rs Mr. Ivory on the Method of computing 
first position, will be ™ pM 2(1—7/); and/', the same dis- 
tance in the second position, will be — j (p -f- $r) 2 — 2 p(p -[- < 5 r) 
. y -f p f *; and if, with Laplace, we neglect the square and 
Since the spheroid is supposed to approach very nearly to 
the spherical figure, the radius of it will fall under this form 
of expression, viz. p — a x (1 -j- « . y ) ; where a denotes the 
2'adius of a sphere concentric with the spheroid and nearly 
equal to it; u, a coefficient so small that its square and other 
higher powers may be neglected ; and y , a function of two 
angles 9 and ■zr which determine the position of p, 6 being the 
angle contained by p and a fixt axis passing through the centre 
of the spheroid, and -sr the angle which the plane drawn through 
p and the axis, makes with another plane passing by the same 
axis. Now, by substituting and neglecting all the terms of 
the order a and the higher orders, the preceding values of V 
and (^) will become 
fore ---- --- = — " • -j ; consequently — - 
dr 
v = + ««o-) +fj 
and, by combining these so as to exterminatey we shall 
get 
which is no other than Laplace’s equation.* 
* Liv. 3, No. 10. Equation (2). 
