ON THE MAGNITUDE OF THE SOLAR SYSTEM. 97 



the sun's disk, at St. Helena, aud in 1681 J. D. Cassini and Picard 

 observed Venus when she was on the same parallel with the sun, but 

 although the observations of Venus gave better results than those of 

 Mercury, neither of them was conclusive, and we now know that such 

 methods are inaccurate even with the powerful instruments of the pres- 

 ent day. Nevertheless Halley's attempt by means of the transit of 

 Mercury ultimately bore fruit in the shape of his celebrated paper of 

 1710, wherein he showed the peculiar advantages of transits of Venus 

 for determining the solar parallax. The idea of utilizing such tran- 

 sits for this purpose seems to have been vaguely conceived by James 

 Gregory, or perhaps even by Horrocks, but Halley was the first to 

 work it out completely, and long after his death his paper was mainly 

 instrumental in inducing the Governments of Europe to undertake the 

 observations of the transits of Venus in 1761 and 1769, from which our 

 first accurate 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 Venus, but not from 

 ]\Iercury or the sun itself. The explanation depends upon two facts. 

 Firstly, the nearest approach of these bodies to the earth is for Mars 

 33,874,000 miles, for Venus 23,654,000 miles, for Mercury 47,935,000 

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

 Venus have very nuich larger jjarallaxes 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 accu- 

 racy is possible in measuring short arcs, it is quite unattainable in long 

 ones. Hence, one of the most essential conditions for the successful 

 measurement of parallaxes is that we shall be able to comj^are 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 Venus is near the earth 

 slie is also so close to the sun that stars are not available, and conse- 

 quently her parallax can be satisfactorily 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 comi>ared are sufficiently near each other, we are still 

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

 tance 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 dis- 

 covery of so many asteroids that circumstance has led to their use 

 for the determination 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 uj) for their greater distance as compared with Mars or Venus. 



After the Oopernican system of the world and the Newtonian theory 

 of gravitation were accepted it soon became evident that trigouomet- 

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