SUN S DISTANCE. 



287 





in introducing more exact ones. It is found by degrees that some 

 alteration must be made in the inferred mean distances of the planets 

 from the Sun; it is found by degrees that this will not suffice, and 

 that the supposition of different degrees of ellipticity and in different 

 directions must be introduced; and at length, by infinite repetitions 

 of the process of trial and error, of which scarcely a trace remains, 

 except in the results, proportions of very considerable accuracy are 

 obtained. In all this there is not the smallest reference to any of the 

 absolute distances. 



In figure 3 is shown the first practical infer- Fi „_ 3 



ence from this knowledge of proportion of dis- 

 til aces, as applied to a transit of Venus. Let 

 Venus V be so exactly between the Sun and the 

 Earth that she can be seen upon the face of the 

 Sun. An observer at A sees her upon the point 

 S, and an observer at B sees her upon the point 

 S'. Suppose the relation between the points S 

 and S' to be such as to admit of record (the 

 mode of making this record will be considered 

 shortly,) and suppose, by means of that record, 

 the angle S A S' is measured. The angle which 

 w r e desire to obtain, in order to measure the 

 Sun's distance is A S' B. Now, the proportion 

 of our measured angle S AS' to the desired an- ^ 

 gle A S' B, is sensibly the same as the propor- ^ 

 tion of S' V to A V, or as 72 : 28, very nearly. | 

 Thus it appears that we measure a large angle ^ 

 in order to infer from it a small one : and this is 

 the circumstance which is the most favorable of ^ 

 all for obtaining an exact result. (If we tried J 

 to use a transit of Mercury in the same way, it <, 

 would be found that the measured angle at A is ® 

 to the required angle at S' in the proportion of ^ 

 4 to 6 nearly, that is, that we measure a small ^ 

 angle in order to infer from it a larger; hence 5 

 the transits of Mercury are inapplicable to the n 

 measure of the Sun's distance.) It is further to 

 be considered that, in this reference of the ap- 

 parent place of Venus to the disk of the Sun, no 

 use is made of stars, and nothing depends on 

 the difficulty of computing refraction, inasmuch 

 as Venus and the Sun are, at the time of the ob- 

 servation, subject to the same refraction. 



This method then appears likely to be excel 

 lent, provided that we possess a practical pro- 



cess for measuring the angle S A S'. 

 be our next consideration. 



The mode of finding this will 



