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XX1U. On Cohesion. By Herbert Chatley, D.Sc. (LoncL), 

 Harbour Investigation Office, Huangpu Conservancy Board, 

 Shanghai, China *. 



fl^HE objects of this note are as follow : — 



(1) To disprove the Kelvin theory of Newtonian 



cohesion. 



(2) To indicate dimensional relations of cohesion to 



gravitation and electric chemical affinity. 



(3) To suggest an empirical gravitation-cohesion formula. 



(4) To indicate cohesion values in certain hydrogels. 



(1) Kelvin's theory of Newtonian cohesion f states that 

 " Cohesion will be a necessary consequence of gravitational 

 attraction provided only that the space occupied by the 

 atoms of a material body is sufficiently small in comparison 

 with its bulk" (de Tunztdman).- 



If two cubes in " perfect contact " be considered, each can 

 be imagined to consist of three sets of n straight bars, each 

 set mutually perpendicular. The bars perpendicular to the 



interface each have a mass "— of the original mass of either 



cube, and "however small may be the masses of two such 

 bars, the attraction between them, per unit of sectional 

 area, may be increased without limit by diminishing the 

 sectional area of the two bars while keeping their masses 

 constant. Now, the total attraction between the two groups 

 (of bars) is greater than the sum of the attractions between 

 the pairs, that is to say, greater than n times the attraction 

 between any pair of conterminous bars. The whole attraction 

 between the two cubes may therefore be made to attain any 

 value, however great, by sufficiently diminishing the sectional 

 area of the bars while keeping their number and the mass of 

 each constant" (author's italics). 



As far as the writer is aware, this reasoning has not been 

 definitely challenged, and has certainly been accepted by 

 many physicists. Nevertheless, it appears not only uncon- 

 vincing but incorrect. The area for which the attraction 

 between two of the postulated conterminous bar elements is 



* Communicated by the Author. 



t Trans. Roy. Soc. Edin. Apr. 21, vol. iv. (1862); Pop. Lect. vol. i. ; 

 Dewar, Encyclovccdia Britannica, 11th ed. Article, "Liquid Gases"; 

 de Tunzelman, 'Electrical Theory and the Problem of the Universe.' 



