434 
distance, or as the attraction exerted by the whole ellipsoid 
A on the point S, when the force is inversely as the fourth 
power of the distance. 
When the point S is on the focal hyperbola, the integra- 
tions, by which the actual attraction is found in either case, 
are simplified, for the surface B is then one of revolution 
round the axis of £, and its semidiameter 7 is independent of 
the angle ¢. 
From the expression for the attraction of a shell we can 
find, by another integration, the attraction of the entire ellip- 
soid, when the law of force is that of nature. And thus the 
well-known problem of the integral calculus, in which it is 
proposed to determine directly the attraction of an ellipsoid on 
an external point, without employing the theorem of Ivory to 
evade the difficulty, is solved in what appears to be the sim- 
plest manner. 
The preceding note having been read, Mr. Graves observed 
that the mention therein made, of the equation which repre- 
sents so simply a cone circumscribing a given surface of the 
second order, reminded him of a circumstance which he thought 
it right to state ; as that remarkable equation had been in cir- 
culation among geometers long before it appeared in print, and 
thus its origin, though generally known, was sometimes mis- 
taken. Mr. Graves stated that he still retains a large part of 
the memoranda, in which he set down, from day to day, the 
substance of Professor Mac Cullagh’s lectures, delivered in 
Hilary Term, 1836, and that the part preserved contains the 
equation in question (the equation (c) of the preceding note). 
In the memoranda it is deduced directly ; that is, the equation 
of the cone is first given in the usual form, and is then reduced 
to the form (c) by a transformation of coordinates. 
