241-244] Rate of Dissipation of Energy 205 



radius of these spheres must be supposed comparable with 10~ 8 cms. The 

 collisions which excite vibrations to the greatest extent will be "direct" 

 collisions, and the vibrations most excited will be those of lowest frequency. 

 For ultra-red light, which may for the present be supposed to represent the 

 vibrations of lowest frequency, we may take p = Z x 10 15 . Let us, using the 

 results of 130, take C = 5 x 10 4 . If we suppose that at a direct collision 

 the spheres penetrate one another to the extent of a hundredth part of their 

 radius, we see that during collision the centre of a molecule would describe 

 a path equal to 2 x 10~ 10 cm. at a mean velocity of ^ x 5 x 10 4 . Hence the 

 time of collision would be about 8 x 10~ 1B sees. The product of this and the 

 value given above for p in the case of ultra-red light is 16. 



This is hardly a great quantity in the sense required ; the value of e~ 16 is 

 about 10~ 7 , and since the average molecule undergoes more than 10 7 collisions 

 in a second, it is obvious that the dissipation of energy per second would be 

 much- too great to agree with observation. 



''243. On the other hand there is not the slightest evidence that it is 

 permissible to assume the molecules to be surrounded by " spheres of 

 molecular action" possessing the properties mentioned in 82. Or, what 

 comes to the same thing, if we suppose the molecules to be surrounded by 

 such spheres, we must also suppose the amount of interpretation to be 

 comparable with the radii of the spheres. If we assume this to be one-half 

 instead of one-hundredth part of the radius the time of collision previously 

 calculated must be multiplied by 50, and the product of this and p will be 

 800 instead of 16. The value of e~ m is about lO" 347 and it will be seen that 

 this is amply small enough to account for the observed slowness of dissipation 

 of energy. If we allow 10 10 collisions per second, it follows that the trans- 

 lational energy will be reduced to e~ l times its value in about 10 337 seconds, 

 or about 10 330 years. 



244. At the same time we must notice that even in a gas at an ordinary 

 temperature, there will be some pairs of molecules which collide with 

 enormously high relative velocities, and for which therefore the time of 

 collision is much shorter than we have supposed it to be. Such a collision 

 may obviously set up large vibrations in the molecules concerned. 



In expression (45) we found the number of collisions of relative velocity 

 between Fand V + dV which occurred per unit time per unit volume to be 



(496). 



The total number of collisions, obtained by integrating this expression 

 from V = to V - oo , was also found to be 



