178 Prof. C. Pritchard. On the Capacities of two [May 3, 



centre of the field, that is to say, beyond a field whose diameter 

 exceeds 1400". 



Over and above this question of the accurate measurement of small 

 distances from stars of known co-ordinates scattered about the field, 

 there is the question of the possibility of accurate measurement of 

 considerable distances from the centre of the plate itself. In other 

 words, can a linear measure on a photographic plate be accurately 

 translated into the corresponding angular distance between two stars 

 by simple multiplication by a constant ? In order to investigate this 

 very important question, I had a series of measures made of sixteen 

 stars of the Pleiades from the star (p) Pleiadum, compared with the 

 corresponding heliometer measures, as given by Dr. Elkin in the 

 Yale College publications. These distances extend from 400" to 

 3200". The form which this examination assumed was that proposed 

 by Dr. Gill in the ' Bulletin du Comite International Permanent pour 

 l'Execution Photographique de la Carte du Ciel,' Paris, 1888, in 

 .which the heliometer distance (s) between two given stars is equated 

 to— 



as + bs 2 + cs 3 + &c, 



where (s) is the distance, measured on the plate in inches. This 

 investigation was first applied to the shorter focus mirror, inasmuch 

 as it was expected to indicate sensible discrepancies from an uniform 

 scale. The solution of the equations of condition give the following 

 form for the conversion of the linear distance (s) into angular 

 measure : — 



2577"'0396 s + 0"-4546 s 2 . 



The probable error of the coefficient of s 2 is + 0"-2831, indicating 

 an amount of insecurity which renders this method of investigation 

 somewhat doubtful ; but taking it as it stands, this formula shows 

 that while in a measured distance of half an inch, equivalent to 1200", 

 no measurable error beyond 0""1 is introduced, yet in a measure of 

 2 inches from the centre there is a possible or even probable cor- 

 rection to be made, amounting to nearly two seconds. This 

 seems to indicate the absolute necessity of a rigid investigation 

 of the photographic field of all instruments in which that field is 

 extensive. 



A similar enquiry, referred also to Dr. Elkin's heliometer measures, 

 war. made though on a more restricted field, in the case of the de la 

 Rue mirror, which has already been so extensively used for exact 

 astronomy. In this case the coefficient (b) of the term depending on 

 the square of the linear distance (s) inches, is 



+ 0"-333 ± 0"-202, 



