SUN S niSTANCK FROM THK KAKTH. 5 



and B near the north. The distance BV is equal to the dis- 

 tance AV without sensible error. So likewise Va --=^ Vb. 

 The triangle BVA is similar to bVa. Therefore : — 



BV : Vb ^ AB : ab 



But BV : Vb ^ 7 : 18 

 And AB is known (say) 6S60 miles. Therefore : — 

 7 : 18 —- 6860 : Answer, 17,640 miles 



on the sun's surface; therefore, ab is 17,640 miles, whatever 

 be the distance of the sun from the Karth. 



These two apparent paths, then, are two parallel chords of 

 a circle whose angular diameter can be observed ; and they 

 are 17,640 miles apart. The difference in their lengths will 

 be as the difference in the times of transit and will be the 

 same number of miles whatever assumption of miles be made 

 as to the distance of the sun. But as in the case of a larger 

 assumed diameter of the sun the paths described are longer than 

 in the case of a less assumed diameter of the sun, this difference 

 will be a smaller part of the whole time in the former case than in 

 the latter. Let us assume for example that the distance is 108 

 millions of miles and the diameter of the sun one million ; then 

 will the difference in the lengths of the apparent paths l)e one 

 fraction of the whole time of transit ; — say one-thirtieth part. 

 Again, let us assume that the distance of the sun is 54 millions 

 of miles and his diameter half a million of miles. The difference 

 of duration will then be another fraction of the whole time of 

 transit, say one-fifteenth. In point of fact, in 1769 the differ- 

 ence in the times of transit, owing to the difference of latitude, 

 was about twelve minutes — a little more than one-thirtieth of 

 the whole duration. It will be seen that by thus comparing 

 observation with assumption an inference can be drawn as to 

 the sun's distance, and that the true distance is somewhere 

 between 54 millions of miles and 108 millions of miles, and 

 that a true assumption would be nearer to 108 millions of 

 miles than to 54 millions. 



