CATALOGUE OP POLAK STABS. 



24 



The following cases occur in which this method of development is applicable 



Case 



(a) 



(*) 



(O 



(d) 



(e) 



Given 



a 



a 



a 



a 



a 



dt 



da 

 dt 



d*a 

 dt 



d a d' 1 a d z a 



a 



dt 



dt' 



dt 



dec d' 2 a d 3 a 



a 



dt 



dt 1 



dt 



d*u 



dt* 



From 



a 



da 



dt 



rf 8 « 



df 



dt 3 



d*a 

 dt* 



To fin« I 



d ii d-a d*a d* a rf'a 



<// 



«//■• 



dt 



( 



IP 



( 



It 



d-a d»a d*a d* 



a 



d 6 a 



d l 



d I 



dt 



a 



d* a d B a 



dP 



dt 



,, &«-. 



d r ' a d' a 



dt 



dt 



df 



dP 



dP 



> A- 



d*u d 6 a d f 'a d~ a d* a 



dt 



dt 



dt 



dt 



dt 



, &c 



d'a d*u <n n d*a d* u 



dt 



dt 



dP df 



dt 



,, &c> 



and similarly for 



d8 



d 2 8 



dt ' dt- 



■i 



For the application of this method in the computation of ihe differential coeffi- 

 cients of Groombridge 1119 we have the following data, for 1, 8, and 1C years. 



CASE (a). INITIAL FUNCTION 



«. 



1871.0 



1872.0 



1873.0 



1874.0 



1875.0 



187G.0 



1877.0 



1878.0 



1879.0 



h. m. 



7 24 



S. 



9.177 



7 25 23.737 



7 26 38.000 



7 27 51.960 



7 29 



5.631 



7 30 18.994 



7 31 32.052 



7 32 44.804 



7 33 57.218 



Foil w = l. 



A, 



+ 1 14.560 



+ 1 14.263 



+ 1 13.96»; 



+ 1 13.665 



+ 1 13.303 



+ 1 13.058 



+ 1 12.752 



+ 1 12.444 



A* 



297 



297 



301 



302 



°05 



306 



308 



4 



3 



+ .000 



.004 



001 



• K >3 



001 



ii02 



*4 



.004 1 



4- .003 



.002 > 



+ .002 



.001 



+ 



