196 
MR. G. H. ftARWIN Ott THE STRESSES 
IE 0 = - i[l(3i+8)-»(i-0)(i+ l)]=t(i+l)(t» 3) 
—2)[ 3 (5i+3)— i(i — 2)(i — 1)] 
IE — ^~ 2 ) 3 /- 
IE 6 = 
(i- 4)[5(7t+ 3) - i(i- 4)(i—3)] 
7! '(t-6)[7(9t+8)-t(»-6)(i-5)] 
' 4 “ 5! 
^-2) 3 (i-4) 3 / . 
&c. = &c. 
Ji^ 0 = ^ 2 ~ 4 ) 
IF a = . , 
2 %—\ 
i— 1 
r’(i 2 --4) (i—2)(i—4) 
3! 
TV _ i\V-4) (i—2)(i— 4) 2 (4—6) 
4 i -1 5! 
rr, __^-4) ^-2)(^-4) 3 (t-6) 3 ^-8) 
6 i-1 71 
&c.=&c. 
r 
• (25) 
^0 — 0! {*(* ^ 3.0} '4 - 9.(^+3)(i-f-2)— — i 2 
*\ 
^ 2 
^ 2 ) 3.2} — (i-j-3)i 
0 ! 
/(?* = 4) - 3.4}+|(i+3)(i—2) 
&c.=&c. 
If I _ ^ + 2) i\i — 2 ) 2 
4— i— 1 
4! 
(® 4) 
&c.=&c. 
• (26) 
These sets of coefficients are all written down in such a form that the laws of their 
formation are obvious, and the general terms may easily be found. I have computed 
their values from these formulas for the even zonal harmonics of orders 2, 4, 6, 8, 10, 
12; the results are given in the following tables both in the form of fractions and of 
decimals approximately equal to those fractions. 
The 6r’s and H’s were not computed because their values were not required for 
subsequent operations. 
