,38 
ARCHDEACON PRATT ON THE EFFECT OF LOCAL 
xdxdz 
{x^ + z^) »^x^ + YH " + Y 2 
xdxdz 
' + z’^) \/x^ + Y‘^ 
-si.rr. xdxdz ! ?>x^ -f 2 Y^ ^ 
=?fl: 
{x^ + Y^)^\ + 
(l— 2(^2^ ' Yg) ), neglecting ;s", &c. 
) 
_£Yf — ^ — 5 |( 3 j?^+ 2 Y^) tan"*-— const. 
2 j(a ^2 + Y 2 )^r ^ ^ a? ^ 
Put 
-iZ 
2 Xx^+Y^)^\ 
+•••+(- 1 )’ 
2n + \' 
X 
{x'^ + Y^^f 
A-(A-H) A3-(^-H )^ 
X 3 a^ 
^ 2 «+l_(^_ JJ) 2»+1 
( 2 w + l)a;^“+' 
K -A_L_/i ^ 
r^ 2 «+l — JJ 2 w+l|^ A 
The maximum value of this coefficient is ^ This may be proved by putting 
A=H sin^^, or H = Asin®^, according as h is less or greater than H, and finding the 
maximum by the Differential Calculus. 
Hence, attraction of whole mass parallel to x 
=1 fY f f-^-i 2^^ + (2 - 3 K 3 /O- 
' + Y 2 ) 
. (2 Y^K3- 3K,/o 5+ ... + (- 1 )n2Y^K,„^- 
h 
or, since the squares of y be neglected 
^{x^+Y^f 
Now by the Integral Calculus, 
dx 2n + 1 dx 
I 
'■■J 
and 
dx 2n+\ 
fX dx 
Jn 
1+^ 
v'a;2 + Y2~Y2\X2™ v^X^ + Y^ -C 
_r_n.l 2 ^”-1 L 
V U 2 4 '“ 2 ra Y 2 ”+* 
a; 2 » + l 
+ 27^YW»{^^^^'^- Y' ( 1 - 2 ^ T2+”- + (~^)"''I'--L:^(y) +•••) 
-y>w(i-|£iS+^^^+(-i)-i.^S($r+^.^)(;)-l. 
. , X^+\/l + Y 2 
L=lo&. - 
m 
1 + 
/ . X 2 
\/ l + ya 
where 
