196 



PROCEEDINGS OF THE AMERICAN ACADEMY 



line of the original system of polar co-ordiuates ; we get for the image 

 of the centre of the apparent sun, 



3in e — B" sin s" "i 



JOS e — i?" cos s" ) 



2/ = i? sin e — 

 X = R cos i 



and for the image of the centre of the apparent Venus 

 y = B' sin £' — B" sin s" 

 x' = R' cos e' — R" cos e" 



(18) 



(19) 



Let it be assumed that when the picture was taken ^^ and A^ were 

 the zenith distance and azimuth of the centre of the plate, as seen 

 from the second principal point of the ol)jective ; and that i^was the 

 reduced distance between the latter point and the sensitive surface of 

 the plate, or in other words, 



F=D-\- E" — T (20) 



as given by equation (2). Further, let the angles subtended at the 

 second principal point of the objective by the co-ordinates, _v, x,y', a;', 

 of the equations (18) and (li)) be, respectively, d'Qg-, 5A> 5^,-, 8Ay. 

 Then, as the plate was perpendicular to, and its centre coincided 

 with, the optical axis of the objective, 



i? sin e — R" sin e" 



tau ou = 



tan bAo = 



tan 8^v = 



tan dAi, = 



F 



(21) 



Denoting by C"s^ ^"s, C'V, A"y, the apparent zenith distances and 

 azimuths of the reflected images of the sun and Venus, as seen from 

 the second principal point of the objective, we now have 



A", = A + ^^* 



A"y = ^0 + ^^y J 



(22) 



