“The problem of the golf ball’s flight is one of very serious difficulty.” That is what was said to a gathering of savants by Professor Peter Guthrie Tait, one of the most brilliant scientists of the latter part of the last century, and the only man who has probed deeply into the real science of the game of golf. He was a wonderful man in many respects. He applied his marvellous scientific knowledge and powers of investigation to everything that came his way. One day he would be extracting cube roots from the most unsuspected quarters, and another he would be analysing the character and formation of the ripples on the surface of a viscous liquid. A few flourishes of the knife of science, a sharp explosion with one of his specially prepared formulÆ—consisting of the most wonderful combinations of the ?’s, the ?’s, the t’s, and the f’s—and the common but stubborn thing of everyday life was made to yield up its innermost secrets, so that thenceforward it was regarded in a quite different way from that which it had been in the past.

Nothing was sacred from the application of the Professor’s science, and golf was not; but to the credit of the game be it said that some of its scientific problems baffled this great man of science as nothing else that he had ever tackled before so seriously had done. He spent weeks, months, and even years, in occasional periods, upon it; he employed the most intelligent men of science with marvellous powers of reckoning as his assistants, he bombarded the game with the most terrible formulÆ that even he had ever invented; but golf still held the upper hand and retained some of its secrets, while it often smiled derisively at the Professor when it had sent him a long way along a false path. The Professor would not give up. He returned always to the attack, and golf and he came to closer grips. He did, indeed, obtain many wonderful secrets from its possession, and he found out more about it—all of it very wonderful and very interesting—than any man had ever done before, or possibly ever will do again. Now and again he told his learned brethren of the difficult nature of the task that he had entered on. Before he died he had found out most things, but golf still held some secrets from him.

Many of the things that he knew, and the way in which he found them out, were never published to the golfing world. He issued one or two papers of a quite popular character, and very elementary; but they did not contain a tithe of what he had discovered or say how he had discovered it. Here we will try to tell the golfer a little of what the Professor found out about the things that happen when the ball is driven from the tee. They will interest him, and perhaps cause him some surprise. Only those conclusions will be given which he proved beyond question, and the truth of them must generally be taken for granted, as it may be safely, since the professor’s lines of study would take a volume to expound with any lucidity, and even then a considerable scientific knowledge on the part of the reader would first of all be necessary.

II

It should be said that, while the Professor played a little golf himself, and was much in love with St.Andrews as a resort, what led him in the first place to make his investigations was watching the play of his famous golfing son, Fred Tait. A few idle, fanciful conjectures on the flight of the ball that was sent skimming through the air from Freddie’s driver led to a more serious calculation, and then, like a siren, the great mystery of golf drew him on. But early in his investigations he committed himself to the statement that nobody could drive a golf ball that would have a carry of more than 180 or 190yards without exerting at least three times the strength that is generally exerted by a strong man when driving; that is to say, that a carry of such distance was practically impossible. But this statement was no sooner before the public than young Fred proved the fallacy of it, by celebrating his twenty-third birthday by driving a record ball which had considerably more carry than that.

“Stuff! Humbug!” said the Professor; but the fact was there, and when the golf world came to know about it, they asked the Professor what was the use of all his calculating—and to this day that error is chiefly what is remembered by the general public about his investigations. This incident may have been largely responsible for the fact that thereafter he only once or twice let the golfers into the secrets of what he was doing and had found out, reserving the story of his investigations for learned bodies who were most closely concerned about them.

The mistake that he made, which was exposed to him by his son, set him out on a new line of thought, and showed him vaguely where his error was, though not the nature of it. And the discovery which he made at the outset was a startling one, and it may cause some astonishment to the player of to-day who will reflect upon it for a moment. The steadiest, most constant, and most persistent force with which we are generally acquainted is the force of gravity. It is always there; it acts unceasingly upon everything. To defeat gravity, therefore, is almost for a while to suspend the working of Nature. Suddenly it burst upon the mind of the Professor that the golf ball was made as it were to defeat gravity, and so in a sense it does. He found this out by observing the time of flight of the ball, and discovering that it was nearly twice as long as it ought to be, if gravity had free and unfettered play. This is to say, that if gravity were allowed to act in the usual way on the ball from start to finish, as it acts on other things, it was quite inevitable by all the laws of nature and science that a drive of 200yards would be completed in three and a half seconds. If a man threw a ball so as to describe as nearly as possible the same trajectory as a golf ball, and to stop at the same spot, it would only take three and a half seconds. But the golf ball takes six and a half seconds! Somehow or other it was clear that gravity was being beaten all the way. If it were not so, it would be impossible for the golf ball to remain in the air so long while it was accomplishing such a short flight. That was the great mystery that the professor had to solve, and he solved it at last. It may be said here, in passing, and will be more fully explained another time, that he found out that it was due to the rotation given to the ball by the club, and the nature of the stroke when it was struck from the tee, a rotation which in many ways was responsible for some most extraordinary happenings; all of which the golfer will be a much wiser man for having knowledge of. But before he could go thoroughly into the mystery of this rotation he had to make many other preliminary investigations, and some of the results of these may be quoted.

One of the Professor’s first efforts was in the direction of finding out the speed with which the ball left the club; and it was a long time—years, in fact—before he came to any definite understanding on the point; so difficult did he find the investigation, despite all the experiments he made, the formulÆ that he applied to them, and the scientific instruments that he brought to bear on the problem. He had a very capable observer, Mr.T. Hodge, making examinations of the flight of balls driven in actual play at St.Andrews, by the help of the instrument known as the Bashforth Chronograph, with which the speed of bullets is measured; and, what with the results arrived at in this way and others, he came to the conclusion that the initial speed of the ball was over 500feet a second, which speed, of course, was lost very quickly as the resistance of the air was encountered.

With this as his starting-point, he made many deductions; but subsequently he found that he was wrong in the original assumption.

A vast number of calculations and experiments followed. In a cellar he constructed a complicated pendulum arrangement, to the bob of which there was attached a large screen with a thick clay surface, and against this he got several well-known golfers to drive their hardest, and made the most minute calculations as to the effect upon the pendulum. The clay was scattered in all directions, damage was done, and the golfers complained that under such circumstances they were not able to drive their best. The pendulum and the strangeness of the whole arrangement “put them off.” Some time afterwards he constructed an improved pendulum, the clay screen being fixed on to lengths of clock spring, and when this was placed in a doorway the golfers were again set to drive at it.

What with one thing and another the Professor at last came to the final and definite conclusion, that the ball started from the club at a speed, in the case of a good drive, of about 240feet a second, but that in the case of exceptional balls it sometimes was as much as 300 or even 350feet per second. This, of course, was with the gutta ball; and the resiliency and initial speed of the rubber-cored ball being certainly much greater, it is fair to believe that the average initial speed of a well-driven ball in these days is quite 300feet a second; or, to put it in another way, over two hundred miles an hour. Great as this speed appears, it might be mentioned incidentally that the muzzle velocity of a bullet from a Maxim gun is generally about 2000feet a second, or about seven times as fast.

III

While he was at work on these reckonings he dispelled one fallacy, which, notwithstanding, is commonly held by golfers to the present day. Most players think that when driving and following through well the ball hangs on the face of the club, as it were, for long enough for the club to do something in the way of guiding it. How brief is the time in which the actual stroke is made for good or ill was proved conclusively in a very striking manner, and that time was set down—the whole time of impact—as that in which the club, moving at 300feet a second, passed through about four times the linear space by which the side of the ball was flattened. Putting this space down, nowadays, at about ?in., and reckoning the time that it would take the club going at the speed indicated to cover that small distance, we have the fact that the duration of impact is only about 1/7000th of a second, and that that is the whole time that the golfer has for the guiding of the ball! As the Professor said, “the ball has, in fact, left the club behind before it has been moved through more than a fraction of its diameter”; and in the case of the gutta, with the smaller extent to which it flattened on the club, he came to the conclusion that the duration of impact was far less than that which has just been mentioned.

Incidentally in this connection he took occasion to expose another of the golfer’s fallacies as to the effect of wind on the flight of the ball, in the following words: “It is well to call attention to a singularly erroneous notion very prevalent among golfers, namely, that a following wind carries a ball onwards! Such an idea is, of course, altogether absurd, except in the extremely improbable case of wind moving faster than the initial speed of the ball. The true way of regarding matters of this kind is to remember that there is always resistance while there is relative motion of the ball and the air, and that it is less as that relative motion is smaller, so that it is reduced throughout the path (of flight) when there is a following wind. Another erroneous idea somewhat akin to this is that a ball rises considerably higher when driven against the wind, and lower if with the wind, than it would if there were no wind. The difference (whether it is in excess or deficit will depend on the circumstances of projection, notably on the spin) is in general very small; the often large apparent rise or fall being due mainly to perspective as the vertex of the path is brought considerably nearer to or farther from the player.”

And Professor Tait was led to make a definite pronouncement on the particular kind of weather in which a ball will fly best and farthest. What golfers do not generally realise is that the atmospheric resistance to the flight of their ball is much greater than in simple proportion to its speed; it is as the square of the speed. This is to say, that if one ball is driven twice as fast as another to begin with, the resistance to that ball is four times as great as it is to the slower one. It is this fact which makes it so difficult to get extra length, beyond a good length, on to a ball, no matter what improvements are made in the ball. Therefore, on the weather question the Professor set it down that, “Of course, other circumstances being the same, the only direct effect is on the co-efficient of resistance. If this be taken as proportional (roughly) to the density of the air, it may vary, in this climate, to somewhere about 10percent. of its greatest value, and the drive is accordingly shortest on a dry, cold winter day with an exceptionally high barometer. The longest drive will, of course, be when the air is as warm and moist as possible, and the barometer very low.”

But he probed most deeply into the mysteries of the flight of the golf ball when he came suddenly to understand the rotation which was subjected to it by the club, and it is of interest and importance to every golfer that he should understand it also. The starting-point of the wonderful investigations that he made is contained first in the simple fact that when an object is poised in the air there is equal atmospheric pressure upon it at all points; and second, that, as several of the most eminent scientists before him, from Newton onwards, had found out, when a sphere rotates in a current of air the side of the sphere which is advancing to meet the current is subject to greater pressure than is that which is moving in the direction of the current; and a step further in this argument is that, as the result of this extra pressure, if a spherical ball be rotating, and at the same time advancing in still air, it will deviate from a straight path in the same direction as that in which its front side is being carried by the rotation.

Therefore, when a ball is sliced, it is made to spin round so that its front side moves round constantly to the right, and, in accordance with the law just mentioned, there is a greater atmospheric pressure on the left side than on the right, and, consequently, the ball is pushed away to the right—as we see it. When it is pulled, the spin is in the opposite direction, and the extra pressure is from the right, and so it is sent away to the left. When the ball is topped the spin on the front side is downwards, and the ball ducks—the extra pressure this time being in the same direction as gravity; and when under-cut is applied, and under-spin follows, the front side of the ball is spinning upwards, and the extra pressure is from below and against gravity.

When this conclusion was first briefly stated, golfers resisted the suggestion that when driving they imparted any under-spin to the ball; but the Professor stuck to his point, and proved it beyond doubt, and it is in this way that the ball takes six and a half seconds over its flight instead of the three and a half that it would otherwise do; and he proved, moreover, that if there was no under-spin imparted to it when driving it would only travel about half the distance that it usually does. The greater the under-spin the greater the upward pressure, and this conclusion leads to others very interesting.

IV

Golfers are in the way of saying that this ball “flies well” or that the other ball “does not fly well.” Sometimes it is imagination born of lack of form; but when great players concur it is not imagination. Some balls are obviously better than others—made of better material, better elastic thread, and more carefully constructed. There is an evident reason why such balls should fly better than others; that is to say, why they should go off the club more quickly, keep their place in the air longer, and travel farther. But then there are many balls of absolutely first-rate quality—and maximum price—that vary considerably in their flying properties, and it very commonly happens that even balls out of the same box, made at the same time and in the same way and of the same stuff, vary also. One frequently finds one or two “bad” balls in a box, and one or two very good ones. The excellent player very soon knows when he has come by the good ones and the bad ones. Now why, under such circumstances, should these balls vary so? What is it that makes them vary? Golfers in general do not know. Often enough they put it down to “pure cussedness”; others, to an idea that it is due to some accidental flaw in the manufacture. It is neither the one nor the other.

The scientific explanation is really a very simple one, and it was set forth very lucidly by Professor Tait. The perfect ball—using the adjective in its most absolute sense—is that which has its centre of gravity, that is to say its centre of weight, dead in the centre of the ball, the centre of measurement. It is by no means to be assumed that these two centres must necessarily coincide. For them to do so exactly is an ideal state, and while matter and man are what they are, and subject to their constant, even though slight, deviations, it is unattainable. But when a ball is properly cored and properly covered, most carefully and by the most exact machinery, the two centres come very near together, and generally, to all intents and purposes, do coincide. That they do not always do so exactly is merely because the greatest human effort is incapable of achieving the scientific ideal, and it must constantly happen that, despite all that effort, the distances between the two centres vary a little. Practically no effort can prevent it, particularly when the exigencies of circumstances demand that balls should be turned out weekly in tens of thousands, and at a price of not more than two shillings each. Now and again the separation of the centres will be greater than normal—accidental again—and then you get a really bad ball, with much bias upon it. When the centre of weight is not at centre of measurement, it means that the ball in effect is heavier on one side than the other, biassed, and that is practically equal to its being not round. Suppose you inserted a small piece of lead just inside the cover of a ball and closed it up again, shaping it as perfectly as it was before. The effect of this would be to remove the centre of weight very far towards that side, and you would have a great exaggeration of the difference between the two centres that commonly exists. If you laid that ball on a table it would promptly roll round until the weighted or biassed side were underneath. If you floated it in water it would wobble about until eventually it did the same thing; and if you floated it in air it would wobble again, and such wobbling would obviously be detrimental to its straight and even flight. There you have it. The farther the two centres are from each other—from the ideal state of absolute coincidence—the greater must be the tendency towards a wobbly or uneven flight, and diminished rotation, and consequently towards a short flight. In the case of many balls other than golf balls, these variations are very considerable. You have an extreme example when a football is out of shape, and it can be seen to make zigzags in the air. But the flight of footballs, or even cricket balls, is not such a delicate and susceptible thing as the flight of a golf ball at its far greater pace.

Professor Tait pointed out two very simple ways of finding out whether a golf ball had its two centres approximately coincident, and whether in consequence it ought to and would fly well. The first was by floating it in a bath of brine or mercury and noticing whether it wobbled or turned over. Many golfers are acquainted with this test, and employ it in a cruder and less decisive form by floating the ball in water. While a ball that had a fairly considerable separation between its two centres might not show any wobbling movement when floated in water, and consequently might not completely establish its claim to be properly centered and of good flying capacity so far as this part of its properties was concerned, the presumption would be greatly in its favour. On the other hand, that which did show any perceptible wobble in water would be self-condemned at once, and would undoubtedly be a bad flyer and a danger to the game of the good golfer.

The second test is one of comparison, and is exceedingly simple. You cannot compare the flying capacities of two or more balls by driving them with golf clubs, for however near to exact similarity you may think the strokes to have been, there is certain to have been an appreciable scientific and mathematical difference, such as would make a proper comparison impossible. But you may give practically exactly the same initial impetus in exactly the same circumstances to two or more balls by shooting them in the same direction from a crossbow, when the string is always pulled out to exactly the same point. Here you will have the balls flying under the simplest possible conditions, with no spin to complicate the flight and interfere with the comparison, and anyone who takes the trouble to make this experiment will find that some balls will regularly fly farther than others when shot forward in this manner. If the size and the weights are the same, these balls are better centered and better flyers, and it is an easy matter for any player to establish a standard by this test, and to judge of the perfection of any particular ball at a moment’s notice. Of course such a test takes no account of the resiliency of the ball; but then, as every player knows, there is a clear difference between good resiliency and good flying properties. In the old days of the gutta, when so much depended upon the even quality of the material all through the ball—and these were, of course, the days when Professor Tait made his investigations and experiments, and drew his conclusions—the variations between centres were greater than they are now, though not so great as in the early period of the rubber-core, when the winding and covering machinery were imperfect. Rubber-cored balls have lately begun to be covered by winding very thin strips of the covering material round the core in just the same way that the core itself is wound, and this should greatly conduce towards more accurate centering. An understanding of the foregoing will help the player towards an appreciation of some of the chief points of a good ball, and he will see how extreme is the necessity for perfect winding machinery and for the most careful supervision of the process. Nobody calls for a hand-made ball in these days: he wouldn’t get it if he did; and it wouldn’t be any good if he got it, for the chances would be enormously against its being so well centered as one made by machinery.

V

Now, however good the ball might be, the chances would be against a perfect stillness upon any axis during flight; that is, of course, when no initial spin was imparted to it by the way in which the stroke was played. It would very likely turn just a little upon an axis, and that little would unsteady and injure its flight, inasmuch as the wobble would be from side to side alternately. This difficulty can be got over by imparting an initial spin to the ball which will always be the same all through its flight, and which will thus stop the wobbling. In a word, rotation will steady the flight. This idea was originally at the bottom of the rifling of the barrel through which a bullet is projected; certainly it was the fundamental principle of the rifling of the old 32-pounders. Better to make the ball rotate on an axis that you know about than that it should wobble on one you do not know about, they said; and so the tubes were rifled inside, the balls were made to rotate, and their flight was made steadier and therefore longer.

In the very earliest days of his investigations upon the flight of the golf ball, Professor Tait thought of the application of this idea to the game. A rotation should be given to the ball to steady its flight and make it longer. A moment’s thought on the part of those whose rudimentary scientific knowledge is a little rusty, will indicate that there are three definite and clearly distinguished axes of rotation. One is a vertical one, and it is chiefly upon that axis that the golf ball rotates when it is pulled or sliced, or upon an axis that has something of the vertical element in it. Then there is the horizontal axis, which is at right angles to the line of flight; and this is the axis upon which it rotates when either under-spin or top has been applied to it. And, thirdly, there is the horizontal axis, which is parallel with the line of flight. This is the axis upon which the rifle bullet spins. At first Professor Tait was inclined to the idea that the last-named would be the ideal axis for the rotation of the golf ball, but it happens to be the one upon which it is impossible to make it rotate when struck by a golf club. However, in this detail of his preliminary theorising he was wrong, due entirely to his not having then investigated the virtues of under-spin as always given to a ball when well driven, and not having come by the great discovery that this under-spin helped the ball to resist gravity and prolong its flight as nothing else could. How exactly under-spin does this, we have just seen, and readers will now have a very definite perception of the qualities of a ball and the importance of rotation, and though the chief advantage of rotation is in resisting gravity, it is an incidental advantage of it, as will now be understood, that the flight of the ball is thereby steadied, and a very slight inaccuracy in centering made of less consequence than it would otherwise be. But remember that a considerable inaccuracy in centering will interfere with the rotation, and therefore the bad flying ball can still be distinguished, because it will fly badly.

VI

Now, in continuation of this brief and simple exposition of some of the points of the Professor’s theorising—backed up by constant practical experiment—upon the merits of under-spin in prolonging and lengthening the flight of the ball which created excited comment in the world of golf at the time, much smaller as that world was then than it is now, it may be mentioned that it was his fair conclusion that good driving lay not in powerful hitting, but in the proper apportionment of good hitting with such a knack as would give the right amount of proper spin to the ball. Thus, while a player who gave no spin to his ball might attain a carry of 136yards, another one who hit his ball with just the same force, giving it the same initial speed, but also a moderate amount of under-spin, would get a carry of 180yards. Of course there would be a great difference between the trajectories of the two flights. By an experiment on a small scale he showed very conclusively what under-spin did. By shooting a ball from a very weak bow, but with the string just below the middle of the ball, so as to impart a slight spin, he made the ball fly point blank to a mark thirty yards off. When he drew the string to the same distance, but applied it to the middle of the ball, it fell eight feet short. It had no under-spin the second time.

Another point is extremely interesting. Some golfers no doubt think that in driving they have to cock their balls up in the air, so to speak; that is to say, that they have to aim at an upward trajectory from the beginning. As a matter of fact they have to do nothing of the kind, and as a matter of common knowledge the best balls, as driven by a Vardon or a Braid or any other first-class player, always “start low” and keep a path quite close to the ground for some distance, after which they begin to rise. If there were no under-spin the ball could not keep this horizontal path for the time that it does; still less could it begin to rise afterwards. It is the under-spin that does it, and the theoretically perfect drive is the one that is hit straight forward with practically no initial elevation or incline. The character of the stroke gives to the ball the necessary under-spin and power to rise, and the way in which the club comes on to the ball in a stroke so perfectly executed makes any considerable initial elevation impossible, just as it is not wanted. But mark, that if the golfer has not acquired the proper knack of driving—i.e. the proper knack of imparting just the right kind and right amount of underspin—then he will need some initial elevation in order to keep his ball in the air; and so he has to depart intentionally from the proper principles of driving, and deliberately cock up his ball, even though slightly. How his driving suffers in consequence may be gathered by taking the extreme case of no under-spin at all, upon which Professor Tait says: “When there is no rotation there must be initial elevation, and even if we make it as great as one in four, the requisite speed of projection for a carry of 250yards would be 1120feet per second, or about that of sound.” Now, as the actual speed of projection in the case of a fine drive by a first-class player is not more than 350feet per second, the reader may have some idea as to how hard he would have to hit if he were dispensing with rotation. Of course “a carry of 250yards” is extremely long, and is rarely if ever done in the absence of a helping wind from behind, but the Professor had just been speaking of the practicability of such a carry “in still air.” Even though it be abnormal, the vast disparity between an initial speed of the ball of 350feet per second and one of 1120feet will make the point clear.

VII

The most interesting question arises, that if the well-driven ball starts off almost horizontally and then begins to ascend, what is the line of its flight or its trajectory? Golfers generally have the crudest notions on this point. For the most part they seem to assume that the trajectory is represented by an even segment of a circle, having its vertex or highest point just about half-way along. This is absolutely wrong. Even if there were no spin at all, this would not be the case, the vertex being much nearer the end of the flight than the beginning of it, as in the case of the rifle bullet. On the other hand, many players on seeing a ball well driven constantly remark on what they think is after all a fancy of theirs, that when the ball has gone a long way it suddenly seems to take a new lease of life, and to rise up in the air before moving down towards earth. They will be surprised to know that it is not fancy, that the ball does rise. The fact is that the line of flight of a well-driven ball with under-spin, from its starting to its highest point, is partly concave upwards, and this fact is only evident to the eye when it has travelled some distance. Such a ball is in effect the pull or the slice turned round from the flat in an upward direction. Eventually gravity gets the better of the ball and pulls it down.

With the help of the formulÆ that he prepared after several years’ study of the matter, and with the assistance of Mr.Wood, whom he regarded as the quickest and most accurate reckoner of abstruse scientific quantities that he had ever encountered, the professor calculated exactly the trajectories of golf balls driven under many different circumstances. Among them he showed the short line of the flight of a ball to which no initial rotation or under-spin was imparted. While the other balls were started off almost horizontally, it was necessary in this case to give the ball an initial elevation of 15degrees—that is to deliberately hit it upwards at that angle—in order to make it rise at all. Regarding this trajectory Professor Tait said most significantly that it is “characteristic of a well-known class of drives, usually produced when a too high tee is employed, and the player stands somewhat behind his ball. Notice particularly how much the carry and time of flight are reduced, though the initial speed is the same. The slight under-spin makes an extraordinary difference, producing, as it were, an unbending of the path throughout its whole length, and thus greatly increasing the portion above the horizon.” The run of this ball on alighting is greater than in the other cases, owing to there being no backspin, but it cannot make up for the short flight.

Concerning another short drive of the same class, Professor Tait remarks: “In spite of its 50percent. greater angle of initial elevation, the carry of the non-rotating projectile is little more than half that of the other, and it takes only one-third of the time spent by the other in the air. But the contrast shows how much more important (so far as carry is concerned) is a moderate amount of under-spin than large initial elevation. And we can easily see that initial elevation, always undesirable (unless there is a hazard close to the tee), as it exposes the ball too soon to the action of the wind where it is strongest, may be entirely dispensed with.”

A question which may have been in the reader’s mind for some time is as to whether, since the effect of under-spin is to make the trajectory turn upwards as it were, excessive under-spin would not result in the ball taking an absolutely upward trajectory and then curling over and right round. In actual practice so much under-spin could not be put on to a golf ball as would enable it to get the better of gravity and other circumstances to this extent, but theoretically such an evolution would be described if the conditions were equal to it. Professor Tait says: “The kink can be obtained in a striking manner when we use as a projectile one of the large balloons of thin rubber which are so common. We have only to ‘slice’ the balloon sharply downwards in a nearly vertical plane with the flat hand.” It must be remembered that in the case of a very bad slice the ball sometimes does actually curl right round towards the finish of its run.

VIII

There are many other incontrovertible and very interesting conclusions arrived at as the result of the reckoning of this distinguished scientist which one would like to discuss if there were room for it. It is enough to say at the finish that while these reflections will serve to give the golfer a more intelligent view of the scientific aspect of the game and its mysteries, and very likely even tend to a change in his policy in some departments, he will not be led towards any disbelief in the standard methods of good driving or to any deliberate seeking or regulation of under-spin, the fact being that more than a century of play and groping about in unscientific darkness brought the player to the discovery of the way in which the longest ball could be obtained, i.e. to the way in which translatory force and rotation were blended to the best effect. The stance and the swing, when properly performed with a proper driver, bring about that blend, though generally the player has been blissfully unconscious of the part they have played in conveying rotation to the ball. A pregnant paragraph by the scientist may be quoted at the end: “The pace which the player can give the clubhead 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. It is mainly in apparently trivial matters like these, which are placidly spoken of by the mass of golfers under the general title of knack, that lie the very great differences in drives effected under precisely similar external conditions by players equal in strength, agility, and (except to an extremely well-trained and critical eye) even in style.”

I should explain that all these things were told by Professor Tait, not in simple language to an assembly of golfers, but in complicated terms to a learned body of scientists, and I have thus endeavoured to explain his meaning in a manner that all can understand, and in some cases—as in that of the question of the proper centering of the rubber-cored ball to carry it forward to its application to the new conditions of play that have been introduced since his life and studies came to an end.

IX

What is the longest possible drive by our best driver under the best conditions? That is a question which it is impossible to answer, simply because the best conditions cannot be defined. In practical golf they are an impossible ideal, and one never knows how far in certain existing circumstances that ideal is approached. This brings us to see the futility of comparing one drive with another, or even of regarding any particular drive as the best on record, in the sense that it was the best that had ever been accomplished, just because it was the longest that had been measured. The very slightest difference in the conditions, or in the circumstances of the run of the ball, may cause one drive to be what some people would call a record, and another, equally good in execution and strength, to be comparatively poor. For example, think of what enormous importance is the nature of the place on which the ball gets its first pitch. Let it pitch against an incline ever so slight, or against a knob in the ground no bigger than a pigeon’s egg, and the sting of the shot is plucked. As in the case of so many other arguments, this one as to the overwhelming influence of conditions in long driving, and record driving, is best set forth by the reductio ad absurdum, and it is sufficient to point out that if a child tapped a ball off a tee on to a tolerably steep and smooth incline, the ball would run to the edge of the world unless stopped by a change in the conditions.

It is more to the point—but not much more—to consider how far a ball might be driven under conditions which might be described an nearly ideal, but strictly fair in the sense that the force of gravity by means of an incline, or wind, should not assist in the propulsion of the ball, while on the other hand neither wind nor slope should be adverse to it. To create such nearly ideal conditions, under which we would solve this question as to the longest possible drive, we would need to enclose a long shed or gallery, down which the ball was to travel, so that it should be entirely protected from wind influence, and then we should have to lay a special fairway of some smooth, hard substance that would afford the least imaginable resistance and friction to the ball when running. Asphalte would be good for this purpose, but polished marble or granite would be better, and if some millionaire enthusiast desired to solve this longest-possible-drive question these are the conditions that I would recommend to him. Now, then, how long would that gallery need to be? How far could that ball be driven? In the open, on perfectly level and on smooth slippery turf, which after wind and warmth is at its fastest, such as one gets often at St.Andrews, a drive that approached 320yards would at the same time be approaching very near record for fair conditions. We have this to work on. How many yards should we have to put on for the perfect pitch and the perfectly level, hard, smooth, and frictionless floor in our driving gallery? When you come to think it over in this way, it is rather a pretty problem. Of course, in the absence of the millionaire and the gallery, there is no satisfactory answer, though Professor Tait would have made a close estimate possibly. But put the question to the next party of golfers among whom you happen to be included, and see what widely varying answers you will get. In the meantime one may suggest 500yards.