542 



and arranged by a competent person, and that he would 

 then offer it to the Academy for publication. 



Professor Mac Cullagh made some remarks, of which the 

 following is the substance, concerning the letter communi- 

 cated by Mr. Lloyd at a former meeting (see Proceedings, 

 p. 520). 



The letter read by Mr. Lloyd at a late meeting of the 

 Academy, was written by me immediately after the examina- 

 tion for Fellowships, which was held in Trinity College, in 

 the year 1831. I had been a candidate on that occasion; 

 and Dr. Bartholomew Lloyd, to whom the letter was ad- 

 dressed, had been one of the examiners. The letter con- 

 tains, among other things, several theorems taken from a geo- 

 metrical theory of Rotation, with which I had been previously 

 occupied. Soon after it was written, I returned to that 

 theory, for the purpose of improving it in one part where I 

 felt it to be defective, and where, indeed, I experienced the 

 chief difficulty ; I mean the part which relates to finding the 

 position of the body at any given time. The method given in 

 my letter for doing this by quadratures, had occurred to me 

 in 1829 ; but I was, of course, not satisfied with it, and I 

 had in the interval made some attempts to find a method 

 more elegant, and, as far as possible, really geometrical. In 

 the autumn of 1831 I succeeded completely in this, and no 

 further additions of any consequence were made to the 

 theory. The position of the line OI within the body, at any 

 given time, was found by an elhptic function of the first kind, 

 the modulus and amplitude of which are given immediately 

 by geometrical considerations ; the modulus of the function 

 being in fact the ratio of the two moduli of the cone which 

 that line, stationary in space, describes within the body. 

 This result was deduced from Theorems I. and IL of the let- 

 ter. The cone reciprocal to that just mentioned was used to 

 find the position of the body in space. This reciprocal cone, 



