much or too little according to results, and knowing also that in either case excess or otherwise was due to faulty stance or swing—most frequently this—or both. In the present case of this high trajectory, the exact amount of under-spin given to the ball is half as much again as that given to the properly driven ball, and under the same normal conditions these would be the relative flights of the two balls.

Now it is obvious that if Professor Tait was under the impression that the beneficial back-spin of golf was obtained merely from the horizontal blow delivered through the centre of the ball's mass, so that the ball took some slight spin by its roll up the face of the club, he had no very accurate idea of the rate of spin of that ball at the moment it left the face of the club, so that any attempt whatever on his part to measure the respective rates of spin of the different flight of these balls must be received with very great caution. As a matter of fact the rate of spin of the golf ball at the moment it leaves the club in a well-played drive with back-spin would be immeasurably faster than anything supposed by Professor Tait, who based his calculations on the ball obtaining this back-spin from the loft of the club, which is undoubtedly a grave error, and Braid wholly subscribes to this error, which is not to be wondered at, for Professor Sir J. J. Thomson, one of the most eminent scientists, has fallen into the same trap.

Professors Tait and Thomson and James Braid talk much about the possibility of obtaining too much back-spin in the drive. This is scarcely theoretically possible in golf, and it is practically impossible. I will give an example taken from practical golf which will, I believe, quite convince any golfer that the possibility of obtaining too much back-spin in the drive need never be considered.

Let us imagine a very badly sliced ball. By a badly sliced ball I do not necessarily mean an extremely quick slice where the ball leaves the line of flight to the hole quite suddenly, nor do I mean a ball pushed away to the right of the line to the hole; what I do mean is a ball which has been so sliced that it takes a tremendous curve from left to right, beginning to develop that slice in a pronounced manner at, say, half to two-thirds of its carry, which is quite bad enough for a slice. We frequently see in such a case, particularly on a windy day, and even on a still one, the great power which the spin has to deflect the ball from the line to the hole. It must be remembered that in this curve the spin is assisted by gravity—the ball is falling much of the time as it is being edged away—and even then it will be apparent that it is easy to get much greater spin in the slice than it is in the wind-cheater, for the simple reason that in the slice one has an unrestricted cut across the ball, whereas one has not this opportunity with the wind-cheater, for one hits the ground immediately one passes the ball.

Now although it is possible to apply an infinitely greater cut to the slice than one can possibly do to the wind-cheater, the deflection from the line, except on a very windy day, is, comparatively speaking, gradual. That is to say that if, for the sake of argument, the trajectory of the slice could be turned upwards there would be no possibility whatever of the ball showing such a thing as a curl backwards towards the hole, which is shown by Professor Tait and, following him, by Professor Thomson. This is clearly so in any slice which is not an extremely exaggerated specimen, so it stands to reason that in the wind-cheater, where one's opportunity for applying cut is so restricted, and where the ball in its effort to climb upwards has to fight the direct pull of gravity, there is no possible chance of applying too much back-spin to the ball.

At page 239 Braid says: "It may be of interest to mention that Professor Tait found that a well-driven ball turns once in every 2½ feet at the beginning of its journey." If Professor Tait found that a golf ball, obtaining this back-spin in the way in which he thought it did, turns "once in every 2½ feet at the beginning of its journey," he would probably have found, if he had realised how back-spin really is obtained, that the number of revolutions at the moment that the ball is leaving the club are at least three or four times as many as he asserted. It is unnecessary to enlarge upon the fact that this would mean a lifting capacity infinitely beyond anything that Professors Tait and Thomson ever ascribed to back-spin in the drive.

Braid continues:

We have so far only been considering the effect of the spinning of the ball in the case of long shots with wooden clubs. As a matter of fact, and as suggested at the outset, it has also very great influence on the play in the case of the shorter shots with iron clubs, as may be understood after a very little consideration of the circumstances. It is the excessive under-spin that is given to the ball by the angle at which the face of the club is laid back, and the peculiar way in which the stroke is played, that make the ball rise so quickly and so high in the case of a short pitched approach, and then make it stop comparatively dead when it comes to the ground again.

It is obvious here that Braid is under the impression that the loft of the club is largely responsible for the back-spin in the approach shots, but this is quite an error, for not one player in a hundred does apply back-spin to his lofted approaches unless he has been specially taught how to do it, for, curiously enough, the more lofted the club is, the greater chance is there that the player will at the moment of impact impart into his stroke that little bit of "upward concavity" which Professor Tait says, and truly says, is the enemy of back-spin. The fact is that very little under-spin, or, as I always prefer to call it, back-spin, is obtained from the loft of the club unless the blow is delivered as the club is travelling downward. That is the whole essence of the secret of back-spin, but it is not mentioned by Professors Tait or Thomson, or by James Braid. Any attempt whatever to obtain back-spin from the loft of the club will be practically useless. It must be obtained by the method of playing the shot, and the only way to obtain it effectually is to hit the ball before the club has arrived at the lowest point in its swing. By this means, and this means alone, is it possible to obtain the beneficial back-spin of golf, and I cannot say too often or too emphatically that anyone who trusts to the loft of the club to produce back-spin will be disappointed.

Braid seems to have a glimmering of this, for he says:

However much a club were laid back it would be impossible to play these shots properly if no under-spin were given to the ball, and it seems to be a great advantage of having the faces of iron clubs grooved or dotted that it helps the club to grasp the ball thoroughly while this under-spin is being imparted to it, so that the full amount is given to it, and none is wasted through the ball slipping on the face.

This is unquestionably sound mechanics. But even here, although Braid is so close to the heart of the matter—although he says, as I have shown repeatedly in many places, that "however much a club were laid back it would be impossible to play these shots properly if no under-spin were given to the ball," thus stating explicitly that something more remains to be done to produce back-spin than merely to hit the ball with a lofted club,—he does not get really to the essence of the stroke and show that it must be played by the club as it is descending.

There is a very important matter which Braid refers to in this chapter on the science of the stroke. Speaking of the follow-through and the impact, he says:

One or two other calculations that were made by Professor Tait may be briefly mentioned at the close of this chapter, each of them seeming to convey an idea to the golfer. The first is, that owing to the speed at which the ball leaves the club, the total length of time during which ball and club are in contact with each other is between one five thousandth and one ten thousandth of a second, and the total length of that part of the swing when the two are together—the length of impact—is half an inch. It has been pointed out that it by no means follows from this that because the time and space of impact are so short that follow-through is of no real account, after all, in the making of the drive. When the follow-through is properly performed it shows that the work was properly done during that half an inch of the swing that was all-important. If the follow-through were short and wrong it would indicate that the work during the impact was wrong too. What it comes to is this, that it is impossible for any man to swing his club round with so much force and regulate exactly what he will do, and be conscious of the fact that he is doing it as he regulated, during such a short space of time as from one five thousandth to one ten thousandth of a second. That is quite clear. What the golfer has to do, then, is to make sure that his swing is right at the beginning, that is, in the back-swing and the down-swing, and also in the follow-through. He knows from instruction and experience that if all these things are properly done the ball will go off well; and what it amounts to is that the beginning being right and the end being right, control being exercised over each, the middle is right also, though in this case there is no control over it.

This quotation emphasises strongly the fact which I have always insisted on, that the matter of impact with the golf ball is an incident in the travel of the head of the club, and that it is practically impossible for the player to consciously perform anything which will affect the flight of the golf ball during impact. Braid has insisted upon this in other places, and it should quite settle any idea which many people have, of juggling with the golf ball during impact, but it is a remarkable thing to see James Braid claiming that at the moment of impact there is "no control over" the swing although there is both in the downward swing and the follow-through! I need not criticise this.

The point, however, which I wish to refer to here specifically is in connection with the follow-through. Braid says, finally:

What the golfer has to do, then, is to make sure that his swing is right at the beginning, that is, in the back-swing and the down-swing, and also in the follow-through. He knows from instruction and experience that if all these things are properly done the ball will go off well; and what it amounts to is that the beginning being right and the end being right, control being exercised over each, the middle is right also, though in this case there is no control over it.

This, it seems to me, is a very bad presentment of the case. Although we admit that the impact is merely an incident in the travel of the club head, it is the most important incident, and it is on that incident that the mind should be concentrated, so that the idea of cumbering one's mind with any thought of the follow-through is very bad golf. The only portion of the stroke which should be on the player's mind at all is that which leads up to impact, for it is obvious that if that has been correctly performed, one need not trouble much about the follow-through, as that will come quite naturally. Also we will observe that Braid says here "control being exercised over each." This, of course, includes the follow-through over which Braid now speaks of exercising control, but it will be fresh in our minds that in describing the moment of impact, he says "Crack! everything is let go," and that really is what should happen after impact has taken place. There should be no thought whatever of the follow-through. That should produce itself, if one may so express it, and the player who encumbers his mind by any thought whatever as to how his club is going to end is simply adding another anxiety to his game.

PLATE XIII.

Braid explained most graphically how the follow-through should be allowed to take care of itself, so that I cannot understand why he should now endeavour to split his pupils' mental idea of the golf stroke into halves with the golf ball in between. This is surely a bad conception of the stroke, and one which is likely to lead the pupil into grave error, for it shifts his mind forward on to the finish of the stroke, whereas it has no business to be anywhere else but on the ball.

Before concluding this chapter I must refer to what Braid has to say with regard to a topped stroke. At page 238 he says:

A final thing to remember in connection with this question of the rotation of the ball is, that when the ball is what we call topped, the stroke is applied in such a way that a motion exactly the reverse of under-spin is applied to it, that is to say, the front part of the ball is made to move in a downward direction. On the principle already explained, there is then an extra air-pressure upon that ball from the top, pressing it down, so that even if the ball that is topped is somehow got up into the air from the tee, as happens, it cannot stay there long, but comes down very suddenly—"ducks," as it is called. However, a ball that ducks for this reason nevertheless gets some benefit from this over-spin when it does come down, for the spin acts in just the same way as "top" does in the case of a billiard stroke, that is to say, it makes the ball run more. If there were no rough grass and no bunkers between the tee and the hole this over-spin might be an exceedingly useful thing, and the principles upon which the game of golf is played might be entirely different from what they are; but as there is rough in front of the tee, and generally a bunker at no great distance from it, topping and over-spin are more frequently fatal than not, the ball coming to grief either in the rough or the bunker.

This quotation makes it quite evident, I think, that James Braid is not very well acquainted with the principles which govern the flight and run of the golf ball. If this were his "knowledge" which we are considering, I should be more loath to deal with it so plainly as I am doing, but as he expressly states that he is indebted to another for much of his "knowledge" on this subject I have no hesitation whatever in criticising it and showing that it is absolutely impracticable from a golfing point of view.

It is not too much to say that top-spin has absolutely no place in golf, for it is there utterly useless, and would be so were golf links like billiard tables, for no ball with top on it can travel any appreciable distance through the air, and to speak of a ball being driven with top is simply to show one's utter ignorance of the game, for even if there were no rough grass and no bunkers between the tee and the hole, this over-spin could never be "an exceedingly useful thing," nor could it ever, by the greatest stretch of one's imagination, alter the principles upon which the game of golf is played, for no stroke in golf could ever supplant the drive with back-spin.

It is nonsense such as this which does much harm to the game. To speak of the possibility of over-spin being such that the "principles upon which the game of golf is played might be entirely different from what they are if the course had no rough grass and no bunkers" is one of the greatest absurdities which I have ever seen put in any book, and when one finds matter of this sort in a book called Advanced Golf, it calls for the severest possible criticism.

The nearest approach to top-spin which exists in golf is the spin of the pull, and there because the axis of spin is turned over to a certain extent, we get the beneficial run at the end of the drive, but anyone who knows the first principles of the flight and run of the ball would know that if the golfer in his drive obtained pure top instead of this much modified over-spin, his drive would be entirely ruined, for the thing which produces the low flight of the ball is that the ball does its ducking sideways, if we may so express it, and the chances are that quite frequently the shock of landing alters the plane of its spin, so that it is converted into pure running, but this latter point, of course, is a matter which we can only theorise about and regard as almost proved from the nature of the run of the ball on many occasions.

We need not here bother about top-spin. The only place where top (not top-spin) is of any use in golf, so far as I can remember, is on the putting-green, and there it is unquestionably useful, and it is not used so much as it should be. The point of outstanding importance, which I venture to think is made fairly clear by this chapter on the flight of the ball, is that the beneficial back-spin of golf is by far the most important spin which it is possible for a golfer to apply to his ball, and that that spin is not obtained in the manner stated by Professor Tait and, after him, by Professor Thomson, but is obtained by the method which I have indicated, viz. by a downward glancing blow, and, so far as regards this statement, we have the corroboration of James Braid to the extent that he says that "no matter what the loft is upon the club, it is impossible to obtain by loft alone the back-spin which one requires in golf."

It may seem that I have been unnecessarily emphatic in dealing with this question, but as a matter of practical golf it is absolutely impossible to lay too much stress upon the value of a complete understanding of the method of obtaining this most valuable and serviceable spin, and unless a player most perfectly understands the theory of the stroke, it is the greatest certainty possible that he will waste many years of his life endeavouring to acquire the practice, whereas if he knows perfectly well what he is trying to do, he may acquire it in as many months as he would otherwise waste years in not getting it.