1888.] Silver on Glass Mirrors of different Focal Lengths. 179 



and, inasmuch as the measures actually made use of hitherto have 

 never exceeded 0*75 inch from the centre of the field, this correction 

 (admitting its reality) indicates an uncertainty of about 0"*16. 

 In the method employed for parallax determinations with this instru- 

 ment, this source of error, small as it is, is effectually eliminated by 

 the avoidance of all but differential measures. 



IY. The Photographic Capacities of the Two Mirrors in respect of the 

 Faintest Stars impressed on Plates with Exposures of given 

 Duration. 



The method employed was that described in the * Proceedings of the 

 Royal Society,' No. 247 (read May, 1886). It consisted in taking 

 with each of the two mirrors three plates of the Pleiades exposed for 

 5, 30, and 60 minutes respectively. The diameters of a few stars 

 whose magnitude had been well determined by the wedge photo- 

 meter were measured five times on each of the plates, and then by the 

 means indicated in the above-mentioned paper, the following results 

 were obtained : — 



Mirror y^-inch. 

 Exposures of 5, 30, and 60 minutes, respectively, gave — 



5 min. :■ — log mag. required = log 11*14 (mag.) — 0*0204 B. 

 30 min. : — log mag. required = log 13*55 (mag.) — 0*0203 B. 

 60 min. : — log mag. required = log 14*79 (mag.) — 0*0193 B. 



In the above formula log 14*79 indicates the magnitude of the 

 faintest star just beginning to be impressed on the photographic plate 

 during its exposure of 60 minutes. This number and the coefficient 

 of B were obtained in the manner already referred to above, where B 

 is the measured diameter of the star whose magnitude is sought, 

 expressed in seconds of arc. 



In like manner, the magnitude of the faintest star, during an 

 exposure of 30 minutes, was 13*55 magnitude, and during an exposure 

 of 5 minutes, was 11*14 magnitude. 



Mirror -|^-inch. 



A similar investigation applied to this mirror gave the following 

 results after exposures of similar duration : — 



5 min. : — log mag. required = log 11*93 — 0*0215 B. 

 30 min. :— log mag. required = log 13*79 — 0*0186 B. 

 60 min. : — log mag. required = log 15*13 — 0*0197 B. 



From this it appears that the photographic capacity in respect of 

 the faintness of the light impressed is slightly in favour of the shorter 

 VOL, xliv. o 



