460 Prof. Challis on the Source and 



that is to say, it becomes a power of the determinant 



a 



b 



c 



d 



b 



c 



d 



e 



c 



d 



e 



f 



d 



e 



f 



<j 



as we know a priori it ought to do, by virtue of the theorem 

 originating out of Jacobi's theorem stated at the beginning of 

 this paper : in fact the two factors of the resultant of X 3 , X 4 each 

 of them becomes equal to X 4 3 ; and so in general we shall find, if 

 we use n instead of 4, each factor of the corresponding resultant 

 becomes A£ -1 , giving X^~ 2 as the complete resultant for that 

 singular case, as previously determined. 



The author is conscious that some apology may appear due for 

 the cursory mode of elucidation pursued in the preceding extended 

 note, and for the absence as regards certain points of the appro- 

 priate proofs; but to have gone into all the details of demonstration 

 would have swollen the paper to a length out of proportion to its 

 importance. Let him be permitted also in all humility to add (as 

 can be vouched by more than one contributor to this Magazine), 

 that in consequence of the large arrears of algebraical and arith- 

 metical speculations waiting in his mind their turn to be called 

 into outward existence, he is driven to the alternative of leaving 

 the fruits of his meditations to perish (as has been the fate of 

 too many foregone theories, the still-born progeny of his brain, 

 now for ever resolved back again into the primordial matter 

 of thought), or venturing to produce from time to time such 

 imperfect sketches as the present, calculated to evoke the mental 

 cooperation of his readers, in whom the algebraical instinct has 

 been to some extent developed, rather than to satisfy the strict 

 demands of rigorously systematic exposition. 



LXII. On the Source and Maintenance of the Sun's Heat. 

 By Professor Challis, M.A., F.R.S., F.R.A.S.* 



THE most recent speculations to which the question of the 

 maintenance of the sun's heat has given rise are chiefly 

 these which follow. In a paper contained in the Transactions 

 of the Royal Society of Edinburgh (vol. xxi. part 1. p. 63) and 

 in the Philosophical Magazine for December 1854, Professor 

 William Thomson has concluded that "the source of energy 

 from which solar heat is derived is undoubtedly meteoric" He 

 contends that the waste of heat by radiation can be supplied in 

 no other way than by the heating effect of the impact of small 



* Communicated by the Author. 



