593 



dratic residuals ; on a new method of determining integrals by ap- 

 proximation founded on Newton's method for that purpose ; on the 

 theory of curve surfaces ; on the theory of capillary attraction, and 

 on various subjects in dioptrics and astronomy : there is one memoir 

 of more than common interest, devoted to the demonstration of a 

 very remarkable proposition in the planetary theory, which is, that 

 the secular variations which the elements of the orbit of a planet 

 would experience from another planet which disturbs it, are the 

 same as if the mass of the disturbing planet were distributed into an 

 elliptic ring coincident with its orbit, in such a manner that equal 

 masses of the ring would correspond to portions of the orbit described 

 in equal times. 



It was in the course of this last investigation that he arrived at 

 some elliptic integrals, the evaluation of which he was enabled to 

 effect by means of a transformation which is included in one of the 

 series of transformations, the discovery of which will immortalize the 

 name of Jacobi. It has been said though we do not vouch for the 

 truth of the anecdote that this distinguished analyst was induced 

 by his knowledge of this fact to seek after his own discoveries 

 were completed an interview with the great mathematician who 

 had thus intruded, prematurely as it were, into one of the deepest 

 recesses of his own province : Jacobi submitted his various theorems 

 to his inspection, and was met, as they successively appeared, by 

 others of corresponding character and import produced from his 

 manuscript stores, concluding with an intimation that there were 

 still many more in reserve. Such an anticipation of discoveries, 

 which totally changed the aspect of this difficult department of 

 analysis, even if it had been as complete as it is here represented to 

 have been, would have been no derogation of the rights which 

 Jacobi has undeniably secured by priority of publication ; but the 

 wide circulation which has been given to this story, as well as our 

 own knowledge of Gauss's habitual delay in the publication of his 

 researches, have tended not a little to increase our anxiety to be put 

 in possession of the various scientific treasures which he is said to 

 have left behind him. It is to Lejeune Dirichlet that this task has 

 been entrusted, and there are few living analysts so likely to perform 

 it satisfactorily. 



We now enter upon the last, and perhaps the most considerable 



