no CARPMAEL ON THK DETERMINATION IN TRRMS. ETC. 



wheu m = 4 



<^' 





n 

 when m = 3 



^C-./^.,.)=$|^^^^0 + 2^^/. ^S-) 



;• 



o 9 



( 



'r 1 /^ -iir 



^ 54 >/ 2 77 180. n v/ 2 t 



when OT := 2 



when w = 1 



1 



when TO ^ 



^ 60. «n/ 2;r • * •■• j 



(w.,...,=^'|:o.v^/"^*) + .^- = >-'fei)-...| 



r 3 



9>(^s/n,m,.)=i+ y^ J/ . ^%/;-__L,.(r_ 1) f ' ' " - I 



when m = — 1 



when »» = — 2 



.?>(^^/»,n,,n)=-^^ " ' ^1 { 1 _ A (3 r' - 10 r + .5) _ ... { 



The values here found for tp (^ '^"' ™' ") when m = 1, 0, — 1, and — 2, agree with 

 those found by Laplace and Cauchy. Laplace did not determine the value when m = 2, 

 3 or 4, and there are numerical errors in the results given by Cauchy in these three cases ; 

 but if these errors be corrected, his results are brought into agreement with those here 

 found. 



