HEAVENS 



51 



Ac' 



Ad' 



Ac 



Ad 



50:26(* — d' sec £ sin 1", 

 50.26 (* — Qc cose sin l", 

 50.26 (t — t )d sees sin l", 

 50.26 (t — t )c cose sin l". 



2. Trail Plates. 



The foregoing investigations contain all that is necessary for the 

 complete reduction of an ordinary polar star-plate. But Professor Donner 

 of Helsingfors and Professor E. C. Pickering of Cambridge, U. S. have 

 suggested the desirability of using polar plates with long star-trails 



for the 



of determinin 



pi 



d arriving at a value of the 



constants of 



d aberration. It will therefore be of 



discuss here the reduction of such plates. Of 



we should 



use 



actual trails, but we would expose the plates in the following way. The 

 telescope being mounted very firmly, and pointed at the pole, we should 

 open the exposing cap for a short time, so that the stars would impress 

 themselves upon the plate. The telescope being left unmoved, a series of 



similar exposures would then be made at intervals 



say, half-an-hour, 



and continued throughout the whole night. After the effects of refraction 

 and aberration have been eliminated by computation, the series of images 

 thus obtained from any star will lie in a circle, provided the telescope has 

 really remained unmoved all night. But if the telescope has moved, the 

 place of the pole on the plate will have described a small curve, the nature 

 of which it is necessary to investigate from the measures on the plate. 

 To do this, let: 



Q\i °^'"°ni De tne sidereal times of the several exposures, the re- 

 maining notation being the same as that already used. 



We shall suppose that the axes on the plate are oriented so that the 

 positive #-axis points nearly in the direction of 0° right ascension at the 





instant of the first exposure made at the time O x . 



Now let us indicate by the subscript n, s quantities that are different 

 for each exposure of each star, and by the subscription s quantities that 

 are different for each star, but not for each exposure. Also put: 



KX ( TC ,)> = assumed approximate values of the right ascension and 



polar distance of any star. 

 Let us also introduce u v s , C,, ?„,,, defined by the equations: 



u s = (ol s ) 



a 



*> 



I 



a 



-n, * 



n,« 



V 



w 



u 



*' 



$H3.~MaT. CTp. 51. 



n,5 



iw 



n*s 





»,), 



. -(8) 



II 



4* 





