KINETIC OR MECHANICAL VIEW OF NATURE. 33 



extent these various properties could exist separately or 

 were mutually dependent. 1 



In the domain of sound and light the early part of 

 the century was thus, as we have seen, witness of a 

 useful interpretation of these various modifications as 

 merely different kinds of motion : both were considered 

 to be vibrations, the frequency of which marked the 

 position of a note or a tint in the musical or chromatic 



1 That is to say, the number of 

 independent constants had to be 

 fixed which would permit isotropic 

 or anisotropic bodies (i.e., bodies 

 which are either equal in all direc- 

 tions, or unequal in the three direc- 

 tions) to be mathematically denned, 

 and in consequence their behaviour 

 studied, if subjected to strains and 

 displacements. Over these defini- 

 tions there arose the great contro- 

 versies of those who believed in a 

 small number of constants (one 

 constant in isotropic and fifteen in 

 anisotropic bodies against two and 

 twenty-one respectively). A good 

 account of these controversies and of 

 their mathematical and physical sig- 

 nificance will be found in the first 

 volume of Todhunter's ' History of 

 Elasticity," by Professor Karl Pear- 

 son, p. 496 sqq. The former theory 

 is termed the rari- (few) constant 

 theory, the latter the multi- (many) 

 constant theory. The rari-constant 

 theory is based upon the assump- 

 tion that a body consists of mole- 

 cules, and that the action between 

 two molecules ... is in the line 

 joining them. It is an outcome of 

 the atomic and action - at - a - dis- 

 tance theory in vogue on the Conti- 

 nent, and is accordingly mainly 

 represented by Naiver, Poisson, 

 Cauchy, and others, notably Saint- 

 Venant. The other school, mainly 

 represented by mathematical physi- 

 cists in this country, starts not from 

 a mathematical formula (which, 



VOL. II. 



after all, loses its precision as the 

 active forces are reduced to the 

 vague statement that they act sen- 

 sibly only at insensible distances) 

 but from physical data. It is an 

 analogue to Young's theory of cap- 

 illarity as against Laplace (see 

 above, p. 20, note). "The some- 

 what unsatisfactory nature of the 

 results of those investigations pro- 

 duced, especially in this country, a 

 reaction in favour of the opposite 

 method of treating bodies as if they 

 were, so far at least as our experi- 

 ments are concerned, truly continu- 

 ous. This method, in the hands of 

 Green, Stokes, and others, has led 

 to results the value of which does 

 not at all depend on what theory 

 we adopt as to the ultimate con- 

 stitution of bodies " (Clerk Maxwell, 

 ' Scientific Papers,' vol. ii. p. 253). 

 " After the French mathematicians 

 had attempted, with more or less 

 ingenuity, to construct a theory of 

 elastic solids from the hypothesis 

 that they consist of atoms in equi- 

 librium under the action of their 

 mutual forces, Stokes and others 

 showed that all the results of this 

 hypothesis, so far at least as they 

 agreed with facts, might be deduced 

 from the postulate that elastic 

 bodies exist, and from the hypoth- 

 esis that the smallest portions into 

 which we can divide them are 

 sensibly homogeneous" (id. ibid., 

 p. 449). 



