786 



NATURE 



[August i8, 1921 



Cohesion. 



By Dr. Herbert Chatley. 



WHEN one turns from an account of the dis- 

 covery of a " dark star " by celestial 

 •dynamics to an investigation of the properties of 

 the excessively minute whirling electrons in an 

 atom, the impression is gained that within these 

 limits at least there is but little more than rela- 

 tively unimportant detail to learn. Such a notion 

 is quite erroneous. More is known of the 

 mechanism of plants on one hand and of 

 electrons on the other than of the most ordi- 

 nary and apparently simple mechanical pheno- 

 mena. The most expert physicist can make only 

 a near guess as to the motion of a billiard ball 

 under given conditions as to stroke, weight, etc., 

 since there is an imperfectly known factor, fric- 

 tion, in the problem. Similarly, although he can 

 calculate with great precision the force with 

 which one piece of iron attracts another when 

 they are a foot apart, he cannot say with any 

 accuracy from first principles what is the tensile 

 strength in each piece of iron. Engineers simi- 

 larly have made countless experiments and have 

 also obtained very many data from constructional 

 experience which give average values from 

 which, by allowing a liberal margin for uncer- 

 tainty, structures can be safely designed ; but that 

 is all. 



Doubt still prevails as to the nature and 

 laws of the force or forces causing cohesion. 

 Lord Kelvin concluded that Newtonian gravi- 

 tation would explain cohesion if it be sup- 

 posed that the particles are exceedingly close. 

 Sutherland and Nernst have regarded cohesion 

 as identical with chemical affinity, and therefore 

 with electrostatic force. Tolver Preston believed 

 it was due to some mvsterious dynamic action 

 arising from the oscillation of the particles. 

 Crehore, an American physicist, deduces it from 

 a residual electromagnetic effect of the omnipotent 

 electrons. Most recent students, following 

 Sutherland, regard it as a residual electrostatic 

 effect of the opposed charges in the atoms which, 

 although in electrical equilibrium, are not coin- 

 cident in space; some, however, prefer to con- 

 sider it as largely electromagnetic. 



The only satisfactory method of commencing 

 a scientific investigation is to state all the known 

 particulars and formulate hypotheses on the basis 

 of the apparent facts. Proceeding so, we may 

 note that : — 



(i) All solids, being such, cohere to an extent 

 which changes with their composition, physical 

 structure, and temperature. Broadlv speaking, 

 cohesion varies with density and decreases 

 with increase of temperature. It is quantitatively 

 of the order of one millionth of a dvne per mole- 

 cular pair. 



(2) The range within which cohesion is effec- 

 tive is very small, not greatly exceeding one mole- 



NO. 2703, VOL. 107] 



cular diameter. Two pieces of material when 

 pressed together cohere only when great force is 

 used, if they are very highly polished or if they 

 are so soft that they readily interpenetrate. 

 Solids, with very few exceptions, break by tension 

 when stretched 25 per cent, of their length, imply- 

 ing that the particles need to be separated only by 

 less than one-and-a-quarter times the usual dis- 

 tance from centre to centre for cohesion to become 

 inappreciable. Even the exceptional substances, 

 such as rubber, break when stretched but little 

 more than twice their length, and do not change 

 much in volume. Solids at the fusing point 

 become liquid with negligible change of tempera- 

 ture and only from 5 to 10 per cent, increase of 

 volume. 



(3) Solids in general, with the exception of the 

 so-called plastic materials, extend with tension 

 and shorten with compression proportionately to 

 the force employed within certain " elastic limits," 

 and are stable within those limits. The volumes 

 insrease slightly up to the elastic limits. 



(4) Beyond the elastic limits the tensile and 

 compressive strengths increase but slightly, and 

 when the strain (extension or compression) 

 becomes appreciable the strengths decrease. 



(5) Liquids and gases show a slight " molecular 

 pressure " or internal attraction, varying approxi- 

 mately as the inverse fourth power of the dis- 

 tances between the centres of the molecules. 



It should perhaps be pointed out that an incon- 

 sistency is involved in the notion of " failure by 

 compression." It is obvious that compression 

 can do nothing but bring the particles into closer 

 proximity, and if lateral expansion is prevented 

 ultimate failure is inconceivable unless there are 

 internal voids. Ordinary compression causes 

 failure either by oblique sliding (" shear ") or 

 by lateral expansion. 



It is required, then, to find a force which 

 has no external resultant under natural con- 

 ditions (save perhaps the normal gravita- 

 tional attraction), resists tension and com- 

 pression proportionately to the displacement 

 of the particles for small ranges, and has but a 

 limited power to resist tension which ceases at a 

 moderate range and a great power of resisting 

 compression. It is difficult to conceive of one 

 force having all these properties, but perfectly 

 simple to imagine an attraction and repulsion 

 combined that will do so, provided that the attrac- 

 iion decreases more slowly with separation than 

 the repulsion. A series of papers by the present 

 writer to the Phvsical Societv of London (1915- 

 19) and a paper in the Phil. Mag. (August, 1920) 

 attempt to deal with the problem on these lines. 

 When the solid is at rest the attractions and 

 repulsions balance. If a tensile force is applied 

 the particles are separated, but since the attrac- 



