of the Rutherfurd Photographs. 237 



For Flates I, II, III and IV, 





Aa 





Ad 



4 



—1 723". 34 





—1856". 74 



5 



— 1220 .23 





+1531 .02 



15 













40 



+1459 -3§ 





—1849 .36 



44 



+ 1948 .13 





+1390 .16 



15 



i28°o7 / 55 // .26 



+: 



>o°i3 / oi // .26 



For Plates V, 



VII, VIII and IX, 









Aa 





J<J 



4 



— 17 25". 40 





— iS56".8i 



5 



— 1219 .75 





+ I53I -17 



15 













40 



+ 1459 -48 





— 1849 -4° 



44 



+ 1948 .19 





+1390 -15 



15 



i28°o7'5 1".75 



"0 

 +2o°i3 / oi // .38 



Aa and Ad are obtained by subtracting the right ascension and 

 declination of Star 15 from those of the five comparison stars. 



The numerical work in the problem before us, namely, to deter- 

 mine the constants of the plates, will be greatly decreased by first 

 assuming an approximate scale-value and then determining how 

 much this is in error. Such an approximate value is furnished 

 by the reduction of Rutherfurd 's photographs of the Pleiades 

 where it was found that 



1 millimetre = 52. "87 



Let us suppose that this scale- value has been applied to the 

 measured coordinates x and y of each of the comparison stars, 

 giving X and F; then the quantities X sec d and Fwill be nearly 

 equal to the corresponding Aa and Ad respectively. The causes 

 of difference are the following : 



a. Transformation Corrections (see below), Refraction, Pre- 

 cession, etc. 



b. Orientation, use of incorrect scale-value, etc. 



c. Errors of observation, both in the measured coordinates and 

 in the meridian places. 



Let us first consider the causes of difference under a ; we shall 

 then determine the orientation, true scale-value etc., by comparing 

 the corrected coordinates with the corresponding values of Aa 



Annals N. Y. Acad. Sci., X, May, 1898—15. 



