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 a′ is in advance of b′ 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 versa.

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.