far to the north of the earth’s equator sees Mars at midnight, when the planet is in opposition, displaced somewhat to the south of his true position—that is, of the position he would have as supposed to be seen from the centre of the earth. On the other hand, an observer far to the south of the equator sees Mars displaced somewhat to the north of his true position. The difference may be compared to different views of a distant steeple (projected, let us suppose, against a much more remote hill), from the uppermost and lowermost windows of a house corresponding to the northerly and southerly stations on the earth, and from a window on the middle story corresponding to a view of Mars from the earth’s centre. By ascertaining the displacement of the two views of Mars obtained from a station far to the north and another station far to the south, the astronomer can infer the distance of the planet, and thence the dimensions of the solar system. The displacement is determinable by noticing Mars’s position with respect to stars which chance to be close to him. For this purpose the heliometer is specially suitable, because, having first a view of Mars and some companion stars as they actually are placed, the observer can, by suitably displacing the movable half-glass, bring the star into apparent contact with the planet, first on one side of its disc, and then on the other side—the mean of the two resulting measures giving, of course, the distance between the star and the centre of the disc.
This method requires that there shall be two observers, one at a northern station, as Greenwich, or Paris, or Washington, the other at a southern station, as Cape Town, Cordoba, or Melbourne. The base-line is practically a north-and-south line; for though the two stations may not lie in the same, or nearly the same, longitude, the displacement determined is in reality that due to their difference of latitude only, a correction being made for their difference of longitude.
The other method depends, not on displacement of two observers north and south, or difference of latitude, but on displacement east and west. Moreover, it does not require that there shall be two observers at stations far apart, but uses the observations made at one and the same stations at different times. The earth, by turning on her axis, carries the observer from the west to the east of an imaginary line joining the earth’s centre and the centre of Mars. When on the west of that line, or in the early evening, he sees Mars displaced towards the east of the planet’s true position. After nine or ten hours the observer is carried as far to the east of that line, and sees Mars displaced towards the west of his true position. Of course Mars has moved in the interval. He is, in fact, in the midst of his retrograde career. But the astronomer knows perfectly well how to take that motion into account. Thus, by observing the two displacements, or the total displacement of Mars from east to west on account of the earth’s rotation, one and the same observer can, in the course of a single favourable night, determine the sun’s distance. And in passing, it may be remarked that this is the only general method of which so much can be said. By some of the others an astronomer can, indeed, estimate the sun’s distance without leaving his observatory—at least, theoretically he can do so. But many years of observation would be required before he would have materials for achieving this result. On the other hand, one good pair of observations of Mars, in the evening and in the morning, from a station near the equator, would give a very fair measure of the sun’s distance. The reason why the station should be near the equator will be manifest, if we consider that at the poles there would be no displacement due to rotation; at the equator the observer would be carried round a circle some twenty-five thousand miles in circumference; and the nearer his place to the equator the larger the circle in which he would be carried, and (cæteris paribus) the greater the evening and morning displacement of the planet.
Both these methods have been successfully applied to the problem of determining the sun’s distance, and both have recently been applied afresh under circumstances affording exceptionally good prospects of success, though as yet the results are not known.
It is, however, when we leave the direct surveying method to which both the observations of Venus in transit and Mars in opposition belong (in all their varieties), that the most remarkable, and, one may say, unexpected methods of determining the sun’s distance present themselves. Were not my subject a wide one, I would willingly descant at length on the marvellous ingenuity with which astronomers have availed themselves of every point of vantage whence they might measure the solar system. But, as matters actually stand, I must be content to sketch these other methods very roughly, only indicating their characteristic features.
One of them is in some sense related to the method by actual survey, only it takes advantage, not of the earth’s dimensions, but of the dimensions of her orbit round the common centre of gravity of herself and the moon. This orbit has a diameter of about six thousand miles; and as the earth travels round it, speeding swiftly onwards all the time in her path round the sun, the effect is the same as though the sun, in his apparent circuit round the earth, were constantly circling once in a lunar month around a small subordinate orbit of precisely the same size and shape as that small orbit in which the earth circuits round the moon’s centre of gravity. He appears then sometimes displaced about 3000 miles on one side, sometimes about 3000 miles on the other side of the place which he would have if our earth were not thus perturbed by the moon. But astronomers can note each day where he is, and thus learn by how much he seems displaced from his mean position. Knowing that his greatest displacement corresponds to so many miles exactly, and noting what it seems to be, they learn, in fact, how large a span of so many miles (about 3000) looks at the sun’s distance. Thus they learn the sun’s distance precisely as a rifleman learns the distance of a line of soldiers when he has ascertained their apparent size—for only at a certain distance can an object of known size have a certain apparent size.
The moon comes in, in another way, to determine the sun’s distance for us. We know how far away she is from the earth, and how much, therefore, she approaches the sun when new, and recedes from him when full. Calling this distance, roughly, a 390th part of the sun’s, her distance from him when new, her mean distance, and her distance from him when full, are as the numbers 389, 390, 391. Now, these numbers do not quite form a continued proportion, though they do so very nearly (for 389 is to 390 as 390 to 391-1/400). If they were in exact proportion, the sun’s disturbing influence on the moon when she is at her nearest would be exactly equal to his disturbing influence on the moon when at her furthest from him—or generally, the moon would be exactly as much disturbed (on the average) in that half of her path which lies nearer to the sun as in that half which lies further from him. As matters are, there is a slight difference. Astronomers can measure this difference; and measuring it, they can ascertain what the actual numbers are for which I have roughly given the numbers 389, 390, and 391; in other words, they can ascertain in what degree the sun’s distance exceeds the moon’s. This is equivalent to determining the sun’s distance, since the moon’s is already known.
Another way of measuring the sun’s distance has been “favoured” by Jupiter and his family of satellites. Few would have thought, when Römer first explained the delay which occurs in the eclipse of these moons while Jupiter is further from us than his mean distance, that that explanation would lead up to a determination of the sun’s distance. But so it happened. Römer showed that the delay is not in the recurrence of the eclipses, but in the arrival of the news of these events. From the observed time required by light to traverse the extra distance when Jupiter is nearly at his furthest from us, the time in which light crosses the distance separating us from the sun is deduced; whence, if that distance has been rightly determined, the velocity of light can be inferred. If this velocity is directly measured in any way, and found not to be what had been deduced from the adopted measure of the sun’s distance, the inference is that the sun’s distance has been incorrectly determined. Or, to put the matter in another way, we know exactly how many minutes and seconds light takes in travelling to us from the sun; if, therefore, we can find out how fast light travels we know how far away the sun is.
But who could hope to measure a velocity approaching 200,000 miles in a second? At a first view the task seems hopeless. Wheatstone, however, showed how it might be accomplished, measuring by his method the yet greater velocity of freely conducted electricity. Foucault and Fizeau measured the velocity of light; and recently Cornu has made more exact measurements. Knowing, then, how
