The Rev. A. Thacker on a case of disturbed Elliptic Motion. 51 



which is a formula of continual application in Quaternions #, and 

 in these extensions also is important. 



Observatory of Trinity College, Dublin, 

 August 16, 1854. 



[Tbis little paper, which I propose to call (as above) Section the Fourth 

 of these Extensions, has been in type for a couple of months, but other 

 occupations have prevented me from revising it till now. Although very 

 unwilling to encroach on the valuable space of the Philosophical Magazine, 

 I have drawn up sketches of some continuations, which I shall perhaps 

 shortly copy and send, to be printed at such times as may suit the conve- 

 nience of the Editors, whose constant courtesy is herebv thankfully acknow- 

 ledged.— W. R. II. 



Observatory, Dec. 22, 1854.] 



[To be continued.] 



IX. On a case of disturbed Elliptic Motion. 

 By the Rev. A. Thacker. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 



YOU may perhaps find a place in your Journal for the fol- 

 lowing investigation, which was suggested by a recent 

 discussion on the subject of the lunar theory. The problem I 

 propose to solve may be stated thus : — A body is acted on by a 



central force equal to ^ + frfr, fJ being small ; to determine the 



motion when the orbit is not nearly circular. 

 The equations of motion are 



and from these we deduce immediately, 



dt~r>> K) 



v* + C=^-f*>r*, (2) 



par. [17.], for "i read a A . And in ( 1 48), of [22.], for .v :t read .s\,w 3 . 

 t This is the equation given bv Professor Challia. 



E2 



