and by photography. The heliometer was the instrument specially used for the former purpose; and as, in one of the new methods to be presently described, this is the most effective of all available instruments, a few words as to its construction will not be out of place.
The heliometer, then, is a telescope whose object-glass (that is, the large glass at the end towards the object observed) is divided into two halves along a diameter. When these two halves are exactly together—that is, in the position they had before the glass was divided—of course they show any object to which they may be directed precisely as they would have done before the glass was cut. But if, without separating the straight edges of the two semicircular glasses, one be made to slide along the other, the images formed by the two no longer coincide.9 Thus, if we are looking at the sun we see two overlapping discs, and by continuing to turn the screw or other mechanism which carries our half-circular glass past the other, the disc-images of the sun may be brought entirely clear of each other. Then we have two suns in the same field of view, seemingly in contact, or nearly so. Now, if we have some means of determining how far the movable half-glass has been carried past the other to bring the two discs into apparently exact contact, we have, in point of fact, a measure of the sun’s apparent diameter. We can improve this estimate by carrying back the movable glass till the images coincide again, then further back till they separate the other way and finally are brought into contact on that side. The entire range, from contact on one side to contact on the other side, gives twice the entire angular span of the sun’s diameter; and the half of this is more likely to be the true measure of the diameter, than the range from coincident images to contact either way, simply because instrumental errors are likely to be more evenly distributed over the double motion than over the movement on either side of the central position. The heliometer derived its name—which signifies sun-measurer—from this particular application of the instrument.
It is easily seen how the heliometer was made available in determining the position of Venus at any instant during transit. The observer could note what displacement of the two half-glasses was necessary to bring the black disc of Venus on one image of the sun to the edge of the other image, first touching on the inside and then on the outside. Then, reversing the motion, he could carry her disc to the opposite edge of the other image of the sun, first touching on the inside and then on the outside. Lord Lindsay’s private expedition—one of the most munificent and also one of the most laborious contributions to astronomy ever made—was the only English expedition which employed the heliometer, none of our public observatories possessing such an instrument, and official astronomers being unwilling to ask Government to provide instruments so costly. The Germans, however, and the Russians employed the heliometer very effectively.
Next in order of proximity, for the employment of the direct surveying method, is the planet Mars when he comes into opposition (or on the same line as the earth and sun) in the order
Sun____________________________Earth__________Mars,
at a favourable part of his considerably eccentric orbit. His distance then may be as small as 34½ millions of miles; and we have in his case to make no reduction for the displacement of the background on which his place is to be determined. That background is the star sphere, his place being measured from that of stars near which his apparent path on the heavens carries him; and the stars are so remote that the displacement due to a distance of six or seven thousand miles between two observers on the earth is to all intents and purposes nothing. The entire span of the earth’s orbit round the sun, though amounting to 184 millions of miles, is a mere point as seen from all save ten or twelve stars; how utterly evanescent, then, the span of the earth’s globe—less than the 23,000th part of her orbital range! Thus the entire displacement of Mars due to the distance separating the terrestrial observers comes into effect. So that, in comparing the observation of Mars in a favourable opposition with that of Venus in transit, we may fairly say that, so far as surveying considerations are concerned, the two planets are equally well suited for the astronomer’s purpose. Venus’s less distance of 25 millions of miles is effectively increased to 34⅓ millions by the displacement of the solar background on which we see her when in transit; while Mars’s distance of about 34½ millions of miles remains effectively the same when we measure his displacement from neighbouring fixed stars.
But in many respects Mars is superior to Venus for the purpose of determining the sun’s distance. Venus can only be observed at her nearest when in transit, and transit lasts but a few hours. Mars can be observed night after night for a fortnight or so, during which his distance still remains near enough to the least or opposition distance. Again, Venus being observed on the sun, all the disturbing influences due to the sun’s heat are at work in rendering the observation difficult. The air between us and the sun at such a time is disturbed by undulations due in no small degree to the sun’s action. It is true that we have not, in the case of Mars, any means of substituting time measures or time determinations for measures of position, as we have in Venus’s case, both with Halley’s and Delisle’s methods. But to say the truth, the advantage of substituting these time observations has not proved so great as was expected. Venus’s unfortunate deformity of figure when crossing the sun’s edge renders the determination of the exact moments of her entry on the sun’s face and of her departure from it by no means so trustworthy as astronomers could wish. On the whole, Mars would probably have the advantage even without that point in his favour which has now to be indicated.
Two methods of observing Mars for determining the sun’s distance are available, both of which, as they can be employed in applying one of the new methods, may conveniently be described at this point.
An observer 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