ESSAY-REVIEWS 653 



Under the heading General Mechanics are papers on the Sand-blast and 

 on the cutting and chipping of glass. Both of these illustrate the interest 

 he felt in simple processes. In the former (No. 386), after quoting far-reaching 

 ^statements of Thomas Young ^ and Osborne Reynolds,^ he proceeds to show, 

 by an application of the method of dimensions, that when two spheres collide 

 the maximum strain is independent of the linear scale, and if rupture depends 

 only upon the maximum strain it is as likely to occur with small spheres as with 

 large ones. The most interesting case is when one sphere is very large 

 relatively to the other, as when a grain of sand impinges upon a glass surface. 

 If the velocity of impact is given the glass is as likely to be broken by a small 

 grain as by a much larger one. But he explicitly recognises that this con- 

 clusion would be upset if rupture depends upon the duration of a strain 

 as well as upon its magnitude. In the paper on glass (No. 417) he asks for 

 information on the theory of the cutting of glass by a diamond in addition 

 to that given in a very suggestive statement by Wollaston ^ ; though at the 

 same time he throws out the warning " that it may be as well to remember 

 W. Taylor's saying that everything calculated by theorists is concerned with 

 what happens within the elastic limit of the material, and everytliing done 

 in the workshop lies beyond that limit." It appears that " the force trans- 

 mitted across internal surfaces parallel to the external surfaces is a pressure 

 all along, but the force transmitted in a perpendicular direction, although 

 at first a pressure, at a very small distance below changes to a tension, which 

 soon reaches a maximum and afterwards gradually diminishes. I suppose 

 it is this tension which determines the crack. . . ." With regard to the 

 chipping of glass by a film of gelatine allowed to dry on it, surprise is 

 expressed that a film of gelatine, scarcely thicker than thick paper, should 

 be " able to tear out fragments of solid glass, but there is no doubt of the 

 fact." 



On the theory of Capillarity there is practically nothing in this volume. 

 This is the more to be regretted because, in his earlier contributions, while 

 he wrote interestingly and in an illuminative way on the theory as founded 

 by Laplace, he never advanced beyond the consideration of continuous 

 [i.e. non-molecular) media. The Dutch School has made a tremendous 

 advance by recognising that the centres of molecules never approach to less 

 than a diameter apart, measured from centre to centre. Some of the in- 

 tegrations which are made in calculating the capillary constant from the 

 attractions between molecules require, in consequence, a lower limit equal 

 to this diameter instead of zero. The consequence is that Rayleigh's objection 

 to a power law for this attraction, that it involves infinite values for all powers, 

 breaks down completely. Objection can only be raised to inverse powers 

 equal to or less than five. It would seem (from a letter from him to the 

 present writer) that he was rather oppressed by a sense of the difficulties 

 in treating the molecular dynamics of liquids in an adequate fashion. His 

 only contribution in this volume is contained in a paper on the lubricating 

 and other properties of thin, oily films (No. 429). Recalling the probability 

 that the point at which surface tension begins to fall corresponds to a thickness 

 of asingle layer of molecules (given first Phil. Mag., vol. xlviii, p. 321 (1899)), he 

 states : "It seems pretty clear that, from pure oil, water will only take a 

 layer one molecule thick. But when oleic acid is available, a further drop 

 of tension ensues. The question arises, how does this oleic acid distribute 

 itself ? Is it in substitution for the molecules of oil or an addition to them 

 constituting a second layer ? The latter seems the more probable. Again, 

 how does the impurity act when it leads the general mass into the unstable 

 fiattened-out form ? In considering such questions Laplace's theory is of 



1 Natural Philosophy (1807). 



2 Phil. Mag., vol. xlvi, p. 337 (1S73). 



3 Phil. Tracts., 1816, 265. 



