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 r is independent of 

 the angle <p. 



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 Cxillagh'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 (r) by a transformation of coordinates. 



