46 



H. JACOBY, 



and tc the corresponding true coordinates, so far as the effect of refr 

 i is concerned. Also let: 







be the sidereal time when the exposure of the plate took pi 



Then it may be shown in a manner similar to that used in my paper on the 

 Pleiades l ) that the refractions in question can be expressed by the follow- 

 ing formulas: 



7C 







it 



k cot 9 cos (G 



%k [cot 3 9 cos 



2 



1] sin 1 



ti 



1 



2tc 



k z cot 2 9 sin 2 (6 



Ak 



Bk\ 







a) ir sin 1 



k cot <p sin (6 — a) -+- 

 k-x cot 2 9 sin (6 — a) cos (6 — a) sin 1 " 



l 



it 



k* cot 3 9 sin (6 — a) cos (9 



A'tc sin 1 



n 



B't? sin 1 



tf 



where: 



A 



dk 



cot <p COS 



2 



5 



B 



k cot cp cos (0 



k cot 



3 



9 cos 



s 



a), 



A' 



dk 





B 



l 



2 



k cot <p sin (0 



^ cot 9 sin (8 — a) cos (0 



k cot s 9 sin (0 



fc cot 8 <p sin 



(5) 



3 



In these expressions k is the usual refraction number of Bess el, which 

 must, however, be increased by l / 65 part of itself to allow for the difference 

 between the photographic and visual refractions. 



The refraction in right ascension is given in the form: 







a) u sin 1 



f 



j 



because it is to be applied to n m in equation (4), and not to n„ in equa- 



te 



(3). We can easily make the changes which would be needed in these 



formulas 



should wish to employ in them the true instead of the 



:ht ascension. The 



values of the coefficients A. B 



A\ and B\ are contained in the following little table, with the arguments 

 log. cot 9 and {0 



1) Annals, N. Y. Acad, of Sci. Vol. VI. p. 253. 



4>H3.-M»T. CTp. 46. 



6 



