XIII. TRANSITS OF VENUS.

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As a transit of Venus, visible in this country, occurs in December, 1882, my readers, although they may not care for an account of the mathematical relations involved in the observation and calculation of a transit, will probably be interested by a simple explanation of the reasons why transits of Venus are so important in astronomy.

Of course it is known that a transit of Venus is the apparent passage of the planet across the face of the sun, when, in passing between the earth and sun, as she does about eight times in thirteen years, she chances to come so close to the imaginary line joining the centres of those bodies that, as seen from the earth, she appears to be upon the face of the sun. We may compare her to a dove circling round a dovecot, and coming once in each circuit between an observer and her house. If in her circuit she flew now higher, now lower, or, in other words, if the plane of her path were somewhat aslant, she would appear to pass sometimes above the cot, and sometimes below it, but from time to time she would seem to fly right across it. So Venus, in circuiting round the sun, appears sometimes, when she comes between us and the sun, to pass above his face, and sometimes to pass below it; but occasionally passes right across it. In such a case she is said to transit the sun's disc, and the phenomenon is called a transit of Venus. She has a companion in these circuiting motions, the planet Mercury, though this planet travels much nearer to the sun. It is as though, while a dove were flying around a dovecot at a distance of several yards, a sparrow were circling round the cot at a little more than half the distance, flying a good deal more quickly. It will be understood that Mercury also crosses the face of the sun from time to time—in fact, a great deal oftener than Venus; but, for a reason presently to be explained, the transits of Mercury are of no great importance in astronomy. One occurred in 1861, another in 1868; another in May, 1878; yet very little attention was paid to those events; and before the next transit of Venus, in 1882, there will be a transit of Mercury, in November, 1881; yet no arrangements have been made for observing Mercury in transit on these occasions; whereas astronomers began to lay their plans for observing the transit of Venus in 1882, as far back as 1857.

The illustration which I have already used will serve excellently to show the general principles on which the value of a transit of Venus depends; and as, for some inscrutable reasons, any statement in which Venus, the sun, and the earth are introduced, seems by many to be regarded as, of its very nature, too perplexing for anyone but the astronomer even to attempt to understand, my talk in the next few paragraphs shall be about a dove, a dovecot, and a window, whereby, perhaps, some may be tempted to master the essential points of the astronomical question who would be driven out of hearing if I spoke about planets and orbits, ascending nodes and descending nodes, ingress and egress, and contacts internal and external.

Suppose D, fig. 42, to be a dove flying between the window A B and the dovecot C c, and let us suppose that a person looking at the dove just over the bar A sees her apparently cross the cot at the level a, at the foot of one row of openings, while another person looking at the dove just over the bar B sees her cross the cot apparently at the level b, at the foot of the row of openings next above the row a. Now suppose that the observer does not know the distance or size of the cot, but that he does know in some way that the dove flies just midway between the window and the cot; then it is perfectly clear that the distance a b between the two rows of openings is exactly the same as the distance A B between the two window-bars; so that our observers need only measure A B with a foot-rule to know the scale on which the dovecot is made. If A B is one foot, for instance, then a b is also one foot; and if the dovecot has three equal divisions, as shown at the side, then C c is exactly one yard in height.

Fig. 42.

Thus we have here a case where two observers, without leaving their window, can tell the size of a distant object.

And it is quite clear that wherever the dove may pass between the window and the house, the observers will be equally able to determine the size of the cot, if only they know the relative distances of the dove and dovecot.

Fig. 43.
Fig. 44.
Fig. 45.

Thus, if D a is twice as great as D A, as in fig. 43, then a b is twice as great as A B, the length which the observers know; and if D a is only equal to half D A, as in fig. 44, then a b is only equal to half the known length A B. In every possible case the length of a b is known. Take one other case in which the proportion is not quite so simple:—Suppose that D a is greater than D A in the proportion of 18 to 7, as in fig. 45; then b a is greater than A B in the same proportion; so that, for instance, if A B is a length of 7 inches, b a is a length of 18 inches.

We see from these simple cases how the actual size of a distant object can be learned by two observers who do not leave their room, so long only as they know the relative distances of that object and of another which comes: between it and them. We need not specially concern ourselves by inquiring how they could determine this last point: it is enough that it might become known to them in many ways. To mention only one. Suppose the sun was shining so as to throw the shadow of the dove on a uniformly paved court between the house and the dovecot, then it is easy to conceive how the position of the shadow on the uniform paving would enable the observers to determine (by counting rows) the relative distances of dove and dovecot.

Now, Venus comes between the earth and sun precisely as the dove in fig. 45 comes between the window A B and the dovecot b a. The relative distances are known exactly, and have been known for hundreds of years. They were first learned by direct observation; Venus going round and round the sun, within the path of the earth, is seen now on one side (the eastern side) of the sun as an evening star, and now on the other side (the western side) as a morning star, and when she seems farthest away from the sun in direction E V (fig. 46) in one case, or E v in the other case, we know that the line E V or E v, as the case may be, must just touch her path; and perceiving how far her place in the heavens is from the sun's place at those times, we know, in fact, the size of either angle S E V or S E v, and, therefore, the shape of either triangle S E V or S E v. But this amounts to saying that we know what proportion S E bears to S V—that is, what proportion the distance of the earth bears to the distance of Venus.[17]

Fig. 46.

This proportion has been found to be very nearly that of 100 to 72; so that when Venus is on a line between the earth and sun, her distances from these two bodies are as 28 to 72, or as 7 to 18.

Fig. 47.

These distances are proportioned precisely then as D A to D a in fig. 45; and the very same reasoning which was true in the case of dove and dovecot is true when for the dove and dovecot we substitute Venus and the sun respectively, while for the two observers looking out from a window we substitute two observers stationed at two different parts of the earth. It makes no difference in the essential principles of the problem that in one case we have to deal with inches, and in the other with thousands of miles; just as in speaking of fig. 45 we reasoned that if A B, the distance between the eye-level of the two observers, is 7 inches, then b a is 18 inches, so we say that if two stations, A and B, fig. 47, on the earth E, are 7000 miles apart (measuring the distance in a straight line), and an observer at A sees Venus' centre on the sun's disc at a, while an observer at B sees her centre on the sun's disc at b, then b a (measured in a straight line, and regarded as part of the upright diameter of the sun) is equal to 18,000 miles. So that if two observers, so placed, could observe Venus at the same instant, and note exactly where her centre seemed to fall, then since they would thus have learned what proportion b a is of the whole diameter S S' of the sun, they would know how many miles there are in that diameter. Suppose, for instance, they found, on comparing notes, that b a is about the 47th part of the whole diameter, they would know that the diameter of the sun is about 47 times 18,000 miles, or about 846,000 miles.

Now, finding the real size of an object like the sun, whose apparent size we can so easily measure, is the same thing as finding his distance. Any one can tell how many times its own diameter the sun is removed from us. Take a circular disc an inch in diameter,—a halfpenny, for instance—and see how far away it must be placed to exactly hide the sun. The distance will be found to be rather more than 107 inches, so that the sun, like the halfpenny which hides his face, must be rather more than 107 times his own diameter from us. But 107 times 846,000 miles amounts to 90,522,000 miles. This, therefore, if the imagined observations were correctly made, would be the sun's distance.

I shall next show how Halley and Delisle contrived two simple plans to avoid the manifest difficulty of carrying out in a direct manner the simultaneous observations just described, from stations thousands of miles apart.

We have seen that the determination of the sun's distance by observing Venus on the sun's face would be a matter of perfect simplicity if we could be quite sure that two observations were correctly made, and at exactly the same moment, by astronomers stationed one far to the north, the other far to the south.

Fig. 48.

The former would see Venus as at A, fig. 48, the other would see her as at B; and the distance between the two lines a a´ and b b´ along which her centre is travelling, as watched by these two observers, is known quite certainly to be 18,000 miles, if the observers' stations are 7,000 miles apart in a north-and-south direction (measured in a straight line). Thence the diameter S S´ of the sun is determined, because it is observed that the known distance a b is such and such a part of it. And the real diameter in miles being known, the distance must be 107 times as great, because the sun looks as large as any globe would look which is removed to a distance exceeding its own diameter (great or small) 107 times.

But unfortunately it is no easy matter to get the distance a b, fig. 48, determined in this simple manner. The distance 18,000 miles is known; but the difficulty is to determine what proportion the distance bears to the diameter of the sun S S´. All that we have heard about Halley's method and Delisle's method relates only to the contrivances devised by astronomers to get over this difficulty. It is manifest that the difficulty is very great.

Fig. 49.

For, first, the observers would be several thousand miles apart. How then are they to ensure that their observations shall be made simultaneously? Again, the distance a b is really a very minute quantity, and a very slight mistake in observation would cause a very great mistake in the measurement of the sun's distance. Accordingly, Halley devised a plan by which one observer in the north (or as at A, fig. 47) would watch Venus as she traversed the sun's face along a lower path, as a a´ fig. 49; while another in the south (or as at B, fig. 47) would watch her as she traversed a higher path, as b b´ fig. 49. By timing her they could tell how long these paths were, and therefore how placed on the sun's face, as in fig. 49; that is, how far apart, which is the same thing as determining b a, fig. 48. This was Halley's plan, and as it requires that the duration of the transit should be timed, it is called the method of durations. Delisle proposed another method—viz., that one observer should time the exact moment when Venus, seen from one station, began to traverse the path a a´, while another should time the exact moment when she began to traverse the path b b´; this would show how much b is in advance of a, and thence the position of the two paths can be determined. Or two observers might note the end of the transit, thus finding how much is in advance of This is Delisle's method, and it has this advantage over Halley's—that an observer is only required to see either the beginning or the end of the transit, not both.

I shall not here consider, except in a general way, the various astronomical conditions which affect the application of these two methods. Of course, all the time that a transit lasts, the earth is turning on her axis; and as a transit may last as long as eight hours, and generally lasts from four to six hours, it is clear that the face of the earth turned towards the sun must change considerably between the beginning and end of a transit. So that Halley's method, which requires that the whole duration of a transit should be seen, is hampered with the difficulty arising from the fact that a station exceedingly well placed for observing the beginning of the transit might be very ill placed for observing the end, and vice versÂ.

Delisle's method is free from this objection, because an observer has only to note the beginning or the end, not both. But it is hampered by another. Two observers who employ Halley's method have each of them only to consider how long the passage of Venus over the sun's face lasts; and they are so free from all occasion to know the exact time at which the transit begins and ends, that theoretically each observer might use such an instrument as a stop-watch, setting it going (right or wrong as to the time it showed) when the transit began, and stopping it when the transit was over. But for Delisle's method this rough-and-ready method would not serve. The two observers have to compare the two moments at which they severally saw the transit begin,—and to do this, being many thousand miles apart, they must know the exact time. Suppose they each had a chronometer which had originally been set to Greenwich time, and which, being excellently constructed and carefully watched, might be trusted to show exact Greenwich time, even though several months had elapsed since it was set. Then all the requirements of the method would be quite as well satisfied as those of the other method would be if the stop-watches just spoken of went at a perfectly true rate during the hours that the transit lasted. But it is one thing to construct a time-measure which will not lose or gain a few seconds in a few hours, and quite another to construct one which will not lose or gain a few seconds in a journey of many thousand miles, followed perhaps by two or three months' stay at the selected station. An error of five seconds would be perfectly fatal in applying Delisle's method, and no chronometer could be trusted under the conditions described to show true time within ten or twelve seconds. Hence astronomers had to provide for other methods of getting true time (say Greenwich time) than the use of chronometers; and on the accuracy of these astronomical methods of getting true time depended the successful use of Delisle's method.

Fig. 50.

Fig. 51.

Then another difficulty had to be considered, which affected both methods. It was agreed by both Halley and Delisle that the proper moment to time the beginning or end of transit was the instant when Venus was just within the sun's disc, as in fig. 50, either having just completed her entry, or being just about to begin to pass off the sun's face. If at this moment Venus presented a neatly defined round disc, exactly touching the edge of the sun, also neatly defined, this plan would be perfect. At the very instant when the contact ceased at the entry of Venus, the sun's light would break through between the edges of the two discs, and the observer would only have to note that instant; while, when Venus was leaving the sun, he would only have to notice the instant when the fine thread of light was suddenly divided by a dark point. But unfortunately Venus does not behave in this way, at least not always. With a very powerful and very excellent telescope, in perfectly calm, clear weather, and with the sun high above the horizon, she probably behaves much as Halley and Delisle expected. But under less favourable conditions, she presents at the moment of entry or exit some such appearance as is shown in figures 51, 52, and 53, while with a very low sun she assumes all sorts of shapes, continually changing, being for one moment, perhaps, as in one or other of figs. 51, 52, and 53, and in the next distorted into some such pleasing shape as is pictured in fig. 54.

Fig. 52.
Fig. 53.

Accordingly, many astronomers are disposed to regard both Halley's method and Delisle's as obsolete, and to place reliance on the simple method of direct observation first described. They would, however, of course bring to their aid all the ingenious devices of modern astronomical observation in order to overcome the difficulties inherent in that method. One of the contrivances naturally suggested to meet such difficulties is to photograph the sun with Venus upon his face. The American astronomers, in particular, consider that the photographic results obtained during the transit of 1874 will outweigh those obtained by all the other methods. The German and Russian astronomers, as well as those of Lord Lindsay's expedition, while placing great reliance on photography, employed also a method of measuring the position of Venus on the sun's disc, by means of a kind of telescope specially constructed for such work, the peculiarities of which need not be here considered.

Fig. 54.

The observations made in 1769 were so imperfect that astronomers deduced a distance fully 3,000,000 miles too great. Of late, other methods of observation had set them much nearer the true distance, which has been judged to lie certainly between 91,800,000 miles and 92,600,000 miles—a tolerably wide range.

But it may perhaps occur to some that the distance of the sun may be changing. The earth might be drawing steadily in towards the sun, and so all our measurements might be deceptive. Nay, the painful thought might present itself that when the observations of 1769 were made, the sun really was farther away than at present by more than 3,000,000 of miles. If this were so, the earth would, in the course of a century, have reduced her distance by fully one-thirtieth part, so that, supposing the approach to continue, she would in 3,000 years fall into the sun, while, long before that period had elapsed, the increased heat to which she would be exposed would render life impossible.

Fortunately, we know quite certainly that no such approach is taking place. It is known that the distance of the earth from the sun cannot change without a corresponding change in her period of revolution—that is, in the length of the year. The law connecting these two (indicated in the note, page 279) is such that, on the reduction of the distance by any moderate portion the period would be reduced by a portion half as great again. For instance: if the distance of the earth from the sun were reduced by a thirtieth part (or about 3,000,000 miles) the length of the year would be reduced by a thirtieth and half a thirtieth—that, is, by a twentieth part, or by more than eighteen days. We know that no such change has taken place during the last century, or since the beginning of history. Nay, from the Chaldean estimate of the length of the year, which only exceeded ours by about two minutes, it is easily shown that the distance of the earth from the sun has not diminished 200 miles within the last 2,500 years. So that, assuming even that the earth is approaching the sun at this rate, or eight miles in a century, it would be 1,250,000 years before the distance would be diminished by 100,000 miles, which is the probable limit of error in the determination of the sun's distance.

If, finally, it be asked, What, after all, is the use of determining the sun's distance? the answer we shall give must depend on the answer given to the question, What, after all, is the use of knowing any facts in astronomy other than those useful in navigation, surveying, and so on? And I think that this question would introduce another and a wider one—viz., What is the use of that quality in man's nature which makes him seek after knowledge for its own sake? I certainly do not propose to consider this question, nor do I think that the reader will find any difficulty in understanding why I do not. But accepting the facts: (1) that we are so constituted as to seek after knowledge; and (2) that knowledge about the celestial orbs is interesting to us, quite apart from the use of such knowledge in navigation and surveying, it is easy to show that the determination of the sun's distance is a matter full of interest. For on our estimate of the sun's distance depend our ideas as to the scale, not only of the solar system, but of the whole of the visible universe. The size of the sun, his mass, and therefore his might, the scale of those wonderful operations which we know to be taking place upon, and within, and around the sun; all these relations, as well as our estimate of the size and mass of every planet, and therefore our estimate of the earth's relative importance in the solar system, depend absolutely and directly on the estimate we form of the sun's distance. Such being the case (this being in point of fact the cardinal problem of dimensional astronomy) it cannot but be thought that, great as were the trouble and expense of the expeditions sent out to observe the transit of 1874, they were devoted to an altogether worthy cause.


Hazell, Watson, and Viney, Printers, London and Aylesbury.

FOOTNOTES:

[1] It might be suggested that the appearance of this blazing comet among the stars drove the more superstitious of the Israelites at that time to the worship of star-gods, as we read how, during the judgeship of Jair, they "served Baalim, and Ashtaroth, and the gods of Syria, and the gods of Moab, and the gods of the Philistines, and forsook the Lord and served not Him." To a people like the Jews, who seem to have been in continual danger of returning to the Sabaistic worship of their Chaldean ancestors, the appearance of a blazing comet may have been a frequent occasion of backsliding.

[2] I do not say we can in any way avoid this far greater difficulty. Our own material universe cannot even be conceived as limited in any way save by void space of infinite extent; and it is as impossible for us to conceive an infinite void as to conceive the infinite extension of matter. Some modern mathematicians, indeed, assert that space is not necessarily infinite, but they accompany the assertion (very justly) with the admission that we cannot possibly conceive any boundary to space; and as one of the things they ask mathematicians to admit is the possibility that a straight line indefinitely produced both ways will at length re-enter into itself, while another is the possibility that in other parts of the universe two and two may make three or five, they are not likely, I conceive, to persuade most mathematicians (profoundly mathematical though they are themselves) that the mystery of infinity has been as yet entirely expounded.

[3] Of course the reader will understand that when I here speak of the earth's weight, I mean simply the pressure which would be exerted by the quantity of matter contained in the earth, if each portion were only subjected to an attractive force equal to that of gravity at the earth's surface. The actual force with which the earth is drawn in any direction, as a weight at the earth's surface is drawn downwards, depends on the distance and mass of the attracting body as well as on the mass of the earth; and strictly speaking, we ought not to say that the earth weighs so many millions of tons, but that she contains so many million times as much matter as a mass which at her surface weighs a ton.

[4] The words of Newton, "Hypotheses non fingo," have been often quoted in such sort as to give an entirely incorrect idea of his real opinion as to the relation between theoretical and practical science. As too commonly understood, they would, in fact, make his discovery of gravitation a great exception to his own rule. They must be taken in connection with his definition of a hypothesis, as "whatsoever is not deduced from phenomena." It is a part of true science, nay, it is the highest office of the student of science to deduce theories from phenomena. Such research stands as high above the simple observation of phenomena as architecture stands above brick-making or stone-cutting. But to frame hypotheses as the old Greeks did, trusting to the power of the understanding independently of the observation of phenomena, is to make bricks without straw and to build with them upon the sand.

[5] The point is explained in a paper called "Our Chief Timepiece Losing Time," in the first series of my "Light Science for Leisure Hours."

[6] In the popular, but incorrect way of speaking, the balance between the centrifugal and the centripetal force will no longer be maintained: the increase of velocity will give the centrifugal force the advantage, and it will slowly draw the body away from the centre. In reality there is no centrifugal force, the only force acting on the earth in her course round the sun being the sun's attraction upon her, which, however, must keep bending her course from the straight line, if she is to maintain her distance. In the case above imagined it would not bend her course actively enough.

[7] Its place is indicated in my School Atlas, as well as (of course) in my Library Atlas, from the latter of which the small maps illustrating the present article have been pricked off. The new star is marked T in the Crown (Map VIII.), and must not be confounded with the star t, as in Roscoe's Treatise on Spectral Analysis, and in some astronomical works. The star t is a well known fifth magnitude star, which has shone with no perceptible increase or diminution of splendour since Bayer's time certainly, and probably for thousands of years before.

[8] This chapter was first published in February, 1877, when the star was already invisible to the naked eye.

[9] It will be remembered by those familiar with the history of solar observation, that when the spectrum of the solar prominence was first observed, the orange-yellow bright line was supposed to be the well-known double sodium line. It is so near to this pair of lines, that while they are called D 1 and D 2, it has been called D 3; and in a spectroscope of small dispersive power the three would be seen as one.

[10] It has been thought by some that, in the beginning, the moon was always opposite the sun, thus always ruling the night. Milton thus understood the account given in the first book of Genesis. For he says,—

Less bright the morn,
But opposite in levell'd west was set
His mirror, with full face, borrowing her light
From him; for other light she needed none
In that aspect; and still that distance keeps
Till night, then in the east her turn she shines,
Revolv'd on Heav'n's great axle.

It was only as a consequence of Adam's transgression that he conceives the angels sought to punish the human race by altering the movements of the celestial bodies—

To the blank moon
Her office they prescribe—

It is hardly necessary to say, perhaps, that this interpretation is not scientifically admissible.

[11] Brown is not the right word for the tint of red where the visible spectrum begins. I know, however, of no word properly expressing the colour.

[12] Suppose there are two planets A and B of equal density, of which A has a diameter twice as great as that of B. Then the volume of A is eight times greater than B's volume. So that if the volume of its atmosphere exceed the volume of B's air in the same degree, the planet A has eight times as much air as the planet B. But the surface of A is only four times as great as the surface of B; so that if A had only four times as much air as B, there would be the same quantity of air above each square mile of A's surface as above each of B's surface. Since then A has eight times—not merely four times—as much air as B, it follows that A has twice as much air over each square mile of surface as B has. And similarly in all such cases, the general law being that the larger planet has more air over each square mile of surface in the same degree that its diameter exceeds that of the other.

[13] By age here I do not mean absolute age, but relative age. I speak of Mars and the Moon as older than the earth in the same sense that I should speak of a fly in autumn as older than a five-year-old raven.

[14] Who assigned to him, as his representative metal, lead—a metal "heavy, dull, and slow," as Don Armado puts it, in "Love's Labour's Lost."

[15] Attention has lately been called, by the astronomers of the Washington Observatory, to the fact that the statement usually made in our books of astronomy, that Sir W. Herschel's latest determination of Saturn's rotation period was 10h. 29m., is incorrect. His only determination of the period gave 10h. 16m. 44s. for the Saturnian day.

[16] "The altar, bearing fire of incense, pictured by stars." A remarkably bright and complex portion of the Milky Way lies near the constellation Ara, giving the appearance of smoke ascending from the altar, only the altar must be set upright, as in my Gnomonic Atlas, not inverted as in all the modern maps. (It is shown properly in the old Farnese globe).

[17] There is, however, a much more perfect way of determining this proportion, by applying the law which Kepler found to connect the distances of the planets from the sun with the times in which they complete the circuits of their orbits. The law is that, if we take any two planets, and write down the numbers expressing their periods of circuit (say in days), and the numbers expressing their distances from the sun (say in miles) in the same order; then if we multiply each number of the first pair into itself, and each number of the second pair twice into itself, the four numbers thus obtained will be proportional; that is to say, as the first is to the second, so will the third be to the fourth. Now, as every one knows who has worked sums in the rule of three, when any three are given out of four proportionals, the fourth can always be found; but we know the periods of circuit both of the earth and Venus (365·2564 days and 224·7008 days respectively) very exactly indeed, because they have traversed their orbits so many times since they began to be observed by astronomers. We can call the earth's distance 100, and then applying the rule just stated, we get Venus' distance relatively to the earth's. The reader who cares to work out this little sum will find no difficulty whatever—if at least he is able to extract the cube roots of any number. The proportion runs thus:—

365·2564 × 365·2564 : 224·7008 × 224·7008
:: 100 × 100 × 100 : (Venus' distance cubed.)

Work out this sum and we get for Venus' distance 72·333. The ratio of Venus' distance to the earth's is almost exactly expressed by the numbers 217 and 300.

Transcriber's Notes:

  • Obvious printer’s errors corrected.
  • Every effort has been made to replicate this text as faithfully as possible, including non-standard punctuation, inconsistently hyphenated words, and other inconsistencies.





                                                                                                                                                                                                                                                                                                           

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