An observer at a station, A, on the northern part of the earth will see the planet pro jected on the sun as at a, while a southern observer will see it at b. The distance of the sun from Venus being about three times her distance from the earth, it is obvious that the distance ab will be three times the distance AB; and it is a great tage to have the stations A, B, as far as possible, as the interval ab is thus increased and its measurement rendered more accurate.
But how is it measured? For each observer sees only one of the spots, and does not know where the other is; and there are no permanent marks on me sun's surface to guide us. The difficulty is got over in the following way: Each observer notes the ex, et duration of the transit, that is, the time the spot takes to travel from 0 to D, or from F to G. Now as we know the rate of Venus's motion in her orbit, this gives us the lengths of the lines CD and FG in minutes and seconds of arc. Knowing then the angular diameter of the sun ( 32') and the lengths of two chords CD and FG, we can easily, by the properties of the circle, find the distance ab between them. This gives us the angle aAb. In the triangle AVb, then, we know the angle at A and the proportion of the sides AV and Vb, and from that we can find the angle AbV or AbB. Now this is the quantity sought, being the parallax of the sun as seen from two stations on the earth. Whatever the distance AB actually is, the angle is reduced to correspond to a distance equal to the earth's semi-diameter. The parallax deducted by Encke, as above referred to, was only 8.5776% while the parallax corresponding to the other smaller measurement above stated is 8.94% The advantage of this roundabout procedure is that a comparatively large angle (aAb) is measured in order to deduce from it a smaller (AbB), so that any error in the measure ment is diminished in the result.
The transit of 1874 was observed at more than fifty stations, astronomers from all the civilized world taking part in the work. The labor of discussing and comparing the observations has not yet been overtaken, but several partial results have been announced, which still show considerable discrepancy. The chief source of uncertainty arises from the difficulty the observers found in determining the exact moment of "ingress" and "egress" of the planet, owing to the dense atmosphere of the latter rendering the limbs of the two bodies indistinct and distorted. Much was expected from the multitude of
photographic pictures taken, but they have proved a failure. They are said to lack the necessary sharpness, and to be liable to other sources of error. The first partial discus sion of the British observations gave, according to the astronomer royal, a result of millions of miles. A more extended discussion since announced results in 92A millions of miles.
It is hoped that when the transit of 1882 comes, the defects of the photographs, as well as the uncertainty of the time-observations, may be obviated., In the meantime astronomers are turning with greater hope to other methods, especially to observations of Mars, and of some of the minor planets. From observations of Mars made in 1862, the American astronomer Newcomb deduced a distance of 92A millions of miles. The velocity of light, which has been determined by the ingenious optical experiments of Foucault and others, has also been pressed into the service of the problem. The aberra tion of light (q.v.) results from the relation of the velocity of light to that of the earth's motion in her orbit; and from the observed amount of the aberration we are thus able to deduce the earth's velocity. From knowing then the time of the earth's revolu tion, we can find the circumference of her orbit, and hence her distance from the sun. The most careful investigation by this method gives a distance of 93 millions of miles. An ingenious method of observing the parallax of Mars at its opposition, first suggested by the astronomer royal, but carried out by Mr. Gill on the island of Ascension in 1877, promises still more satisfactory results. The essence of the method consists in this, that instead of depending upon two sets of observers at different parts of the earth, one observer and one station are made to suffice. One observation is taken in the evening when the planet is rising, and another in the early morning when it is setting. In the mean time the rotation of the earth has transported the observer 6,000 or 7,000 m. through space, and this forms his base line. Mr. Gill's observations were made by means of the heliometer, the most effective of instruments for such purposes. From such of his observations as had been reduced at the end of 1878, Mr. Gill announces his belief that the sun's distance will prove to be nearer to 93 than to 92 millions of miles.