CATALOGUE OF 1'OLAR STARS. 



liO.'J 



Whence 



5 



u 



v 



X 



y 



1 



w 



[6 a 



15 ,20 15 , 6 



— H c— ~ d + — e 



2 3 4 5 



1 







1 r!17 





4 



6 



1 



w 



3 



1 r!37 



2 



to 



1 



w 



[•20 a 



87 254 

 — a 



5 



9 



33 J 27 137 n 



5 



180 



L s « o ^ J 



8 



8 



r xai * o, 242 107 . 17 i 



3 



2 



6 



05 



85 



6 



£ + 60 c- — tf + 16 c 



2 2 2 



(60) 



z 



1 



w 



[l5 6 



6a 



20 c + 15 d 



6c + 



The final equation for a will then become : 



a 



a« 



« 



c?« 1 # « , 1 d 8 a , 1 a* 4 « , 1 d 8 « . 1 



«„+ — - « + — - — - f 2 + t* + t* + t* + — 



dt 2 a 7 * 2 6 dt % 24 aV 120 </< 5 720 dp 







/*, «&<■. 



cVa 1 d' 2 a . 1 d' s n . 1 c?' 4 « 

 -j- £ -j- £ 2 + t s + 



tf« 2 a** 2 6 (*<■ 24 dt* 



« 4 + — *» + ( s , <fcc. 



120 dp 



720 </*" 



«o+ ( 



a*« a*' a 

 + 



tf« 



a*£ 



+ 



1 



o 



a^« a*' 2 «\ 1 



■ + — T W 2 + 



dt 



dt 2 



6 



rf'rt tf' 8 «\ 1 A/ 4 a d'*u 

 + I t* 4- — ( - + — 



dt* dt 9 J 2i\dt* dt 



-\&c. 



and similarly for S. 



K 







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

 Y4 given on page 267. For intervals of sixteen years from 1875 to 1779 



w r e have: 



Epoch. 



t 



1859 

 1843 

 1827 



16 

 32 



48 



a = - 0*.001 

 b = +0.102 



c= +0.480 



Epoch. 



t 



r„ - r. 



1811 

 179.". 



1779 



64 

 80 

 96 



d 

 e 



f 



+ 0.012 



- 2.577 

 -17.270 



Whence by equations (GQ) 



+ 6 a 



¥-d 



+ I e 



hf 



Sum 



0.00600 

 0.76500 



5 



a 



$. 



+ iji&= + 2.98350 



+ 0.01740 



0.07907 



Sum 



+ 0.31907 



+ 29 a 



-Aftlft 



0.02900 



5.87778 



+ 3.20000 



-z§±c = 



: - 13.54067 



+ 02 c = 



= + 29.76000 



-2.29500 



+ *$ d= 



= + 10.09800 



~a|irf= 



- 23.48650 



- 3.09240 



- V- e = 



: +13.91580 



+ 13 = 



: -33.50100 



+2.87933 



+m/= 



: -13.14896 



-v/= 



= + 32.39250 



Sum 



0.74078 



