CATALOGUE OF POLAR STARS. 291 



We shall have by Taylor's Theorem: 



For Three Equidistant Values of w. 

 ^„ d'rc d"a , d'a 



2 b 



wx + to'^i/ + — m' 3 = — (59) 



o ^ 



3,3 c 



W X + — ic- u A w'2= — 



"Whence 



1 3 1 



z= — VBa b + — cl 



10 ^ 2 3 -■ 



y = — ,[4 6 - 5 a - c] (60) 



1 



2 



= — [3a-3«. + c] 



w" 



J'Vw Four Fquidistant Values of w. 

 -, da d'^a d^a d'^a 



it "^ - "' 3^7 = ^' "7:7 = y. "T^ = 2' we have 



2 6 ^ 24 



2 1 5 



^ov + v3'x-\ w' y + — w* z = — 



3 3 2 



3 , 3 , 9 , c (61) 

 W V + — IC^ X + — w' V + — to* z = — 



2 2 8 3 



8 , 8 , f? 



MU + 2w'x+ — M!'V+ — W''2= — 



3^3 4 



Whence 



« = — r4a-36+— c dl 



w ■- 3 4 



1 rll , 19 , 14 26-1 

 M^ Li2 2 3 3 J 



3 ,1 (62) 



y 



M 



1 Q 



= — [9 a - 12 ^. + 7 c dl 



m' L 2-1 



-^ [(? - 4 c + 6 ^. - 4 a] 



z = 

 w 



