358 Royal Society : Prof. Faraday's Experimental 



where ^ is a definite integral, such that 



9 = 7T '^» 9 



d\ ' ' ' dX' 

 i? = X A' and r^ = (X — X'y, 

 which equations apply exclusively to ellipsoids with three unequal 

 axes, and solve the problem with regard to that class. From these 

 he derives another equation, which he states is no other than a trans- 

 formation of his first fundamental equation, and is equivalent to 

 other transformations of the same equation found by M. Jacobi and 

 M. Liouville. 



He also remarks that a limitation of one of the constants, which 

 the verification of this formula requires, agrees with the limitation of 

 M. Jacobi ; and further, that the relations which may subsist be- 

 tween the constants proves that there does exist an infinite number 

 of ellipsoids not of revolution, which are susceptible of an equili- 

 brium. 



After determining the corresponding limits of these relations of 

 the constants, p being contained between the limits 1*9414 and 1, 

 while T' increases from zero to infinity, he remarks that an elliptical 

 spheroid formed of a homogeneous fluid can be in equilibrium by the 

 action of a centrifugal force only when it revolves about the least axis. 



He next deduces the general value of g (the ratio of the forces,) 

 and thence its value in one extreme case, when r^ = 0, or when 

 A and A.' are equal, and remarks that this is no other than the deter- 

 mination of 5^ in a spheroid of revolution having its axes equal to 



k and k V 2-9414 =kX 1*7150. 

 In the other extreme case, when r^ is infinitely great, g is zero. 



From this investigation the conclusion is arrived at, that for every 

 given value of r^ there is only one value of ^;, and only one ellip- 

 soid ; and that to every such ellipsoid there is an appropriate value 

 of g : and, further, that for every possible value of g there will be 

 only one value of t-, and consequently only one ellipsoid susceptible 

 of an equilibrium. 



Also the reading of a paper, entitled, " Experimental Researches 

 in Electricity." Eleventh Series. By M. Faraday, Esq., D.C.L., 

 F.R.S., FuUerian Professor of Chemistry at the Royal Institution, 

 was commenced. 



December 21, 1837. — The reading of Mr. Faraday's eleventh 

 series of Experimental Researches in Electricity was resumed, but 

 not concluded. 



The Society then adjourned over the Christmas vacation to meet 

 again on the 11th of January 1838. 



January 11, 1838. — The reading of a paper, entitled "Experi- 

 mental Researches in Electricity," Eleventh Series, by Michael 

 Faraday, Esq., D.C.L., F.R.S., Fullerian Professor of Chemistry at 

 the Royal Institution, &c., was resumed and concluded*. 



* Having inadvertently inserted in our number for February a notice of 

 this paper in an incomplete form, we now give the complete and corrected 

 official abstract of it. 



