Vaporization of Liquids : 293 



quantity proportional to the total volume of the molecules it 

 contains. 



A molecule moving up to the boundary plane at an angle 

 to its perpendicular would experience in passing through a 

 layer dz, dz/l cos collisions. We may determine the effect 

 of a collision by assuming that the molecule struck takes up 

 a similar motion to that of the striking one at an average 

 distance s in advance of it in the line of motion. But this 

 distance s in a direction with the perpendicular to the 

 plane is accomplished without motion against the molecular 

 forces, so that for each collision the work necessary for the 

 molecule to do in moving upwards may be considered to be 

 diminished by 



S COS -t~. 



dz 



The minimum kinetic energy a molecule must have to pass 

 upwards through the division plane of the layers, may there- 

 fore be written 



|mVcos 2 = #--^# = #.— . . . (3) 



by (2). Eliminating dcf> between (1) and (3), we obtain, 

 since Nm=/), 



*'i 



= y/2J^L;. — .sec (4) 



If we now take the motion of the molecules of the liquid 



to be that given by Maxwell's law of velocities, the number 



of molecules per c.c. of the layer dz, moving with velocities 



between q and q + dq, and in directions making angles 



between and 0-\-d0 with the perpendicular to the boundary 



plane, is 



91ST 

 ~^=- sin 0.q 2 e-M« 2 dqd0, .... (5) 



SI IT Of 



where a is the " velocity of maximum number " of the 

 molecules. If there were no collisions the number of these 

 striking against the boundary plane of the layers per second 

 would be obtained by multiplying this expression by q cos 0. 

 The effect of the collisions may, however, be determined as 

 before, by assuming that for every distance Z— s that a 

 molecule moves, another molecule takes up its motion at a 

 distance 5 in advance of it. The apparent velocity with 



