740 



PHILOSOPHICAL TRANSACTIONS. 



[anno 1790. 



The situation of the spot « calculated for July 28, 13^ 53"^ 39^ ; p for Sept. 

 16, 7^45"" 48»; £ for Nov. 2, 1^ 15"™ 58^ 



XXiy. On spherical Motion. By the Rev. Charles Wildbore.* p. 496. 



This paper, which has cost me much pains in patient investigation, says Mr. 

 W. is occasioned by that of Mr. Landen, in the Philos. Trans, vol. 75. I am 

 no stranger to this gentleman's great judgment and abilities in these abstruse 

 speculations, but have a very high opinion of both ; yet I could not but think it 

 strange, that two such mathematicians as M. D'Alembert and M. L. Euler 

 should both follow each other on the same subject, both agree, and still not be 

 right. I therefore resolved to try to dive to the bottom of their solutions, 

 which those who are acquainted with the subject know to be no light task ; and, 

 if possible, to give the solution, independent of the perplexing consideration of 

 a momentary axis changing its place both in the body and in absolute space every 

 instant ; and which I consider as not absolutely essential to the determination of 

 the body's motion. But finding that I could not thus so readily show the agree- 

 ment or disagreement of my conclusions with those of the gentlemen who have 

 preceded me in this inquiry ; I have also added the investigation of the proper- 

 ties of this axis. And I suppose it will be found that I have added many proper- 

 ties unknown before, or at least unnoticed by any of them. 



M. Landen's very important discovery, that every body, be its form ever so 

 irregular, will revolve in the same manner as if its mass were equally divided and 

 placed in the 8 angles, or disposed in the 8 octants of a regular parallelopipedon, 

 whose moments of inertia round its 3 permanent axes are the same as those of 

 the body, serves admirably to shorten the investigation, and render the solution 



* Mr. Wildbore died Oct. 30, 1802, being 65 years of age, at Broughton Sulney, Nottingham- 

 shire, in which village he had been pastor naore than 30 years. He commendably raised himself 

 from a low origin, by his industry and natural talents, to an eminent rank in mathematics and clas- 

 sical learning. Before his care of the parish of Broughton, he kept an academy for young gentle- 

 men several years, at Bingham, in the same county. Though an eminent philosopher and mathe- 

 matician, Mr, W. never favoured the world with any separate publication of his own ; but com- 

 monly amused himself in various periodical publications } as in Martin's Miscellaneous Correspon- 

 dence, the Magazines, the Ladies' and Gentleman's Diaries, the Monthly Review, &c. After he 

 became compiler of the Gentleman's Diary, in 1780, his writings in that annual little work were 

 given under the signature Eumenes) and from that time, till his death, under that of Amicus in the 

 Ladies' Diary. 



