II. — On the Reduction of Stellar Photographs, with Special Ref- 

 erence to the Astro-Photographic Catalogue Plates. 



BY HAROLD JACOBY. 



Read October 14, 1895. 



The following paper has been prepared at the request of Dr. Gill, 

 who asked me to put together the formulae which seemed to me best 

 for the reduction of the Astrophotographic catalogue plates. In so 

 doing I have drawn freely upon the work of others, particularly 

 that of E,ambaut, Turner and Henr3\ I have also had very 

 valuable help from Mr. Finlay, Chief Assistant at the Cape 

 Observatory, especially in the preparation of the tables. The 

 methods here given are suitable for the reduction of any photo- 

 graphic plates, whether taken under the programme of the Perma- 

 nent Committee or not. The only limitations are that the centre 

 of the plate shall be more than 15° from the pole, and the extent 

 of the plate not more than 2° square. 



The fundamental problem with which we have to deal is the 

 transformation of rectangular co-ordinates measured on the plate 

 into the corresponding differences of right ascension and declina- 

 tion upon the sky. For the present I shall assume that the plate 

 is correctly oriented, and that the scale-value is known. We 

 -shall then find the problem under consideration involves only 

 five quantities. If we let : 



a, 5, be the right ascension and declination of the center 



of the plate, 

 a', 8\ be the right ascension and declination of a star, 

 X, y, be the rectangular co-ordinates of the star's image 

 on the plate, x being positive both in the Northern and South- 

 ern hemispheres when the star's right ascension is greater than 

 that of the centre of the plate, and y being positive when the star 

 is nearer than the centre of the plate to the North Pole. 



Now put : 



A a ^ a' — a, A rf = 6' — rf, 



then the five quantities involved are : 



X, y, A a, Ad, 6. 



Annals N. Y. Acad. Sci., IX, April, 1896.— 8 



