D 2/i 



Law of Partition of Energy. 59.' 



Hence 



ri^ _ D 1 D n 



Similarly 



And therefore 



And of course 



dQ 1 x 



Wj -p- = U 2 j— — &c. 



^ ........ (A) 



</q «;g ^Q 



W— = «— - = W-j— I 



rtM rtU «W J 



1 ( J. Let us now write 



~ £?l = (»»1 + »W«) &««> +(»»! + Wl g ) ?'i3?/ 3 4- &c. 



— %= («H + wig) ^12^2 + (wi< + mg) 6 13 u 3 + &c. 



— Ki — ( m i + w« s )i 12 w a + (mi 4- m 3 )& 13 tc g + &c. 

 Similarly 



— Ia= ( m 2 + m i )^i2"i + (wi 2 + m z )b 2Z u z + &c. 

 &c. 



Then 



Q = 2m(w 2 + v 2 + w' 2 ) - i % (u% + v V + wQ , 



the summation including all molecules. The factor ^ comes 

 in because in %(ug+vr] + w£) e\ T ery product as ?n 1 // 12 t/ 1 w 2 

 occui*s twice. 

 Our equations 



Mi — — = m 9 - — = &c. 

 av x " du 2 



now become 



1^]Ul'— ■2»]£l) = m 2'*V~ i^2^ 2 )=&C. . . (B) 



These are the equations which take the place of 



m x Ui = m 2 u 2 , &c, 



and we have to consider the significance of these equations B 

 as bearing on the law of equal partition of energy. 



20. Now (I.) if we could prove that the ratios vjij/mu 9 , 

 vrj/mv*! &e. .are the same for each molecule, we should have 



