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 LXXIV. Intelligence and Miscellaneous Articles. 



ON THE OSCULATING TWISTED CUBIC TO A CURVE OY DOUBLE 

 CURVATURE. BY SIR WILLIAM ROWAN HAMILTON, LL.D., ETC. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 

 TT may interest some readers of the Philosophical Magazine to 

 know that one of the applications which, in my forthcoming- 

 work (Elements of Quaternions), have been made of my calculus to 

 geometry relates to the determination of the osculating twisted cubic 

 (or gauche curve of the third degree) to any proposed curve of double 

 curvature. 



Another application relates to the locus of the osculating circle, 

 which is at the same time the envelope of the osculating sphere, to any 

 such curve in space. 



If permitted, I shall be happy to give some short sketch of each of 

 those two investigations, in the Philosophical Magazine : and, in the 

 mean time, I have given an outline of one of them to the Royal Irish 

 Academy, at their general meeting. 



ON THE INDUCTIVE CAPACITY OF INSULATING BODIES. 

 BY M. GAUGAIN. 



The new theory of induction, propounded by Mr. Faraday twenty 

 years ago, has given rise to numerous controversies ; and it is not 

 generally allowed that the inductive capacity is a special property, 

 distinct from ordinary conductibility. But the problem of the deter- 

 mination of inductive capacities, viewed in the manner I am about to 

 point out, is a purely experimental question, and can be treated quite 

 independently of any theoretical idea. 



According to Faraday's views, the inductive capacity consists in 

 the greater or less facility with which neutral electricity is decom- 

 posed and recomposed in the interior of the same molecule, while 

 conductibility consists in the greater or less facility with which the 

 electricity of one molecule is transmitted to the adjacent ones. But 

 holding to these notions, it would appear difficult, if not impossible, 

 to distinguish the effects of the inductive capacity from those of 

 ordinary conductibility ; and to isolate the first, Mr. Faraday has 

 found no other means than that of rapidly charging and discharging 

 the condensers which he used. But it seemed to me that, by work- 

 ing in this manner, a new principle is virtually introduced, which 

 consists in assuming that the inductive capacity may be completely 

 manifested in an inappreciable time, while conductibility always 

 requires, to develope its effects, more or less of time. Taking this 

 character as a definition, the problem of the determination of the 

 inductive capacities may be stated in precise terms. 



As I have pointed out in a previous note (Phil. Mag. vol. xxiv. 

 p. 495), the charge of a given condenser put in communication with 

 a source of electricity depends on the time during which contact is 

 established (at all events when the dielectric is a solid body). Hence 

 the charge ought to have a maximum and a minimun* value ; 

 and the investigation of these two limits constitutes two perfectly 



