96 Mr. J. Fl . Jeans on the Partition of 



and at a temperature of 15° C. in a cubical enclosure of edge 

 equal to I centimetres. For this system N=4xl0 19 / 3 very 

 nearly. The free vibrations o£ the aether are known (cf. Lord 

 Rayleigh's ' Sound/ § 267), each vibration corresponding to 

 values of X, Y, Z, a, j3, y of the type 



cos (P™\ cos (9^\ cos (^\ fK< 



sin \ I ) sin I / J ^ \ I P ' ' ' ' K } 



where p, q, r are integers. These principal vibrations cannot 

 be compounded into plane waves, as was don e in § 2 when the 

 space was unlimited. 



The frequency k o£ this vibration is given by 



(p 2 +g 2 +r°)Y = T» ■ ■ (6) 



where V is the velocity of light. For air at 15° C. the mean 

 duration of a collision is of the order of 10 ~ 13 seconds. Let 

 us suppose the s degrees of freedom to consist of ail those 

 for which the period is greater than 10~ 14 seconds. The period 

 given by equation (6) is 



2tt _ 21 



K ~ V^fTqt + r 2 ' 



If we take V = 3 x 10 10 , we find that the upper limit of 

 ^y'pV _j_ ^2 _(_ r 2 i n orc [ er that the vibration may have a period of 

 not less than 10" 14 seconds, is 200002/3. 



The number of sets of positive integral values of p, q, r for 

 which \/p 2 -\-q 2 + r 2 <6, where 6 is large, is approximately 

 ^7r0 3 , so that in the present case the number of sets of values 

 of p, q, r is approximately 



s/ i n 

 -Z 3 . 



4tt x 10 12 



81 



Each system of values of p, g, r gives four principal co- 

 ordinates, so that for our present purpose 



167TXl0 12 7 ., 



'= -Mr- l ' 

 Taking the value N = 4 x 10 19 / 3 , we find 



?Tx? = i^rr, — 77^ = 5 x 10 -9 roughly, 

 3N 243 Xl0 7 & J ' 



so that the energy of the sether is almost inappreciable, no 

 matter how large the enclosure may be. 



