SUN S DISTANCE. 



285 



tronomy, to give the smallest ehance of an accurate re- 

 sult. A third reason is, that.upon this measure depends 

 every measure in astronomy beyond the Moon; the dis- 

 tance and dimensions of the Hun and every planet and 

 satellite and the distances of those stars whose paral- 

 laxes are approximately known. 



The received measure of the Sun's distance depends 

 on the transits of Venus of 1761 and 1769, hut mainly 

 on the latter. Very careful discussions of these will be 

 found in the two books published by Encke, and in a 

 memoir of great value by Don Joachim Ferrers, printed 

 in our own memoirs. On examining these it will be found 

 that, though there is very close accordance in the results 

 obtained by the different investigators and from the 

 different transits, yet all investigators have expressed 

 their doubts upon those results. In the transit of 1761 

 the result depended almost entirely upon an accurate 

 knowledge of the differences of longitude of very dis- 

 tant stations, which are undoubtedly subject to great 

 uncertainty. In the transit of 1769 it happened that 

 the result depended almost entirely upon the observa- 

 tions made by Father Hell at Wardhoe; and to these 

 great suspicion has attached, many astronomers having, 

 without hesitation, designated them' as forgeries. It is 

 evidently desirable to repeat the practical investigation 

 when opportunity shall present itself. 



Figl. 



I 



It is desirable, for clearness, to begin with a reference *> 



to the simplest operation for measuring distance by 

 parallax; as applied, for instance, to the Moon. In figure 

 1, let A and B be two observatories on the same meri- 

 dian, and at A let the star C be observed to touch the 

 moon's limb, and at B let the star D be observed to 

 touch the limb. (It will readily be understood that it 

 is not essential that the observatories should be on the 

 same meridian, if, as is in fact true, the Moon's appa- 

 rent change of place can be exactly computed; nor is 

 it necessary that the star touch the limb, if its angular 

 distance can be very exactly measured.) After commu- 

 nication of the observations, the observer at A can mea- 

 sure the angle CAD. This angle differs from A M B 

 by the angle A D B; but such is the distance of the 

 stars that the angle A D B is in every case unmeasurably 

 small; and A M B, therefore, is to be taken as equal to 

 CAD. Now, the dimensions of the Earth being known, 

 the length and direction of the line A B will be known, 

 and the directions of AM, B M, are known; and there- 

 fore the length of A M, B M, or of any other line drawn 

 from M to any other part of the Earth is easily found. 

 A small error in the angle at M — that is, in the angle 

 C A D — will produce a great error in the result for A M or 

 B M. With this caution the problem is completely solved. 



