369 
"from P the right line PT, touching the hyperbola in T, and 
denoting the angle EPT by 0, we have 
a— ob 
va =" cos @ 5 
cos 9 = 
whence it may be shown that if p be the point to which P 
moves when @ becomes ¢ + d@, the interval Pp multiplied by 
cos @ will be proportional to the attraction of the matter dM 
contained between the surfaces of two right cones having B 
for their vertex and OB for their common axis, provided 
and @ + d@ be the angles which the sides of these cones make 
with OB. The whole attraction is therefore proportiona. 
to the difference between the tangent PT and the hyperbolic 
are ET, the position of T being that which corresponds to the 
supposition ¢ = 0, orp =c. 
‘«* When the attracted point is at the extremity of the great- 
est axis of the ellipsoid, we’ cannot employ a similar method, 
because there is no focal curve perpendicular to that axis. 
But if a, B, c be the attractions at A, B, C respectively, we 
have the known relation 
A B Cc 
gt ano 
of which a geometrical proof will be found in the Proceedings, 
vol. ii. p. 525 ; and from this relation we can find a in terms 
of B and c. 
«« The preceding method of treating the question of the 
attraction of ellipsoids was given at my lectures in Trinity Col- 
lege, in the beginning of last year. I have since observed 
that the same results may be obtained, and perhaps more rea- 
dily, by dividing the ellipsoid into concentric and similar shells. 
For the attraction of dM is equal, in each case, to the attrac- 
tion of the shell bounded by the surfaces of two! ellipsoids 
whose semiaxes are acosp, bcos, ccosp, and acos(~ + dp), 
beos(@ + do), ecos(¢ + d@), these ellipsoids having O for their 
