Laws of Molecular Force. 289 



fraction-equivalent is a function of the two variables only, 

 namely, the volume of the atom and the velocity of light 

 through it. Now we have seen that the expression M% as a 

 whole, in one aspect appears to be not dependent directly on 

 the molecular mass M, seeing that M 2 l can be represented in 

 terms of certain quantities which we have called dynic equi- 

 valents. Hence, as I is proportional to A in our expression 

 3Am 2 /r 4 for molecular force, we see that in one aspect mole- 

 cular force seems to be not directly dependent on the mass of 

 the attracting molecules ; and yet, on the other hand, in con- 

 sidering solutions we found that the quantity A asserted its 

 individuality as separate from the whole expression Am 2 , so 

 that in another aspect there does appear to be a mass action 

 in the attraction of two molecules. However, regarding 

 M 2 Z or Am 2 as a whole, the simplest hypothesis we can make 

 about the mutual action of molecules is that it depends most 

 on the size of the molecules. This would make Am 2 a simple 

 function of U ; so that the dynic and refraction equivalents 

 would have this in common, that they are both simple functions 

 of U. Suppose, now, that the velocity of light through all 

 matter in the chemically combined state is approximately the 

 same, or that N is approximately the same for all atoms as 

 constituents of compound molecules, then the refraction-equi- 

 valents given by Gladstone are directly proportional to the 

 volumes of the atoms in the combined state, and then the 

 parallelism between dynic and refraction equivalents would 

 mean that S is nearly proportional to the volume. It is very 

 interesting, therefore, to inquire briefly whether there is any 

 evidence to prove that Gladstone's refraction-equivalents are 

 proportional to the volumes of the atoms ; and I think that 

 in Kohlrausch's velocities of the ions in electrolysis we have 

 such evidence. If different solutions, such as those of KC1, 

 NaCl, or ^BaC^ 2 re electrolysed under identical circum- 

 stances, then we knosv, according to Faraday's law, that 

 each atom of K and of Sa, and each half-atom of Ba, may be 

 considered to receive the same charge, so that they acquire 

 their ionic speeds under the action of the same accelerating 

 force. Accordingly, the ionic speed characteristic of an atom is 

 reached when the " frictional " resistance to its motion is equal 

 to this accelerating force ; hence the " frictional " resistance is 

 the same for all atoms, or rather for all electrochemical equi- 

 valents. Now the " frictional " resistance will be a function 

 of the velocity of the atom and of its domain (atomic volume) 

 and of its actual volume as well as of the domain and actual 

 volume of the molecule of the solvent ; but if water is the 

 solvent in all cases, the only quantities which vary from body 



