250 Mr. William Sutherland on the 



But if W is the total mass in the vessel, then 



W = iir^p/3, 



and we get 



Wa7rp{31og2R/a-4}. 





When W = 1 the first term of this becomes identical with the 

 value of the internal virial previously given, with 2R written 

 instead of L. Eeplacing E by its value in terms of W and p, 

 we get for the internal virial of mass W, 



WAirp(\og 6W/7rpa 3 -4:). 



As pa 3 is constant, we see that for a given mass the internal 

 virial for molecular force varying inversely as the fourth 

 power is rigorously proportional to the density, but it is not 

 purely proportional to the mass. Although the number 

 6W/7rpa 6 is a large one, and has a logarithm varying slowly 

 with W, yet large enough variations in W can affect it 

 appreciably, as we see if provisionally we accept Sir W. 

 Thomson's estimate of 2 x 10" 9 centim. as the lowest possible 

 value for a. Suppose nrp = 3, then 6W/7rpa 3 is 10 27 W/4, and 

 if W is 4000, 4, or '004 grin., then the values of log 6W/7rpa 3 

 are as 30, 27, and 24, and we have a larger mass variation of 

 the internal virial than is likely to have escaped detection in 

 its effects, such as a difference in the density, expansion, com- 

 pressibility, latent heat, and saturation-pressures of a liquid as 

 measured on a milligramme, from their values as measured on 

 a kilogramme. The raising of this difficulty suggests to us 

 in passing that there exists a department of microphysics in 

 which little has as yet been done by the experimenter, and 

 that great interest would attach to a research determining 

 when a mass variation of the properties usually spoken of as 

 physical constants actually sets in. 



But meanwhile we must scrutinize more closely the meaning 

 of our last result. According to the views of Laplace (and 

 of the early elasticians), if a plane be drawn dividing a mass 

 of solid or liquid into two parts, then, in consequence of mole- 

 cular force, the one part exercises a resultant attraction on 

 the other, and this has to be statically equilibrated by a 

 pressure (called the molecular or internal pressure) acting 

 across the plane, a conception which is necessary in any purely 

 statical theory of elasticity. Adopting for the moment this 

 mode of viewing things, we see that our result amounts to 

 this, that the internal pressure is measurably greater at the 

 centre of a kilogramme than of a milligramme. 



But if we try to carry out the kinetic theory in its integrity, 



