X. On the Motion of a System of Particles, considered with reference 

 to the Phenomena of Sound and Heat. By Philip Kklland, B.A. 

 Fellow and Tutor of Quee?>s' College, Cambridge. 



[Read Mat/ l6, 1836.J 



INTRODUCTION. 



In a former Memoir, it was my endeavour to simplify the equa- 

 tions of motion of a system of particles attracting each other with 

 forces varying according to any law. The discussion of these equations 

 was restricted to their bearing on the phenomena of Light, on which 

 account one of the three was left untouched. 



It appeared that the hypothesis of attractive forces led to the result 

 that two of the equations corresponding to the motion in a plane 

 perpendicular to the direction of transmission, indicated vibratory motion, 

 whilst the third assumed a form altogether different, shewing that, as 

 far as it was concerned, the motion was not vibratory. 



On the other hand, the hypothesis of repulsive forces would give 

 the motion in the direction of transmission vibratory, whilst the con- 

 trary would be the case in a plane perpendicular to this direction. 



The discussion of the equations corresponding to motion in the 

 direction of transmission is the object of the present memoir. 



It is not improbable that to the action of forces, such as those of 

 which we are treating, a considerable number of the phenomena of 

 nature may be referred; but on account of our imperfect knowledge 

 of the analogies subsisting between phenomena which apparently differ 

 widely from each other in some essential points, we are obliged to 

 restrict ourselves to the most simple, or to those which have been the 

 most carefully examineu. 



Vol. VI. Part II. H ii 



