654 SCIENCE PROGRESS 



little service, its fundamental postulate of forces operating over distances 

 large in comparison with molecular dimensions being plainly violated." 



A communication to Nature on Breath-figures (No. 353) is delightfully 

 characteristic of the author's love of examining into familiar phenomena. 

 " One of the first things is to disabuse our minds of the idea that anything 

 wiped with an ordinary cloth can possibly be clean." " Quincke employed 

 hot sulphuric acid." " An even better treatment is with hydrofluoric acid, 

 which actually renews the surface of the glass. . . . The parts so treated 

 condense the breath in large laminae, contrasting strongly with the ordinary 

 deposits {i.e. in lens-shaped drops)." 



A difficulty arises in the comparative permanence of breath-figures which 

 often survive wiping with a cloth. " The thought has sometimes occurred to 

 me that the film of grease is not entirely superficial, but penetrates in some 

 degree into the substance of the glass. , . . We know but little of the 

 properties of matter in thin films, which may differ entirely from those of 

 the same substance in mass." 



Attention may also be called to the theory of the capillary tube 



(No. 399)- 



Thirty-four articles on Hydrodynamics form a group surpassing the 

 limitations of a short review. Thirty-two articles (many of them the same) 

 appear under Sound. Amongst those of chiefly theoretical interest is one on 

 iEolian Tones (No. 394). Many are of very great practical importance in 

 connection with the developments of aerial flight. The characteristic feature 

 is the recourse to the theory of dimensions in all these problems. This is 

 indicative of the backward state of the dynamical theory of viscous fluids. 

 A special article in Nature on the principle of simihtude (No. 392) summarises 

 what can be proved by means of this principle. This article gave rise to 

 some discussion in subsequent numbers of Nature, especially in connection 

 with heat problems when the temperature is taken as a thing sui generis. 

 A different set of " dimensions " is obtained if temperature is regarded as 

 measuring the mean kinetic energy of agitation of the molecule. The proba- 

 bility is that the last possible word was not said in this discussion. It would 

 appear that two systems are not completely dynamically similar unless at 

 least the temperature is made to vary in the appropriate manner. In this 

 case no duplicity in sets of dimensions would be obtainable. 



The principle of simihtude is applied in No. 420 to elucidate the laws 

 governing the flow of heat from moving liquids to solids. Considering a 

 liquid enclosed between two parallel plates, one of which is fixed while the 

 other moves parallel to its own plane with a given velocity, v, he shows that 

 the heat, H, transmitted per unit area per unit time is given by — 



H ^^ 



kd T- (av cv\ 

 a \v' K J 



where a is the distance between the plates, 6 the difference of temperature 

 between them, v the kinematic viscosity of the hquid, c the thermal capacity 

 per unit volume, k the thermal conductivity, and F stands for any 

 function of the two fractions inside the brackets. For a given fluid Cv/k is 

 a constant and may be omitted. Dynamic similarity is attained when av is 

 constant ; so that a complete determination of F does not require the 

 variation of both a and v. There is an advantage in keeping a constant, 

 for otherwise any roughness of the surfaces would have to be changed in 

 proportion. The chief object of the paper was to show that the principle 

 assumed by Osborne Reynolds and others (that the passage of heat from solids 

 to liquids moving past them is analogous to that governing the passage of 

 momentum) is not always true. A term in the equation for the fluid motion 

 involving drop of pressure in the fluid is absent from the thermal equation. 

 It is pointed out, however, that the analogy may hold for average values of 



