28 



The Law of Distribution of Velocities [CH. n 



This shews that the velocities of molecular motion are distributed equally in 

 all directions in space. The law of distribution of the magnitudes of these 

 velocities independently of their directions in space is found, upon integration 

 of expression (38) with respect to 6 and </>, to be 



47rAe- h>H *c?dc (39). 



The law indicated by expression (37) can also be written in the form 



A [e~ hmu2 du] [e- hm ^d\i] [e~ hm ^d\N] (40), 



shewing that the distributions of u, V, w are independent. 



i.o 



\ 



7\ 



\ 



\ 



-2 -4 -6 -8 1-0 1-2 1-4 1-6 1-8 2-0 2-2 24 



FIG. 3. 



In fig. 3, the thick line is the curve 



while the thin line is the curve 



The factor 2 is introduced in the former equation in order that the two 

 curves may have the same area, namely | \ltr. The former curve shews the 

 grouping of the magnitudes of the velocities independently of their directions 

 in space, the latter that of the magnitudes of a single component. 



