Dr. H. Chatley on Cohesion. 215 



infinity when 8 = 0, and alludes lo this in the words "perfect 

 contact" ; but it is quite certain that 8 cannot be less than 

 the distance between the centres of the atoms (because it 

 may be taken anywhere when considering a solid piece). 

 This consideration appears to the writer a clear disproof of 

 Kelvin's hypothesis, and shows that cohesion immensely 

 exceeds Newtonian gravitation. 



[%) Van der Waals's gas formula indicates that the 

 " molecular pressure " per molecule pair varies inversely as 

 the inverse fourth power of the distance between the mole- 

 cules *. The mere existence of the fluid phase at almost the 

 same temperature as the solid pliase of the same substance 

 with only very slight expansion also seems to show that the 

 rate of diminution of the cohesive forces is higher than the 

 inverse square. 



If the space variation is higher than the inverse square, 

 then the additive effect of distant atoms in the solid is much 

 less important and even negligible, so that the forces per 

 atom pair may be considered as indicating roughly the actual 

 bonds between the atoms. In the case of the special steels 

 referred to above, if the number of atoms per sq. cm. is 10 15 , 

 the ultimate tension at rupture (with less than 5 per cent. 

 mean separation of the atoms) is over 10" 5 dyne per atom 

 pair. 



As Sutherland has pointed out, pairs of electron doublets 

 at atomic distances may have differential attractions of this 

 order at close proximity. The electrostatic bond of a 

 doublet is of the order . 



2xlO- 19 -H(10- 8 ) 2 = 10- 3 dyne, 



and differential effects may easily exceed 10 ~ 5 dyne at 

 small distances. There does not, on the other hand, seem 

 to be a complete basis in the Sutherland theory for the 

 chemically indifferent character of cohesion (as distinguished 

 from adhesion). Van der Waals's gas formula also implies 

 that " molecular pressure " is to some extent a function of 

 mass. 



The writer suggests that, as far as the fragmentary 

 information goes, it may be stated that cohesive forces are 

 less, but not greatly less, than the electrostatic tractations of 

 chemically active atoms, and that in homogeneous substances 

 they are functions of the mass and positions of the individual 

 atom or a torn -group (molecule). 



Crystallization shows that cohesive forces are vectorized. 



* Chatley, Proc. Phys. Soc. Lond. vol. xxx. pt. iii. April 15, ]918. 



