Mr. Ha3rward on a Method of estimating Velocities, ^c. 399 



direction to that of angular momentum, as the radius of the central 

 ellipsoid with which it coincides to the normal at its extremity. 

 Hence an angular momentum constant in intensity and direction, 

 in general gives rise to an angular velocity variable in both respects, 

 and vice versd. The question then becomes, to determine the acce- 

 leration of angular velocity due to the motion of the system. This 

 is obtained by determining the acceleration of angular momentum 

 for a line fixed in the body, which is then shown to be a maximum 

 for the normal to the plane containing the axes of angular momentum 

 and velocity ; then the acceleration along this line is the total acce- 

 leration of angular momentum due to the motion, and the accelera- 

 tion of angular velocity determined from it (just as the angular velo- 

 city is determined from the momentum) is that due to the motion 

 of the system. Also the acceleration of angular velocity due to the 

 forces is related to the resultant couple and its axis, just as the an- 

 gular velocity to the angular momentum. Thus the accelerations 

 of angular velocity due both to the motion and to the forces being 

 determined, the intensity and direction of the angular velocity at any 

 time is to be found by combining these effects by integration. The 

 problem is worked out in the case of the axis of the resultant couple 

 being coincident with that of angular momentum, so that this remains 

 fixed. The paper concludes with a simple solution of the problems 

 of Foucault's gyroscope as applied to show the effects of the earth's 

 rotation, the simplicity arising from the method of this paper enabling 

 us at once to refer the motion to those axes (neither fixed in the 

 body nor in space) whose motion it is desired to determine. 



April 28. — A paper was read on the Theory of Heat, by Mr. A. 

 A. Harrison of Trinity College. 



The object of this paper was to show that there is considerable 

 reason for supposing that radiant heat is identical with light, and that 

 they both consist of vibrations of the ultimate particles of matter. 



There is a strong presumption of this from the facts, that every 

 body heated to a certain temperature, dependent only on the nature 

 of the surface, emits light as well as heat ; and that " whenever light 

 manifests itself, heat appears along with it" (Kelland) : the difference 

 between radiant heat and ordinary heat is, that radiant heat is due 

 to vibrations in planes normal to its direction of propagation, and 

 that ordinary heat consists of vibrations in all three dimensions. 



The author endeavoured to show, in the first place, that the mo- 

 tions of the particles of matter, which must be caused by friction, or 

 in the union of two gases in combustion, is suflEicient of itself to 

 account for the following phsenomena of heat : — 



I. That a body once heated continues of the same temperature, 

 with the exception of heat lost by radiation, conduction, &c. This 

 follows immediately from the principle, that in any system of par- 

 ticles held together by mutual attractions and repulsions, the vis viva 

 is independent of the time, and depends merely on the position of 

 the particles. 



n. That bodies expand by heat. 



Before proceeding to this, the author argued that in gases the 



