PHOTOGRAPHIC RESEARCHES NEAR THE POLE OF THE HEAVENS. 57 



d n '<l = d' n '1—sm\Jd x—cosAjd y.\ 

 Forming mean equations from these, and remembering that: 



. . (20). 



sin A B 6 = 0, 



we get: 



d l = d' \ -+- cos A n 6 d x, 

 d n = d\n— cos A n 6 d y. 



(21) 



In order to make a further discussion possible, we shall for the pre- 

 sent assume that the motion of the pole is continuous, and capable of being 

 represented by the following series: 



^=Yo-A n e Tl ^A n e2 T2 



CO = Y'o -+- A„ 6 y' z -*- A„ 0' T 



(22) 



2 



• • 



where the y's are constants to be determined. 



Such an assumption seems fully justified, if the exposing shutter 

 employed in making the plates can be attached to the observatory dome, so 

 that the telescope will not be jarred by the necessary operations connected 

 with making the exposures. 



Let us now employ the notation: 



a. e = J (a, e -*- a, e -h . . . -+-A n e), 



A 2 = -i (A, 2 -*- A 2 6 2 -h . . . -*-A n 6 2 ). 



If we then form a pair of mean equations from equations (22) and 

 remember that: 



we get: 



A e = o, 



tfoS = yo-*-V 2 Y 2 



* • 



5 



d "4 —• y'o -*- A o Q2 Ts ~*~ • • • J 



(23) 



Combining these equations with equations (21), we obtain: 



d n x 



Yo <M _^ ^o^Ta 



o 



C0S A„& C03 A n 6 C0S A„6 



) 



^y 



d'o t) A 6 s t' 2 



. . . (24). 



To 



cos b n & coa <l n cos A n 9 



• • • 



Let us now equate the values of d n l and d n f\ given by equations (20) 

 and (22), and eliminate d x and d y by means of equations (24). 



*H3.-Mar. ctp. 57. 17 



