202 PROCEEDINGS OF THE AMERICAN ACADEMY 



Hence if SS' does not exceed 120° the value of c?/ -f" ^^ cannot 

 be so great as 9 ditg. Adding to this the value of dB, fiona equation 

 (39), we find th;it, under the circumstances specified above, the total 

 variation of the sum of the angles ZS'S and PSS' cannot be so great 

 as 10 djts. But it is not possible tliat the value of the solar parallax 

 now generally adopted can be in error by so much as ()".2, and there- 

 fore the value of 10 d;ts cannot be so great as 2" and will probably be 

 less than 1". 



Referrino^ to the fijjure, it is evident that 



ZS'V + PSV = ZS'S + PSS' or 



|3 4- w = ZS'S + PSS' (44) 



As the angle ^ must be obtained from measurements made upon a 

 photograph, it is not probable that it can be depended upon to within 

 5". It has just been shown that the right-hand member of (44) will 

 not be vitiated so much as 2" by any possible error in the adopted 

 value of the solar parallax. It therefore follows that the left-hand 

 member of (44) may be regarded as constant, within the limits of 

 eri'or of observation, and thus it appears that 



— d^ = dco (45) 



In the triangle ZS'V we have 



o 



tan 1 (^ -f ;/) = cot ^{A's^ A',) 



(46) 



from which ^ and y are derived. In the same triangle we also have 

 the relations 



cos Q = cos ^'i, cos (^'s -\- sin ^'y sin ^, cos (A's ~ A' J) ) 



[ (47) 

 sin (A's ~ A'y) cot ^ = sin i^'j cot ^y — cos (A's ^ A'y) cos ^'s ) 



Considering all the parts as variable, differentiating and reducing, 

 we find 



dQ =z sin ^y sin yd(A's ~ A'y) -4- cos yd^'y -\- cos ^d^g 



— smQd^=sin^'y cos y d(A's r^ A'y) — sin y c? ^^ -)- cos p sin ^ djs 



