January 2, 1908J 



NA TURE 



199 



than it is in the complete structure, because in the 

 former case the slab can expand freely, whereas in the 

 other case this lateral expansion is prevented. 



If some portion of the total load was taken by the dam 

 acting as a horizontal beam, this claim would not be 

 challenged by me, but Prof. Pearson states that his pro- 

 position is true independent of any action of this character. 

 On a question of pure mathematics it is no doubt very 

 rash for a mere engineer to differ from Prof. Pearson, 

 but as the point is of great practical importance I make 

 the venture, since the statement appears to me to be 

 opposed to the mathematical theory of elasticity as usually 

 taught. The sole diflference between the two cases lies in 

 the fact that when the slab constitutes a portion of a 

 complete dam it is subject to a certain normal stress 

 which Prof. Pearson calls yy. 



Now the characteristic of this stress is that it produces 

 no appreciable shear in planes parallel to itself or in planes 

 at right angles to itself. In fact, Prof. Pearson states that 

 in both cases we mav put yA: = yc = o, and that xz is 

 identically the same in both cases. 



Consider, then, the slab, taking first the case in which 

 the sides are left free to e.xpand, but in which stresses are 

 produced in it due to the water pressure and its own 

 weight. Taking .v.v as the stress parallel to the horizon 

 and 2z as that parallel to the weight, we have. Prof. 

 Pearson says, the following equations which these must 

 satisfy : — 



c - a~ 



Under these Internal stresses the sides of the slab undergo 

 a displacement v = f{x:), say. This displacement, it should 

 be noted, Is everywhere finite and continuous. 



Now apply, to the slab, forces yy = F(.v3), so distributed as 

 to cancel the above displacement, and we get the conditions 

 of the equilibrium when the slab forms part of a complete 

 dam. 



Next consider these forces yy = F(xs) to act alone. The 

 characteristic of the Internal stress then produced is, as 

 already pointed out, that yA; = y2 = s.i: = o, so that the con- 

 ditions of internal equilibrium reduce to 



? —- 

 ^5— - xx=o 



These and the boundary conditions are obviously 

 satisfied by putting xx = sz = o and yy = F{xs) throughout. 

 If, at the same time, the conditions of continuity are 

 satisfied, this should be the solution. It would seem that 

 the continuity of the material Is necessarily satisfied by 

 the fact that v, the displacement of the surface under the 

 forces. Is everywhere finite and continuous. If I am right 

 in this, the stresses xx and sz should be the same in the 

 complete dam as thev are In the slab, but Prof. Pearson 

 says this Is not the case. H. M. Martin. 



Croydon, December 22, 1907. 



LORD KELVIN: AN APPRECLITION. 



LORD KELVIN occupied for a long time a unique 

 and cosmopolitan position as the universally 

 venerated head of the physical science of the age. 

 Where he did not himself create new knowledge, he 

 constantly inspired discovery. Always accessible, 

 always keenly attracted by the work of others and 

 ready to learn, with universal interests, and mental 

 activities untiring even to the end, he for more than 

 half a century was the main practical scientific influ- 

 ence in this country; while for the latter portion of 

 this period his point of view, through the generous 



NO. 1992, voi . yy] 



advocacy of Helmholtz and other fellow-workers^ be- 

 came naturalised throughout the world. He was re- 

 presentative, more than any other person, of the com- 

 bination of abstract scientific advance and mechanical 

 invention which led to the still recent electrical trans- 

 formation of modern engineering ; he sustained and 

 elevated industrial progress by the fire of intellectual 

 genius. 



In his earliest scientific work he was the interpreter 

 of Faraday, at a time when support and mathematical 

 elucidation of the intuitions of his genius were much 

 required. In addition to special advances of his own 

 into new domains, such as the theoretical prediclion 

 of electric vibrators and their laws fortv years before 

 they were utilised by Hertz, and the assertion of the 

 thermochemical principles controlling voltaic batterie-, 

 he early became the founder, or rather restorer, of a 

 school — the modern British school of physical science — 

 which aims at moulding the course of general physical 

 theories, even of abstract mathematics itself, by aid 

 of intuitions drawn from exact formulation of the ob- 

 served course of nature, assisted by illustrations such 

 as ma}' be gleaned even from the study of artificial 

 practical mechanisms. A typical example of this kind 

 of activity was the vortex theory of the molecular 

 structure of matter, which he built on Helmholtz's 

 fundamental discovery of the absolute permanence of 

 vortical motions in a frictionless fluid medium ; to a 

 superficial view this is now in the main only an aban- 

 doned theory ; but those most conversant with the 

 history of the coordination of physical activities, which 

 is the ultimate aim of the science, will allow that the 

 vortex-atom theory was the first illustration that in- 

 cluded any adequate idea of the type of interaction 

 of the material atoms and the universal a;ther in which 

 they subsist, and as such has been the direct ancestor 

 of all subsequent advances towards the mental repre- 

 sentation of ultimate physical reality. 



In particular Lord Kelvin was the inspirer of Clerk 

 Maxwell, his avowed pupil in all important respects, 

 and was therebv an essential factor in that consoli- 

 dation and reconstruction of physical science, on a 

 refined electric, or subelectric, basis, which is still in 

 progress, and has been a main glory of recent years. 



In another region of his activity he combined deli- 

 cate mathematical methods of investigation with 

 broad industrial application of the results. It was 

 largely the determined and prolonged struggle to carry 

 through to success the enterprise of Atlantic sub- 

 marine telegraphy that led to the invention of those 

 appliances for exact measurement which afterwards 

 made general electrical engineering feasible. In this 

 new branch of applied science, his active perception of 

 the essentials for progress assumed the form of 

 generalship ; most of the details of development natur- 

 ally came from others, but he was always ready to 

 emphasise the salient problems, and to acclaim, early 

 and enthusiastically, such nascent inventions as would 

 be pertinent to their mastery. 



An example of his firm grasp of the connection of 

 theory and practice is afforded by his work on the 

 prediction of the tides. The recognition that the tidal 

 oscillation is compounded of a limited number of 

 simple harmonic constituents, of known periods, was 

 an outgrowth of physical astronomy, and is mainly 

 due to Laplace ; the principle that any oscillatory move- 

 ment arising from permanent causes is resolvable into 

 simple harmonic constituents, and is to be treated on 

 that basis in all exact science, was the fundamental 

 contribution of Fourier. It remained largely for Lord 

 Kelvin to combine these two principles, supplying the 

 mechanical contrivances necessary for rapid computa- 

 tion, and thereby to control all that is requisite to be 

 known about the tides, while avoiding the complexi- 



