ON ASTRONOMY. 117 



of the moon from some star in the vicinity. This method is applicable 

 to the moon, to Venus in conjunction, and to Mars in opposition. We 

 shall again have occasion to refer to it. The strict mathematical 

 treatment of the subject is quite elementary, but, to avoid tedious- 

 ness, I shall omit further reference to it. 



The moon's mean distance from the earth is found, by measure- 

 ments of this kind, to be very nearly 240,000 miles. Herschel gives, 

 more exactly, 237,000. 



But the great problem is, to determine the distance of the sun from 

 the earth. This, which gives the means of expressing the distance of 

 all the planets in miles, the British Astronomer Royal pronounces to 

 be the grandest problem in astronomy. It is solved by two different 

 methods. One is by observations on the planet Mars in opposition, 

 when it is, of course, nearest to the earth ; or on the planet Venus 

 when in conjunction, and also nearest to the earth. The other is by 

 the transits of Venus across the sun's disc, 



I have already stated that the relative distances of all the planets 

 from the sun have been known, with considerable accuracy, since the 

 time of Kepler. It only remains to find the absolute distance of one, 

 and then, as the periodic times are known with great precision, 

 Kepler's Third Law will furnish all the other distances. 



The semi-diameter of the earth, seen from the sun, subtends an 

 angle of a little more than 8^", (8. "6.) This is the sun's horizontal 

 parallax. It reduces the earth, as seen from the sun, to less than 

 one-half of the apparent diameter of Jupiter, as seen from the earth. 

 To appreciate the delicacy of this problem, it must be borne in mind 

 that an error of one second of arc in the parallax involves an error 

 of about 12,000,000 of miles in the distance of the sun. Moreover, 

 one second of arc is an extremely small quantity. None but the most 

 perfect instruments can pretend to measure it directly. The j-qVo 

 part of an inch, as any one will perceive, is an extremely small quan- 

 tity to deal with. But a circle must have nearly 18 feet radius in 

 order that 1" may occupy the space of j oVir P<'^rt of an inch. Kepler 

 found reason to reduce the solar parallax from 3', as given by Ptolemy, 

 to 49", which necessarily placed the sun at nearly four times the dis- 

 tance assigned by his great predecessor. And yet Kepler's measure 

 was only one-sixth part of the true distance. 



To settle this question, or at least with the hope of getting a nearer 

 approximation, tlie French Academy, in 1672, sent Richer to Cayenne, 

 in South America, to mnke observations on the parallax of Mars in 

 opposition, while Cassini made contemporaneous observations at Paris. 

 by computation based on these observations the sun's parallax was 

 reduced to 9". 5 as the probable value, which removed the sun to five 

 times the distance adopted by Ke[)ler. 



Flamsteed compared his own observations on Mars with those of 

 Richer, and deduced 10". With the hope of obtaining still nearer 

 results, Halley visited the island of St. Helena to observe the transit 

 of the planet Mercury across the sun's disc in 1677, October 28, but 

 the result was not satisfactory. He was inclined to adopt 15" as the 

 true value. 



The celebrated astronomical expedition of La Caille to the Cape 

 of Good Hope, in 1750, had for one of its objects to observe the 



