W. Harkness — Magnitude of the Solar System. 235 



transits of Yenus in 1761 and 1769, from which our first accu- 

 rate knowledge of the sun's distance was obtained. 



Those who are not familiar with practical astronomy may 

 wonder why the solar parallax can be got from Mars and 

 Yenus, but not from Mercury, or the sun itself. The explana- 

 tion depends on two facts. Firstly, the nearest approach of 

 these bodies to the earth is for Mars 33,874,000 miles, for 

 Yenus 23.651,000 miles, for Mercury 47,935,000 miles and for 

 the sun 91,239,000 miles. Consequently, for us Mars and 

 Yenus have very much larger parallaxes than Mercury or the 

 sun, and of course the larger the parallax the easier it is to 

 measure. Secondly, even the largest of these parallaxes must 

 be determined within far less than one-tenth of a second of the 

 truth, and while that degree of accuracy is possible in measure- 

 ing short arcs, it is quite unattainable in long ones. Hence 

 one of the most essential conditions for the successful measure- 

 ment of parallaxes is that we shall be able to compare the place 

 of the near body with that of a more distant one situated in 

 the same region of the sky. In the case of Mars that can 

 always be done by making use of a neighboring star, but when 

 Yenus is near the earth she is also so close to the sun that stars 

 are not available, and consequently her parallax can be satis- 

 factorily measured only when her position can be accurately 

 referred to that of the sun, or in other words, only during her 

 transits across the sun's disk. But even when the two bodies 

 to be compared are sufficiently near each other, we are still 

 embarrassed by the fact that it is more difficult to measure the 

 distance between the limb of a planet and a star or the limb of 

 the sun than it is to measure the distance between two stars, 

 and since the discovery of so many asteroids, that circumstance 

 has led to their use for determinations of the solar parallax. 

 Some of these bodies approach within 75,230,000 miles of the 

 earth's orbit, and as they look precisely like stars, the increased 

 accuracy of pointing on them fully makes up for their greater 

 distance, as compared with Mars or Yenus. 



After the Copernican system of the world and the Newtonian 

 theory of gravitation were accepted it soon became evident 

 that trigonometrical measurements of the solar parallax might 

 be supplemented by determinations based on the theory of 

 gravitation, and the first attempts in that direction were made 

 by Machin in 1729 and T. Mayer in 1753. The measurement 

 of the velocity of light between points on the earth's surface, 

 first effected by Fizeau in 1849, opened up still other possibili- 

 ties, and thus for determining the solar parallax we now have 

 at our command no less than three entirely distinct classes of 

 methods which are known respectively as the trigonometrical, 

 the gravitational and the photo-tachymetrical. We have 



