•888 Mr. Wilson Taylor on the Coalescence oj 



therefore, take a greater number of molecules in the initial 

 stages of the condensation to produce the same amount of 

 heat, which would account for the larger values of N for 

 these substances. Another cause may be in the long range 

 of temperature for which these substances are liquids. 



It would appear, then, that the undetermined elements of 

 these experimental data point to the idea that, if we knew 

 the true values of T m , p , and L for all stable substances, the 

 value of N calculated as indicated in our formula would be 

 the true Avogadro's number, which would be a little greater 

 than that obtained in the table for water. Also, the evidence 

 from the data more carefully selected by Hammick points, 

 under the same conditions and with the same limitations, to 

 the same conclusion. 



Assuming, therefore, that the conclusion is justifiable, we 

 have, by equating the two expressions for the potential 

 surface energy of the free molecule, 



In 



LJ/-=T m X7rJ 2 , 

 / m 



from which 



_ / /?iLJ \ 

 ~UT m NJ 



This on substituting for LJ the value obtained previously 

 reduces to 



The value of d will thus depend upon the value of p Q and 

 will be subject to the same uncertainty as that which belongs 

 to p . However, as p 6 is less than p , d e will be larger 

 than d , so that d 9 may be regarded as the average diameter 

 of the space which the actual molecule whose diameter 

 is d occupies at temperature 0° A. For water w T e are 

 fairly certain that p does not greatly exceed 1 and is not 

 less than 1. The formula gives for water, where /o =l, 

 ^ = 3*85 x 10"" 8 . For mercury, where p is taken equal to 

 14'25, d = 3'56 x 10" 8 . As p e decreases with rising tempera- 

 ture, d e increases, thus making room for the heat vibrations 

 of the real molecule in the solid or liquid. 



The following is a brief summary of the views presented 

 in the preceding pages : — 



(a) Latent heat is the surface energy of the free molecules 

 of the substance in its gaseous state. 



