520 



culturist, from the high price of all the compounds of 

 cyanogen. 



Mr. George Yeates read a paper containing the results of 

 a Meteorological Journal for the year 1843. — See Appen- 

 dix V. 



The Rev. H. Lloyd communicated a letter written many 

 years ago to his father, the late Dr. Lloyd, Provost of 

 Trinity College, by Mr. Mac Cullagh, who was then a 

 Fellowship-Candidate in the College. It relates principally 

 to a mechanical theory (that of the rotation of a solid body) 

 which Mr. Mac Cullagh was occupied with at that period, 

 and which he had occasion to allude to at the last meeting 

 of the Academy. The following is an extract from the letter. 

 The beginning and the date are wanting. 



" Theorem I If a rigid body, not acted on by any extraneous 



forces, revolve round a fixed point O, and if an ellipsoid be described 

 having its semiaxes in the direction of the principal axes passing 

 through O, and equal to the radii of gyration round them ; then a 

 perpendicular to the invariable plane being raised from O to meet the 

 surface of the ellipsoid in I, the line OI (which is fixed in space, as 

 the ellipsoid revolves with the body) will be of a constant length 

 during the motion ; and a perpendicular from O upon the plane which 

 touches the surface at I, will always be the axis of rotation, and will 

 vary inversely as the angular velocity. 



" Corollaries. 



" 1. Since every radius which is nearly equal to the greatest or 

 least semiaxis of an ellipsoid must lie near that semiaxis, it appears 

 that if, in the beginning of the motion, the point I be near the vertex 

 of either of these semiaxes, it will always be near it, since O I remains 

 constant ; and therefore, by the preceding construction, the axis of 

 rotation will always remain near the same semiaxis. Hence the ro- 

 tation about the axes of greatest and least moment in any body is 

 stable. The rotation about the axis of mean moment is unstable, 

 because the radii of an ellipsoid, which are nearly equal to the mean 

 semiaxis, do not all lie near that semiaxis. 



