472 Lord Rayleigh on the 



egale le produit de l'attraction au contact par le volume, on, 

 ce qui equivant, le travail de desagregation totale de Funite 

 de volume egale l'attraction au contact." Attraction au 

 contact here means what we have called intrinsic pressure.' 

 The following reasoning is substantially that of Dupre. 



We have seen (2) that 27rmafy(z) represents the attraction 

 of a particle m placed at distance z from the plane surface of 

 an infinite solid whose density is or. The work required to 

 carry m from z~0 to z — x> is therefore 



r% 00 



27rmo- I ylr(z)dz = maJL , 



In 



by (4) ; so that the work necessary to separate a superficial 

 layer of thickness dz from the rest of the mass and to carry 

 it beyond the range of the attraction is a 2 dzK Q . The com- 

 plete disaggregation of unit of volume into infinitesimal slices 

 demands accordingly an amount of work represented by 

 o- 2 K , or K. The work required further to separate the 

 infinitesimal slices into component filaments or particles and 

 to remove them beyond the range of the mutual attraction is 

 negligible in the limit, so that K is the total work of complete 

 disaggregation. 



A second law formulated by Dupre is more difficult to 

 accept. " Pour un meme corps prenant des volumes varies, 

 le travail de desagregation restant a accomplir est propor- 

 tionel a la densite ou en raison inverse du volume." The 

 argument is that the work remaining to be done upon a given 

 mass at any stage of the expansion is proportional first to the 

 square of the density, and secondly to the actual volume, on 

 the whole therefore inversely as the volume. The criticism 

 that I am inclined to make here is that Dupre's theory 

 attempts either too little or too much. If we keep strictly 

 within the lines of Laplace's theory the question here dis- 

 cussed cannot arise, because the body is supposed to be 

 incompressible. That bodies are in fact compressible may 

 be so much the worse for Laplace's theory, but I apprehend 

 that the defect cannot be remedied without a more extensive 

 modification than Dupre attempts. In particular, it would 

 be necessary to take into account the work of compression. 

 We cannot leave the attractive forces unbalanced ; and the 

 work of the repulsive forces can only be neglected upon the 

 hypothesis that the compressibility itself is negligible. Indeed 

 it seems to me, that a large part of Dupre's work, important 

 and suggestive as it is, is open to a fundamental objection. 

 He makes free use of the two laws of thermodynamics, and 

 at the same time rests upon a molecular theory which is too 

 narrow to hold them. One is driven to ask what is the real 



