THE VALUES OF 



2 ft 



Vtt, 



ft 2 



Jo 



(It. 



And, by means of (23) we may thus obtain the values of A^, A' 2} Ag, etc. 

 transposition, we have 



n 10 A' 10 = A 10 = J ST+ etc. 



269 



Or, by 



}" (25) 



w 7 A' 7 



7(^-1) ^, 77(n*-l) 7 _ 49(^-1) 

 7_a ? 2n 12«2 6» 3 



ne A ' fl = A fl - fcll) G- 19(n'-l) g _ 21(n»--l) / . 1087(n« - j) etc _ 



4w 2 



4% 3 



240n* 



, etc. 



In actual calculation, it is convenient to compute and arrange the quantities in 

 equation (23) thus, — the sum of the quantities in each column being equal to the value 

 of A at the top of it : — 



A 10 

 K. 



A 9 



A 8 



A 7 



A 6 



A 6 



A 4 



A 3 



A 2 



A, 



3 



$* 



1087 „ 

 A. 



240 



45 V 

 J2 K - 



6821 

 3.7.12.120 ' 



311 v 



73 



2.9.120.120 



I5V*-* 



2.7.12.120 





I. 



4 7. 



Hi. 



12 



21 7. 



4 



331 7 



144 ' 



* 7 /. 



72 



605 

 7.12.12.12 



17 I 



^ 



7.12.12.12" 







H. 



7 H. 



2 



4 



25 



81 77 



23 

 1*6* 



127 

 2.7.12.120 " 



^-*- 









G. 



2,0 . 



> 



5 -G. 

 3 



43 r 



la. 



40 



1 _ 



7"! 6 '• 











F. 



1- 



%'■ 



4 



360 



n*-'- 













E. 



IE. 

 D. 



4 

 3 

 2 D - 



a 



4 



la 



12 



C 

 5. 



l |fet 



5! 

 4! 



2 





















.4= a. 



After K- A 10 , the values of /, H, G, etc., are successively 



found by subtracting the 



sum of the quantities in the proper column from the value 



of A n above it. If the 



values (a, b, c, etc.) in the last column are determined with 



extreme accuracy, they 



ifford a ready means of verification of the whole operation, sine 



e 









V 



„-V = 



an + bn 



i + cn 3 + dn 4 + 



+kn 10 . 







