140 



SCIENTIFIC THOUGHT. 



had employed before. How little these ideas, which 

 have now been introduced into elementary text-books 

 as the very alphabet of physical knowledge, commended 

 themselves in that age, except to a few intellects that 

 had been occupied for many years trying to fix precise 

 terms which should be capable of mathematical defini- 

 tion, and at the same time correspond to common-sense 

 experience, is evident, inter multa alia, from the criti- 

 cism by Sir John Herschel in 1866,^ Here it is 

 maintained that the use of the term " potential energy " 

 " is unfortunate, inasmuch as it goes to substitute a 



425. A very complete and careful 

 historical account of the gradual 

 invention and crystallisation of the 

 vocabulary of the energy concep- 

 tion is given by Helm, ' Die Lehre 

 von der Energie,' Leipzig, 1887, p. 

 36 sqq. 



^ The passage quoted appears in 

 an article " On the Origin of Force," 

 by Sir John Herschel, in the first 

 volume of the ' F'ortnightly Re- 

 view,' 1865, p. 439. The article is 

 well worth reading for those who 

 wish to realise the enormous benefit 

 which has been rendered to science 

 by banishing the indefinite use of 

 the word force and by introducing 

 the term energy, restricting the use 

 of force to the meaning attached to 

 it by Newton. Sir John Herschel 

 still speaks of the ' ' conservation of 

 force " (as did likewise Helmholtz, 

 who, however, very early introduces 

 the term Arbeitskraft, power to do 

 work, thus removing all ambiguity). 

 Rankine replied to Herschel's criti- 

 cism in a paper read before the 

 Glasgow Philosophical Societj^ 23rd 

 January 1867 (reprinted in 'Mis- 

 cell. Scient. Papers,' p. 229 sqq.) 

 He there states that the quantity 

 itself occurs as a mathematical sj-m- 

 bol in Newton's ' Principia ' (prop. 

 39), but till recently had received 



no appropriate name. He closes his 

 remarks by the still more import- 

 ant reflection : " One of the chief 

 objects of mathematical physics is 

 to ascertain, by the help of experi- 

 ment and observation, what phy- 

 sical quantities or functions are 

 'conserved.'" As such he enum- 

 erates mass, resultant momentum, 

 resultant angular momentum, 

 total energy, thermo-dynamic func- 

 tion. Whilst this physical problem 

 was being defined by Rankine, 

 Cayley, Sylvester, and Hermite 

 were working at the corresponding 

 problem in pure mathematics to 

 decide what properties or quanti- 

 ties remain unaltered {i.e., in- 

 variant), if an arrangement of 

 several algebraical symbols is sub- 

 jected to algebraical operations. 

 It is the modern doctrine of " in- 

 variants." This doctrine has led to 

 an enormous extension and simpli- 

 fication of the theory of mathema- 

 tical forms or quantics. It is the 

 key to all mathematical tactics, and 

 prepares a useful instrument for 

 the application of mathematics to 

 physical problems. See Major Mac- 

 Mahon's Address to the Mathema- 

 tical Section of the British Associa- 

 tion, Glasgow, 1891. 



