553 
figure of the earth. 
B Z /(o) + B Z' (I) -f- B Z' (z) + &c., where B o , &c. are 
functions of a, and. Z! ^ ^ is a function of f* that satisfies the 
equation - <7—jr dz'W > j-r- m 
0 = d7i 1 —^--d7'^+ k - k + 1 - / ‘- 
This equation is exactly similar to the equation above for 
since R does not depend on cJ — a, and therefore 
r - -- i + 3 
d . R' 
d a 
i^!iis = o. The„R' + ^= 7 ^ 
d a 
rn- 57 (b o Z' (o> +B,Z' < 0 + B 2 Z' (2) + &C.), the general 
term of which is . * — - — - • Z The value of V then 
* t 3 a cl 
for the interior strata is the sum of all the quantities 
pr+r f ?-ST /,/,Q ( ° Z ' W upon giving to i and k 
(* + 3). r J a J a p 
the values 0,1, 2, 3, &c. ; and the integral with respect to a 
must be taken from a = o to a = the value which it has in 
the stratum of equal density passing through the given 
point, which we shall call a. 
(6.) For the strata exterior to the given point we must 
i r r t' d r 
take the sum of the different values of r I p I I -77, . 77 
J a v J d J jx'R 
Now 
R 
= rb -TJ- . except i = s, when 
ex- 
ir • —-I7 ■ lo S- R - Suppose then -4^ or R 2 ‘ 
panded into the series h y o) + 6 , 2 ,(i) + b ^ %1^ 2 \ &c. where 
d® satisfies the same equation as before ; then for the 
value of V we must take the sum of all the quantities 
— f p d,b k . C f Q®d k \ upon giving to k the values 
2 ~* ^ a da » ul ' 
