CATALOGUE OF POLAR STARS. 293 



Whence 



1 r^ 15 , ,20 15 , 6 In 



s = — \Ga b + — c d + — e f\ 



mL 2 3 4 5 G-'J 



„ 1 r^l' A ^^ -5-1 ^ 33 ^ 27 137 T 



M = — I— -0 -a c + ~ d e + — f\ 



w' L 4 5 9 2 5 180 -1 



v = \[29a-'-^b^,2c-'^d^l3e-'-^fl 

 «5» L 8 8 8 J 



1 rl3" , 242 107 17 -1 



w^t-2 3 2 cJ 



1 r,. ^5, _ So , „ 5 



2/ " 



(66) 



= — pJO a - — 6 + GO c - — (? 4- 16 e - - fl 

 w^ L 2 2 2 *^ J 



z = —[l5b - Qa- 20c + 15d- Ge +f~\ 

 The final equation for a will then become : 



da 1 fP rt ^ , 1 (7' « , , 1 f7^ « ,. . 1 d^ a _, , 1 «' 



« = «„+ ^ t + f- + t^ + t* + ^ '-^ t^ + -^ ^^-^* t\ &c 



2 df- 6 (?<= 24 c?<* 120 (/i'^ 120 dt" 



d'a 1 f?' = a „ 1 d'^n , 1 rf'*« ^ 1 fZ'5„ i <?'6„ 



+ t+ C + <' + t* + t^+ — — — t\ &c 



(f« 2 dt^ 6 </<= 24 f?<^ 120 dt^ 720 <fi!« 



= «o + 



/ da d' a \ l^f(^ d"'tt\ ^ 1 /d^a d" h \ 1 /d*tt d'*a\ 



\dt^dc)^2 \dtr ^ di^ J' '^ 6 \dt^ ^ dt^ ) '^ "^ 2i\d7* '^ J^y^"-' 



and similarly for S. 



As an illustration of the application of this method, we select the values of 

 Yq— 3^4 given on page 267. For intervals of sixteen years from 1875 to 1779 

 we have : 



Epoch. t ^0— Tt Epoch. t r„ — }', 



1811 64 d= + o!(512 



1795 SO e = - 2.577 



1779 96 /= -17.276 



Whence by equations (66) 



»■ 



+ 6 « = -0.00600 +111 J = + 2.98350 + 29 a = - 0.02900 



"4 



-JjS 5= -0.76500 -»/«=+ 0.01740 -i|i6=- 5.87778 



+ 2g0- c = +3.20000 -2gi c = -13.54667 + 62 c = +29.76000 



-J^(Z= -2.29500 + 3^ <?= +10.09800 -^ld= -2SA^bbO 



+ |e = -3.09240 - V- e = +1.3.91580 + 13 e = -33..50100 



-if= + 2.87933 + ^1 J / = -13.14896 - Y / = + 32.39250 



Sum = - 0.07907 Sum = + 0.31907 Sum = - 0.74078 



