296 EXAMINATION OF SOME OF MR WRIGHT'S CALCULATIONS. 



[The following is a specimen of the mode of testing the correctness 

 of the results of the calculations.] 



Take 6V for //, = '80. 



0735623529 '1689846154 



80 65 



0588498823,2 8449230770 



10 139076924 



323 ) 10-9840000010 

 -0340061919,5 

 0588498823,2 



6V 0248436903,7" 

 Next for p. = '81. 



0837131460 '1834118254 



18 65 



6697051680 9170591270 



83713146 11004709524 



0678076482,6 323 ) 11-921768651,0 



-0369095004,7 ^036909500,47 



0308981477,9 



Since G w 4 , 6V 6' 10 C , &c. are the respective successive differential co- 

 efficients of a function, each multiplied by a constant, and since 6 10 4 is of 

 six dimensions in //, and the coefficient of the highest power of /j. in each of 

 them is 1 ; it is clear that the coefficients of the successive terms in the 

 expansion of G w * + SGV in powers of Sp. will be the same as those of a 

 binomial raised to the sixth power. 



Thus GV + S 6V = GV + 6 GV . S M + 1 5 6 10 6 . V 



+ 206 I0 7 . 8^+ 156V- S^ + 66V. V + #S V. 

 where G=p- and = 1. 



Now take S/A successively ='01 and '01 and p. = '80. 



GV -0248436903,7 6^.8^ 57214811,1 



ISGV.S/r 3251739,9 20G w \8 fJ c > 77136,8 



1 5 GV . 8/* 4 881,0 6 GV V _ 4,8 



" 



_ 



0251689524,6 "57291952,7 



57291952,7 



. = -81, GV = -0308981477,3 

 . = -79, g m 4 = -0194397571,9 



