Josiah Willard Gibbs. 281 



they had done in a more moderate degree over Maxwell, the interpreter 

 of Faraday in this respect ; his generalising tendency was illustrated 

 in the formal address, in which he expounded to the American 

 Association the fascinations of the mathematical notations and opera- 

 tions appropriate to this subject, where he could not reach finality until 

 his treatment had got into n dimensions of space. This bent towards 

 exhaustive survey of his subject probably served Gibbs in good stead, 

 l)y driving him to mathematical completeness in his exposition of 

 thermodynamics, where others would have stopped short with the 

 fragment of the theory that covered the physical applications then 

 prominent or likely to arise. But his tendency to wind up the 

 exposition and regard the account as closed when the logical fabric has 

 l>een welded together, and to assign a subsidiary place to the details of 

 such particular physical illustrations as then existed from restraint, 

 be it noted, not from lack of knowledge retarded for many years the 

 application of his methods by experimenters, to whom the behaviour of 

 actual things is of more interest than the perfection of an abstract 

 formulation of their relations. 



The achievement by which Prof. Gibbs will chiefly be remembered 

 as his development, into their full scope, of the fundamental principles 

 which regulate equilibrium and the trend of transformation in inanimate 

 matter in bulk, that is, in general chemical and physical phenomena. 



The laws of mechanical equilibrium of material systems, when 

 constitution and physical state remain unaltered, have received 

 attention ever since the ancient beginnings of the science of Statics. 

 Their co-ordination was fruitfully considered by Galileo, who fixed 

 his attention on the indications then current of a general law of 

 compensation in mechanical transformations, revealing itself in the rule 

 that what is gained in force is usually lost in the distance over which 

 it operates. This principle of conservation of work, for all possible 

 virtual displacements, in balanced frictionless systems, was afterwards 

 briefly noted in a form independent of special systems, by Newton ; it 

 appeared as a generalisation of the third of his " Axiomata," or funda- 

 mental unresolvable laws of inertia and motion, which asserted that 

 to every intrinsic dynamical action of one part of a system on another 

 there is an equivalent (or compensating) reaction of the second part on 

 the first. After this idea of compensation in mechanical work had 

 become more familiar, in connexion with special problems of increasing 

 complexity, during the succeeding century, the thread of Newton's 

 brief generalisation was again picked up by Lagrange, who, in the 

 "Mecanique Analytique," made this principle of work the unique 

 foundation of all statics that is, of the dynamics of steady systems 

 thus, as he expressed it, eliminating from the general principles of 



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