[GARVER] POLYMERIZATION OF LIQUID SUBSTANCES 107 
proportional to the polymerization. Hence it seems possible to express 
the polymerization as a function of the critical temperature; and that 
is what the Ramsay and Shields formula actually does. The two theor- 
ries, then, instead of being in opposition, as at first appeared, really 
afford each other mutual support. To be accurately compared the 
values of r and k should represent the same temperatures. The value 
of kis determined from 
y (Mv)4 
(r-d) 
where y is the surface-tension, (Mv) the volume of a gram. mol. 7 a 
temperature difference measured from the critical point, and d a con- 
stant to be determined for each substance. It is not intended at present 
to discuss the relation of the two theories further than to call attention 
to the fact that they are not necessarily antagonistic. 
In conclusion, attention may be directed to the three necessary, 
experimentally determined values required by the present theory— 
the ratio of the two densities, p/g, the heat of vapourization, and the 
corresponding temperature. The separate densities need not be known, 
hence the method of Sidney Young! which gives this ratio directly 
and accurately without necessarily determining the separate values is 
particularly applicable. Different observers frequently give quite 
different values for the heat of vaporization, L. The temperature may 
easily be observed with sufficient accuracy, since a whole degree varia- 
tion would be unimportant as compared with the accuracy attainable 
in the other quantities. 
The heat of vapourization L has been found for a large number of 
substances; also the densities for most liquids and for many vapours. 
But I can find the necessary complete data mentioned above for com- 
: : L 
paratively few substances. The value of r — woe such substances 
whose data are accessible to me will be computed and appended. 

1 Phil. Trans. 178, 908 (1891), Winkelmann, p. 934. 
