OF ARTS AND SCIENCES. 193 



collodion side of the plate being nearest the observer) a motion of the 

 radius vector iu the opposite direction to that of tiie hands of a watch 

 corresponding to increasing angles. Then the distance from tlie origin 

 of co-ordinates to the sun's limb is measured at every thirty degrees, 

 throughout the whole circumference ; an<l the distances and angles to 

 the centre of Venus, and to the centre of the plate, are also measured. 

 Owing to the effect of refraction, the outline of the sun's image will 

 not be circular, but may, with sufficient accuracy, be assumed to be 

 an ellipse whose minor axis coincides with the vertical circle passing 

 through the sun's centre. To find the position of the image of this 

 vertical circle upon the photographic plate, we refer to Fig. 4 ; and 

 remark that, owing to the equality of the angles of incidence and re- 

 flection, S^M = S'^M, vM = v'M, and the angle S^My is equal to 

 the angle S'^i^My'. Hence t^'S^S'ju = ^^S'^v', and ZS'^v' = ZS'^S^ 

 -\- S^S'^r' = ZS'*S^ -|- ZS^S'^. But ZS'^ is the direction of the 

 plumb line upon the plate, and S'^u' is the semi-minor axis of the 

 elliptical image of the sun. To find the value of the angle ZS'j^w' 

 we require the zenith distance and azimuth of the true sun, which 

 are given by the formulae (8) ; the necessary data being, the exact 

 instant at which the picture was taken, the right ascension and polar 

 distance of the sun, and the latitude of the place of observation. 



cot As 

 tan JU = ■ 



cos tg 



tan fg cos }f 



tan As = ^ TTT 



sin ((^ — Ji) 



tan ^a 



tan {(p — M) 

 cos Ag 



(8) 



The zenith distance, ^"s, and azimiith A"g, of the reflected image 

 of the apparent sun, are found by methods explained in a subsequent 

 part of this paper. Then, in the spherical triangle ZS^S'^^, the angle 

 S*ZS'« is equal to Ag ~ A"s, ZS'» = C"«, and ZS, = Lg — r -\- 7t', 

 where r and n' are the refraction, and parallax in altitude. Whence, 

 putting the angle ZS>' = 180° — 0, 



Thus the anjrle upon the photographic plate, between the fixed line 

 of reference and the major axis of the image of the apparent sun, will 



VOL. XII. (n. S. IV.) 13 



