Determination of the Sun's Distance. 127 



sun's disc as a means of determining the sun's distance. 

 The method consisted of observing at two different stations, 

 separated by a considerable arc of latitude, the intervals of 

 time occupied by Venus in passing across the sun's disc. 

 The time occupied would be different to each observer in 

 proportion to their distance apart, indicating that the path 

 of Venus described parallel chords of different lengths ; the 

 difference of times, therefore, would afford a measure of the 

 separation of these two cords, which itself gives the parallax 

 of Venus in terms of the distance between the two observers, 

 and as by Kepler's third law we know that the proportional 

 distances of Venus and the sun are as twenty-eight to 

 seventy-two, all the necessary data for computing the sun's 

 distance can be obtained. 



The practical solution of the problem of course involves 

 the nicest calculations and many mathematical difficulties 

 connected with the elliptical motions of both Venus and the 

 earth. This method is, nevertheless, without doubt the best 

 of any known, but, unfortunately from the rare occurrence 

 of the transits of Venus, ages almost elapse between the 

 opportunities of its application. Since it was first proposed 

 by Halley, in 1725, only two have occurred, namely, in 

 1761, and 1769. The next will take place in 1874, and 

 again in 1882. They generally, not always, occur in pairs. 



The method of determining the sun's distance from the 

 measurement of the parallax of Mars, although not sus- 

 ceptible of quite so high a degree of accuracy as that by 

 the transit of Venus, has, however, the great advantage of 

 being practicable at every opposition of Mars, which occurs 

 about every two years ; it must, however, be mentioned 

 that the oppositions in which Mars approaches nearest to the 

 earth (as in 1862) are much more favourable than the distant 

 oppositions, from the fact of the parallactic angle being 

 larger. 



The method may be thus briefly described : when Mars is 

 in opposition, observers, separated by large arcs of latitude, 

 obtain the differences of declination between it «and certain 

 fixed stars situated near him selected for the purpose ; it is 

 then found that Mars appears in a somewhat different 

 position at the same instant among the stars to the different 

 observers, due to their difference of latitude. The distance 

 between the observing stations being known, and the 

 amount of displacement of Mars being measured, the parallax, 

 and hence the distance, are determinate. 



