more kinds of Moving Particles among one another. 33 



that of a stratum of copper of equal thickness. It would be almost 

 impossible to establish the value of the conductivity of a gas by 

 direct experiment, as the heat radiated from the sides of the vessel 

 would be far greater than the heat conducted through the air, 

 even if currents could be entirely prevented. 



Part III. On the Collision of Perfectly Elastic Bodies of any 

 Form. 



When two perfectly smooth spheres strike each other, the 

 force which acts between them always passes through their cen- 

 tres of gravity ; and therefore their motions of rotation, if they 

 have any, are not affected by the collision, and do not enter into 

 our calculations. But; when the bodies are not spherical, the 

 force of compact will not, in general, be in the line joining 

 their centres of gravity ; and therefore the force of impact will 

 depend both on the motion of the centres and the motions of 

 rotation before impact, and it will affect both these motions after 

 impact. 



In this way the velocities of the centres and the velocities of 



rotation will act and react on each other, so that finally there 



will be some relation established between them ; and since the 



rotations of the particles about their three axes are quantities 



related to each other in the same way as the three velocities of 



their centres, the reasoning of Prop. IV. will apply to rotation 



as well as velocity, and both will be distributed according to the 



law 



rfN AT 1 _'* 

 — =N — jh.t « 2 . 

 ax u Vit 



Also, by Prop. V., if x be the average velocity of one set of par- 

 ticles, and y that of another, then the average value of the sum 

 or difference of the velocities is 



\/x* + y*; 

 from which it is easy to see that, if in each individual case 

 u — ax-\-by + cz, 



where x, y, z are independent quantities distributed according to 

 the law above stated, then the average values of these quantities 

 will be connected by the equation 



Prop. XXII. Two 'perfectly elastic bodies of any form strike 

 each other : given their motions before impact, and the line of im- 

 pact, to find their motions after impact, 



Phil. Mag. S. 4. Vol. 20. No. 130. July 1860. D 



