4 Rutherfurd Photographic Measures. 



stars from ^ Cassiopeise, and the difiference of that sum from an 

 adopted mean given at the foot of the fourth eolun)n. In the sixth, 

 seventh, and eighth column are placed the difference of the dis- 

 tances as given in the second and third columns ; the scale correc- 

 tion, which is simply a proportional part of the quantity given 

 in the column "mean minus sum "; and finally the corrected differ- 

 ence, to be used in forming the parallax equations. The latter 

 equations, together with their solutions, are to be found in table Y. 

 (p. 20); and with regard to them I have only to remark that the 

 absolute terms are expressed in units of the second decimal place, 

 equivalent to o".28oi. The parallax coeflScients in the observation 

 equations of table V. are computed by the customary formula;, as 

 follows : — 



Let a, S, be the coordinates of ^ Cassiopeiae for 1872. 



r, O, be the radius vector, and longitude of the sun ; 

 and compute — 



g sin G^ = sin 5 coso, h sin ^=sin 8 sin a, /"sin i^:= A sin {H -\- {) 

 grcosG = sina, hcosH=z — cos 6, fcosF^ — cos a cos s 



then if we put : 



S, = f sin (p 4- F) 



S, = g sin {p -\- G) 



P.^ = — r sin 



P^ = — r cos O 



the parallax coefficient for any one of the equations will be : 



{s,-s:)p, + {s,-s:)p,, 



where 5^3' and S/ refer to the second comparison star of the pair. 

 The corresponding coefficient for the sum of the distances of the 

 two comparison stars of any pair is 



{S,+s:)P,.\-{s,-\-s;)P„ 



which 1 have found sufficiently small to be negligible for all the 

 pairs used in the present research. 



The values of ^'3, S^, P^, P^, are found in table III. (p. 13). 



Before proceeding to discuss the parallax results, as obtained in 

 table v., attention should be called to table IV. A, which throws 

 some light on the question of variation of scale value. The first 

 five columns of this table give for each plate, and for each pair of 

 stars, that fraction of "mean minus sum," from table IV., which 



