Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/866

While the shape of the earth s orbit and the position of its centre (whose longitude=long, of perih. + 180) thus undergo continual alteration, her mean distance from the sun remains appreciably constant. This we know from the length of the year, which certainly has not changed ten seconds in length since the time of the Chaldean determination of that element.

There are various ways of determining the sun s distance from the earth in terms of the earth s semidiameter. The distance of a planet from the sun may likewise be obtained if we can find the means of measuring its distance from the earth at any epoch, for the geocentric positions of the sun and the planet being known from the theory of their motions, the radius vector of the orbit, or planet s distance from the sun at that epoch, may be found by a simple trigonometrical computation. To determine the distance of a planet from the earth, it might seem only necessary to determine its horizontal parallax ; but in general the parallaxes of the planets are quantities by far too small to be directly observed. That of Mara, however, becomes very appreciable in particular circumstances, that is to say, when Mars is in opposition with the sun, and at the same time near the perihelion of his orbit. Thus, in the year 1751, on the 6th of October, that planet, being near his opposition, was observed at the same instant of time by Lacaille at the Cape of Good Hope, and by Wargentin at Stockholm j and the horizontal parallax deduced from the two observations, was found to amount to 2 4" 6, corresponding to a solar parallax of 9" 4.

This method requires that observations should be made from opposite sides of the earth; but Flamsteed long ago pointed out that the distance of Mars might be determined by observing how much the planet s place is shifted by the diurnal rotation of the earth. Both methods have been employed very successfully in modern times. Stone, of Greenwich, by combining the two methods, discussing obser vations of Mars at the opposition of 1862, made (1), at Greenwich, (2), at Greenwich and Cape Town, and (3), at Greenwich and Williamstown, deduced a solar parallax of 8" "9 4 3. Winnecke, from the discussion of the same opposition as observed at Poulkowa and Cape Town, deduced the solar parallax 8" 964. Professor Newcomb of Washington, U.S., deduced the value 8" -855.

A more accurate method of determining the sun s distance, and thence the dimensions of the planetary orbits, is afforded, though rarely, by the transits of Venus over the sun s disk. When Venus is at her inferior conjunction, and at the same time very near either node, her body will be projected on the disk of the sun; and through the effect of her proper motion, combined with that of the earth, she will appear as a dark spot passing over the disk, and describing a chord which will be seen under different aspects by spectators placed at different points on the earth, because, by reason of the parallax, they refer the planet to different points on the solar disk. The position of the spectator not only occasions a difference in the apparent path described by the planet, but has also a very sensible influence on the duration of the transit, in consequence of which the parallaxes both of Venus and the sun can be determined with great exactness. In order to illustrate this, let E (fig. 33) represent the earth, V Venus, and S the sun. An observer placed at E, near the north pole of the earth, would see Venus projected on the sun s disk at v, and she would appear to describe the line Ivm. An observer placed at E , near the south pole, would see the planet at v, and she would appear to describe the chord I v m. This is a necessary result of the difference of the parallaxes of Venus and the sun; and as the chords lv } I v differ in length according as they are more or less remote from the centre of the disk, the duration of the transit will be longer or shorter according to the situation of the observer and the geocentric latitude of the planet. If by reason of the relative parallax the time of a transit is longer than the true time in one hemisphere, it will be shorter in the other ; and hence the difference of the times (which may be observed with great accuracy) at places having very different latitudes may serve to determine the relative parallax, or the difference between the parallax of Venus and that of the sun. But the parallaxes are reciprocally proportional to the distances ; and the ratio of the distances being known, therefore the ratio of the parallaxes is also known ; and having thus the ratio and the difference of the two parallaxes, it is easy to compute the separate amount of each.

Fig. 33.—Diagram illustrating Transit of Venus.

This particular application of the transits of Venus to the determination of the sun s distance was first pointed out by Dr Halley, when he announced the transit of 1761. The transit of Venus in 1769 was observed in many different parts of the world. The result of the whole of the observations led to the conclusion, that the parallax of the sun is included within the limits 8" - 5 and 8" 7. The mean 8"*6 was adopted by Delambre and Lalande ; and later the value 8" 5776 was deduced by Encke from a careful re-examination of all the observations made in 1761 and 1769. But several methods have been since applied to the determination of the solar parallax, with results which appear to agree in indicating a larger value for the parallax, or in other words, a smaller value for the sun s distance, than had been deduced from the transits of 1761 and 1769.

One of these depends on the moon s motions, and was first indicated by Laplace towards the close of the last century. Since the moon s distance from the earth, though small compared with the sun s, bears yet a measurable ratio thereto, it follows that there is not a perfect symmetry between the perturbations produced by the sun when the moon is passing from third to first quarter, and from first to third. The effect of this circumstance is recognisable in the lunar motions, which are affected by a minute variation arising from this cause, and called the Parallactic Inequality. It amounts at the maximum to about 2 ; and as it depends on the proportion of the sun s distance to the moon s known distance, its amount supplies a means of determining the solar parallax. In 1854 Hansen announced, in a letter addressed to the astronomer royal, that this method, applied to his new tables of the lunar motions, gives a parallax of 8" 9159.