I 



PHOTOGRAPHIC RESEARCHES NEAR THE POLE OP THE HEAVENS . 45 



A = W~Wv e = " W - *', e= [bn'j - !eQm, 



tap] ' L * J [pp] 



^ = -"Z^> .Weight of dl = A-*-D, 



*Q = — zrz§f Weight of rfq = A ■+- D, 



dA f = — i 



tap] 



j — [pa] d% -*- [p6] dij h- [p n'J |, 



* 



Weight of <M' = M - Jjg£M, 



*>=— ra IM ^-»-M ii+W!i 



Weight of A, = to] - <g£±flS| 



(aa] -+- [66] 



With regard to the approximate values of \ and t\ to be used in the 

 foregoing calculations, we may remark that when the centre of the plate is 

 within a few seconds of the pole, we can take as approximate values: 



0, i} = 0. 



When, however, the centre of the plate is at a considerable distance 

 from the pole, and the other method of orientation has been used, we 

 can take: 



ri 



tangP 



u sin 1 



" 



where P is the approximate polar distance of the point on the sky corre- 

 sponding to the centre of the plate. For A we should put: 



A = the approximate right ascension of the point toward which the 



axis of x is directed. 



The foregoing considerations hold true only if x and y are the actual 

 coordinates, as measured on the plate, and a, it, the actual right ascension 

 and polar distance of the star as we see it on the sky. These I shall call 

 the apparent a and tc of the star. We must therefore use the apparent pla- 

 ces of the known stars in the equations for determining dl, dt\, da, and dA: 

 and conversely, if we do this, we shall obtain apparent places for the un- 

 known stars. 



Let us therefore now take up the consideration of the refraction. As 

 we have defined a and « to be the apparent coordinates, let us denote by 



I 



$U3. -Mai. ctrp. 45. 5 



