DUE TO THE WEIGHT OE CONTINENTS. 
195 
P=r‘cos^(^ 0 + J d 3 tan 3 Z-fH 4 tan 4 Z+ . . .) 
+aV” 3 cos tan H-\-B t[i tan T-f- . . .) 
R=f* cos %C Q + C 2 tan H-\-C A , tan H-\- . . .) 
+aV -3 cos tan tan H-\- . . .) 
T —r* sin l cos i - l l(B 0 +E 2 tan 3 /+i? 4 tan H-\- . . .) 
+ aV -2 sin l cos tan 3 /+W 4 tan 4, Z+ .. 
Q=r* cos *7((r 0 +(r 3 tan 3 £+(x 4 tan H-\- . . .) 
+aV~ 2 cos tan 3 £+iif 4 tan H+ . . .) 
Then introducing for J and for the /3 s their values in terms of i, I find that the 
coefficients A, B, &c., are reducible to the forms given in the following equations :—• 
M=-^{^+ 2 )(»“0)-3.0.(t+l)}+0.(i+3)(i+2)(i+l) = --t^+2) 
IAo = 
-{*•(*•—0)(i— 2)—3.2(t—1)}—-(i+3)(i+0)(*-l) 
I A, 
IA, 
&C 
IB, 
IB t = 
IB,— 
41 4) —3.4(/—3)} + — (f+3)(/— 2)(/— 3) 
-- £ -4)(i 6) 3.6(t 5)} 4]" ( l '“l"3)(^—4)({—5) 
&c.=&c. 
Irf S(.-»Ki-3) 
&c.= 
i—1 
&c. 
4! 
(23) 
lC' 0 = -{(« ; +3)^-P( 1 (-2)- 1 )+3.0.1]}='|:( ? : +l)(j+2) + l] 
= 4{(*+3)(i—2) a —[*'(3.0 — 1) +3.2.3]} 
/& = 
2 ! 
/a= 
41 {(*+3)(»-4)8-[i(5.2-l) + 3.4.5]} 
i 3 ^-2)S(i-4) 8 
6 ! 
•{(*+3)(i—6) 3 —p(7.4—1)+3.6.7]} 
&c. = &c. 
^ + 2 ) & 
' i-l~ 01 
i{i+ 2) ^Q'-2) 3 
1 2 ! 
_ ffi + 2) ^^-2) 2 ^-4) 2 
i~ 1 4! 
&c. = &c. 
> (24) 
m= 
m= 
m= 
2 c 2 
