A.— MATHEMATICAL AND PHYSICAL SCIENCES 29 



which sufficed to describe, succinctly and clearly, the series of perceptions 

 involved in such phenomena as the motion of a pendulum, a billiard 

 ball, a railway carriage, and (with certain reservations concerning fine 

 points) the complex motions of the bodies of the solar system. The 

 physical science of the eighteenth and nineteenth centuries was occupied 

 in extending and clarifying these concepts, although eighteenth-century 

 science in England was hampered by an excessive devotion to the memory 

 of Newton, which committed the English mathematicians to the fluxional 

 notation. It required the formation of a society at Cambridge ' to 

 inculcate the principles of pure J-ism, and to rescue the University from 

 its dot-age,' before the British physical school could rival the advances 

 of their continental brethren. 



As we have said, the attitude of the physicist to the fundamentals of 

 his science was, in general, naively realistic. Mass was quantity of 

 matter, and matter itself was defined as ' that which can be acted upon 

 by, or can exert force,' or alternatively ' that which may have energy 

 communicated to it from other matter.' Obscurum per obscurius, with a 

 vengeance ! 



Quantitatively, mass was defined, following Newton, as the product 

 of volume and density ; and even Thomson and Tait are roused to a hint 

 (without attempting to resolve the difficulty) that such a process results 

 in a circular argument, inasmuch as we have no other way of defining 

 density than as the ratio of mass to volume. 



Early in the nineteenth century discoveries, mainly in the realm of 

 chemistry, gave fresh interest to atomic doctrines, and the simple concept 

 of the billiard-ball atom proved to be brilliantly successful in explaining 

 old happenings and in predicting new ones. It is not immediately 

 obvious that an extrapolation of those laws which described the motions 

 of bodies of the dimensions of a locomotive or a planet down to bodies 

 of the indescribably minute dimensions given to an atom or molecule is 

 likely to be successful in subsuming certain perceptual events ; the 

 extraordinary thing is, not that such an extrapolation should break down 

 somewhere, but that it should have any validity at all. And the triumphs 

 to be put to the credit of the hypothesis are sufficiently remarkable, 

 as afty treatise on the kinetic theory of gases will testify. 



It is an odd fact that these days of probability and indeterminacy 

 mark a period in which atomic and molecular constants have been 

 evaluated to a degree of accuracy of which electrical standards need 

 hardly be ashamed. And we may perhaps be pardoned a little local 

 patriotism when we remember that a Manchester man, James Prescott 

 Joule, made the first determination of an absolute molecular magnitude — 

 the mean speed of a hydrogen molecule, which he evaluated as 6,055 ft- 

 per second at the freezing point of water. This paper, which was 

 published in 1848, is not the paper which was denied publication in 

 extenso by the Royal Society, concerning whose refusal Joule remarked 

 to Schuster, ' I was not surprised. I could imagine these gentlemen in 

 London sitting round a table and saying to each other : " What good can 

 come out of a town where they dine in the middle of the day ? " That 

 particular paper dates back to 1840, and marks an important stage in the 



