The irregularities of the moon and of Mars have been studied out and calculated on the theory of interplanetary attraction modifying the attraction of the sun. Though the results vary somewhat, yet they all tend in the same direction. Leverrier found 91,759,000 miles; Hansen, the Dane, found 91,659,000 miles; Airey, the Astronomer-Royal of England, whose earlier opinion of Encke's estimate we quoted above, has changed his opinion, and now proposes 91,400,000 miles.
A fact in practical optics, calculated to affect some observations rather seriously, has been discovered within the last few years. It is this: When a white body is viewed on a dark ground, its size is exaggerated by some illusion of our vision; and, on the contrary, a dark body seen on a bright ground appears smaller than it would were the ground of a dark color, differing from that of the body only as much as is required to render them distinguishable. Now, in the transit, a dark body is seen on an intensely bright ground. It becomes necessary, therefore, to bring in a correction which will compensate for the error arising from this optical illusion. This has been done by Stone, who studied out the whole matter, arrived at certain modes of correction, applied them to Encke's calculation, and maintains that the true result of the observations of 1761 and 1769 should be 91,730,000 miles.
Thus all seem to agree that the sun's distance must be less than 92,000,000 miles, and that Encke's [pg 156] estimate was too great by 3 or 4 per cent.
This is the stage at which our astronomers now take up the question, and aim to obtain a yet more definite and precise result. Will they succeed? They are full of confidence now; what they will say after their observations we may know a year hence.
Some of our readers may like to know what is the course followed in making the observations and in calculating the results. We will give a slight account of the chief points, sufficiently detailed to enable one with an ordinary knowledge of trigonometry to understand how the conclusion is reached.
The astronomers will follow two methods, known as those of Halley and of Delisle. They each require two suitable stations, so far apart on the surface of the earth as to give a satisfactory base-line. In fact, the further apart, the better, all things else being equal. For Halley's method, the two stations lie as nearly north and south as may be. For Delisle's, they lie east and west.
Let us suppose two such stations to be chosen on or nearly on the same meridian of longitude, and 6,000 miles apart. From each of these stations the planet is seen to traverse the disk of the sun, like a dark spot moving steadily across an illuminated circular dial-plate. The lines as seen from stations so far apart are sensibly different. What the observers first seek to know is the apparent distance between these lines, the angle they form, when seen from the earth. Were both visible at once from the same station, through the same telescope, it would not be difficult for a skilful observer to measure the angle directly. But at each station only one line is seen, if, indeed, we may properly give that name to the course of the dark spot that passes on and leaves no trace behind. Each observer must determine correctly the position of his line on the face of the sun, in order that it may be afterwards compared with the other line similarly determined at the other, and the apparent distance between them is then determined by calculation.
How to determine the true position of such a line is the delicate and difficult task. One mode is to take the measurements in two directions on the face of the sun, northward and eastward, from the position of the planet to the edge of the solar disk. This must be done for a number of positions which the planet occupies successively as it moves onward. But such measurements are very hard to be obtained with the desired precision. The edge of the sun, viewed in a large telescope, appears always tremulous, on account of the action of solar heat on our own terrestrial atmosphere. The better and larger the telescope, and the brighter the day, the greater and the more embarrassing does this tremulousness appear. Such measurements are difficult, and are open to too much uncertainty.
There is another mode, which, if successfully used, is far more accurate. The lines or paths which the planet, viewed from the observatories, is seen to follow are chords across a circle—largest when they pass through the sun's centre and become diameters, smaller as their course is more distant from the sun's centre. Being both due to the motion of the same body moving at what we may hold to be a uniform velocity, their lengths must [pg 157] be proportional to the times required for tracing them. Being chords, a knowledge of their relative lengths determines with accuracy their position on the circular disk of the sun, and consequently their distance apart. Hence the importance of catching, with the utmost exactness, the beginning and the ending of the transit. The first exterior contact is noted when the circular edge of Venus just touches the circular edge of the sun; then the first interior contact when the entire little, dark circle of Venus is just fully on the sun. Midway between the two, the centre of Venus was just on the edge of the sun. Similarly, the second interior contact and the second exterior contact, if accurately and successfully observed, will show the instant of time when the centre of Venus passed off from the sun's surface. It was, as we saw, in making these delicate observations, that the observers of 1761 and 1769 failed, to a great extent, on account of the mysterious appearance of the black band, of which we gave an account. Will this embarrassing phenomenon again make its appearance next December? If it be due, as some think, to an aberration of sphericity in the lenses of the instruments, it may not be seen. For our telescopes are far more perfect than those of 1769. If it is due, as others maintain, to an interference of light in the observation, a more delicate manipulation of the instrument may, it is hoped, avoid it. If it is due to some optical illusion in our own eye, it will, of course, appear again, and must be grappled with. The observers now being trained at Greenwich, in preparation for the grand day, have a facsimile of the sun and Venus, which are made to move in such manner as to give as exact a representation of the transit as is possible; and they practise observations on this artificial transit. It is said that even in this fac-simile the black band has shown itself, and that one important lesson now being learned is how to judge of the instant of contact, despite of this obstacle.
There is, however, a still better safeguard—the use of photography. The transit will record itself more minutely and more accurately than any ordinary observations for measurement could do. Various plans will be used. One proposed is to have one hundred and eighty prepared and highly sensitive plates along the circumference of a suitable wheel made to revolve regularly by clock-work. During three minutes, these plates come, one every second, successively into position to receive and record the images of the transit, as the planet for those three minutes is entering on the sun. Other plates, at stated and accurately measured intervals of time, will similarly record its regular progress across the sun; and another wheel, with one hundred and eighty other plates, will record the successive changes each second for the three minutes occupied by its exit over the sun's border. These are all, of course, negatives on glass. From them any number of impressions can be taken, in the usual way, for general distribution among the scientists. In order that such impressions may still serve for the finest measurements, despite of any variations of expansion, contraction, or warping which the atmospheric changes may produce, a system of fine, spider-web lines is placed inside the telescope, producing on the photograph itself a network of fine lines, some running north and south, others crossing them east [pg 158] and west. These lines are at equal distances apart, and serve admirably for measuring the position of the planet on the solar face. If the photographic sheet should become quite distorted, these lines would show it; for they would of course follow the distortion, and yet, after that distortion, they would still guide us to accurate measurements. It is hoped that this means and the many other photographic devices to be used will secure a degree of accuracy far beyond what Halley anticipated and would have been satisfied with.