265 



Logocyclic Curve by a continuous motion ; arid a very ingenious 

 instrument has been contrived by Mr. Henry Johnson of Crutched 

 Friars, to describe the spiral of Archimedes, which is as simple as 

 it is effective. 



June 17, 1858. 

 The LORD WROTTESLEY, President, in the Chair. 



The Earl Granville, Professor Hennessy, and the Rev. Samuel 

 Haughton were admitted into the Society. 



In accordance with notice given at the last Meeting, the Earl of 

 Rosse proposed the Right Hon. Sir John Pakington, Bart, for 

 election and immediate ballot. 



The Ballot having been taken, Sir John Pakington was declared 

 duly elected. 



The following communications were read : 



I. " On the Problem of Three Bodies." By CHARLES JAMES 



HARGREAVE, LL.D., F.R.S. Received May 3, 1858. 



(Abstract.) 



The author states that the principal object of this memoir is to 

 set forth two new methods of treating the dynamical equations by 

 processes of variation of elements, differing from the ordinary pro- 

 cesses of this nature principally in this particular, that the variations 

 are represented in explicit terms of the elements themselves and of 

 the time, and not through the medium of partial differential coeffi- 

 cients. It has been his object to render the processes as elementary 

 as possible ; and to preserve them in a rigorous form, by post- 

 poning all attempts at approximation until the formulae are actually 

 applied to practical problems. The applications given in the paper 

 comprise the circular and spherical pendulums, and the planetary 

 and lunar theories, and a special theorem as to the movement of 

 the plane of a planet's motion under the influence of several other 

 planets. 



The original normal problem which is taken as the basis, is that 



