416 



SCIENCE. 



[N. S. Vol. II. No. 39. 



it. Huygens pursued the second method, with- 

 out at all restricting himself to it." (p. 250.) 



When we recollect that the adoption of ' work ' 

 as the fundamental concept of mechanics by J. 

 R. Mayer, scarce a half century ago, was the 

 introduction of modern ^^ews and methods in 

 physics, and that when Professors Clifford and 

 Tait, in still more recent times, were wont to 

 dwell upon the consideration of force as a space- 

 rate of change in work or energy (or potential), 

 their ideas were regarded as novel and rather 

 disturbing, it is reft-eshing to find Huygens 

 ranged alongside of the nineteenth century 

 physicists, though chronologically sandwiched 

 between Galileo, who founded the science of 

 dynamics, and Newton, of whom the author 

 says, 'since his time no essentially new principle 

 has been stated.' But, as Professor Mach re- 

 minds us, Huygens' principle was by no means 

 well received by his contemporaries, notwith- 

 standing it was his chief performance. 



Naturally the achievements of Newton come 

 in for the largest share of attention. The ex- 

 tent of his achievements aud the profound and 

 lasting impression which they made upon sci- 

 ence compel, in any critic, the most searching 

 scrutiny. It is necessary, too, to distinguish 

 those discoveries and reflections which are New- 

 ton's OAvn from those which he accepted from 

 his predecessors and made more available by 

 his clear perception of their relation to physical 

 science in general and by his lucid formulation 

 of them in laws and principles. This distinc- 

 tion has been made many a time, and doubtless 

 many a one has wished to protest against cer- 

 tain of Newton's views, but it must be admitted 

 that except for the old fashioned form of his 

 statements, and the geometrical form of the 

 demonstrations, surprisingly little of his writ- 

 ings has been altered to advantage. So far as 

 his investigations are confined to facts, with ab- 

 stention from every form of speculation, that 

 is, so far as he conforms strictly to his assertion 

 that he does not frame hypotheses. Professor 

 Mach finds little but pleasure in his great work, 

 and only objects to its form. But in his famous 

 view concerning absolute time, space and mo- 

 tion, Newton departs from a consideration of 

 pliysical facts, enters into psychology and, in 

 the estimation of the author, makes statements 



and distinctions that are not justifiable and 

 which he criticises severely. Yet after reading 

 the fifty pages or more that are devoted to the 

 rather unfavorable consideration of Newton's 

 fundamental statements in mechanics, one can- 

 not help feeling that the last word on the sub- 

 ject has by no means been said. When the 

 author says, " We arrive at the idea of time, to 

 express it briefly and popularly, by the connec- 

 tion of that which is contained in the province of 

 our memory with that which is contained in 

 the province of our sense perception," we feel 

 that Maxwell's statement that the idea of time 

 originated probably ' in the recognition of an 

 order of sequence in our states of consciousness ' 

 is an improvement in form upon the author's, 

 and is more satisfactory, while conforming much 

 more nearly to the Newtonian conceptions. As 

 substitutes for Newton's enunciations Professor 

 Mach offers three experimental propositions and 

 two definitions as being 'much more simple, 

 methodically better arranged, and more satis- 

 factory. ' In so far as his criticisms are endorsed 

 the substitute propositions might be approved 

 in substance, but their form savors of pedantry 

 and they have the defect of excessive concise- 

 ness ; they are therefore technical, and in con- 

 sequence they require, each on its own account, 

 a good deal of explanation. They can only be 

 called simple for those who are already pretty 

 well aware of what they state, but they pre- 

 pare us for the remark: "We join with the 

 eminent physicists Thomson and Tait in our 

 reverence and admiration of Newton. But 

 we can only comprehend with difficulty their 

 opinion that the Newtonian doctrines still 

 remain the best and most philosophical foun- 

 dation of the science that can be given." (p. 

 245.) 



A chapter is devoted to the extension of the 

 principles, in which the reader will find an in- 

 teresting treatment of the controversy between 

 Descartes and Leibnitz, with their respective fol- 

 lowings, over the conservation of momentum 

 and of vis viiKi, with D'Alembert's final adjust- 

 ment of it. The merits of D'Alembert's principle 

 are enlarged upon we think justly, it being shown 

 to embody within it all that is involved in Gauss' 

 priviciple of least constraint. The work abounds 

 in such comparisons and analyses as, after an 



