On the Mean free Path of the Molecules. Ill 



is that which leads to Fechner's law. It is possible that this 

 law may not be accurately and rigorously true : that would 

 only be to say that our fundamental hypotheses err in the 

 same manner, which is not at all improbable. But until ex- 

 periments of a far more careful and extensive character than 

 any yet made come to decide the question, we may take Fech- 

 ner's law to be highly probable. 



This law will always probably be best led up to by the phy- 

 siological reasoning commonly employed. But I have thought 

 it not useless to examine the consequences of the various ele- 

 mentary assumptions as to the measure of the sensation of 

 sound, from a different point of view. 



P.S. — Since the above was written, my attention has been 

 drawn to an experimental verification of Fechner's law, for 

 the sounds produced by falling weights (Carl Norr, Zeitschrift 

 fur Biologie, 1879, p. 297). 



XXIV. On the Mean free Path of the Molecules. 

 By N. D. C. Hodges*. 



THE free path of a molecule is dependent on the amount 

 of obstruction it meets with, or the density of the medium. 

 0. E. Meyer gives for the mean free path (on page 308 of his 



Kinetische Theorie der Gase) , L = _ ^ n . Here N is the num- 



ber of molecules in the unit volume. 



I consider the length of path in a medium of variable den- 

 sity. At the surface of a liquid, if there is no sharp transition 

 from the liquid to the gaseous state, we shall have a succession 

 of layers of less and less dense vapours, from where there is 

 liquid to the surrounding atmosphere. The layers V are what 

 I refer to. The depth of these vapours is, of course, much 

 magnified. 



I propose to find the pressure upon the particle p, when the 

 surface of the liquid is plane and when it is spherical. Taking 

 the molecules moving with any definite velocity, they will 

 reach p and give it an impulse when they are at a distance 

 from p less than their mean free path. Now the molecules 

 from below come from denser layers than those from above. 

 A greater number will come from below than from above ; 

 there will be a tendency to drive p upward. To find this ten- 

 dency, we must find how much denser the lower layers, from 



* Communicated "by the Author. 



