CATALOGUE OF POLAR STAKS. 269 



Ai A. A3 Ai Aj Ae 



+ a; -8a; +45x -220a; 



+ a; —7a; +36a; —165a; 



+ x -Gx +28x -120a; +495a: 



4-a; -5a; +21x -84a; +330x 



+ 3. -4a; +15a; -56a; +210a; -792a: 



+ x -3a; +10x -35a; +126a; -462a; 



F(a + x) -2a; +6x -20a; +70a; -252a; +924a; (51) 



-a; +3a; -10a; +35a; -126a; +402a; 



+ a; -4a; +15a; -56a; +210a; -792x 



-X +5a; -21.r +84a; -330a; 



+ x -Gx +28a; -120a; +495a; 



-X +lx -3Gx +165a; 



+ x -Sx +45a; -220a; 



— X + 9a; — 55a; 



+ x -10a; +66a; 



-x +lla; 



+ x -12a; 



— a; 



+ a; 



The total effect e of the error x in changing the values of the difeerential 

 coefficients will be expressed by the equation: 



'= .^.[-'^^-^(+^^)sV--'-^^-5^^^''^^^-'i^o(-'''^)----H 



L_ [-, 6_ 1 (_ 20.) + ^^ (. 70a;) - ^ (- 252.) . . . . &c. 



2.3 



13 



r- 20 a; - - (+ 70 .1;) 4- — (- 252x) - . . . Ac] (52) 



2.3.4.5.6 w'^l 4 ^ 240 -I 



2.3.4.5 

 1 



2.3.4.5.6.7.8.9.10 w" 



r+ 70a; - - (- 252x) + . . . &c.1 



.6.7.8 w8 L 3 J 



["- 252a; - ... &c.1 



r+ 924 a; + . . . &c.l 



2.3.4.5.6.7.8.9.10.11.12 m;>2 L -J 



