702 Mr. J. ED Jeans on the 
The essential point to be noticed is that these expressions 
are necessarily pesitive for all values of a and 0, so that 
whatever the velocity of the second molecule may be, the 
expectation of the velocity of the first molecule after collision 
is definitely in the same direction as its velocity before 
collision, If @ is the expectation of velocity in the same 
direction as a, the formula just found leads to the following 
table of values :— 
: =°500; “475, °400, °368, °354, 523, oaee 
We have now proved the tendency for the original velocity 
of a molecule to persist after collision. If we define the 
ratio = ~ to be the “ persistence,” the table just given shows 
that the pe sistence is measured by a quantity which varies 
from 3 to 4 of the original velocity, according to the velocity 
of the colliding helene: 
§ 2. By averaging over all possible velocities for the 
colliding molecule, we can obtain the mean value of this 
per setenie averaged over all collisions. 
The proportion Mok collisions for which the greater velocity 
stands to the less in a ratio between & and k-+dk (k>1) is 
easily found to be 
ORB +) ah a 
J/ 20+)” Ss Ge 
and the values of the persistence for the two molecules taking 
part in such a collision are respectively 
Lae 4-7 5k +3 
and 
10k? (34? +1) 5@R +1)" 
The mean persistence for the two molecules, 7. e. the mean 
of the two foregoing expressions, is 
25k* + 647 +1 
20k? (3k? +1)° 
Multiplying this by expression (il.) and integrating from 
k=1to k=, we find for the mean persistence of all velocities 
