488 Notices respecting New Books. 



space a substance ; thereby all but reproducing one of the wildest 

 vagaries of Descartes, though from a totally different point of view 

 and for a totally different purpose. The remarks of Clerk-Maxwell 

 on this subject are well worthy of reproduction here. He says : — 



" When a man has acquired the habit of putting words together, with- 

 out troubling himself to form the thoughts which ought to correspond 

 to them, it is easy for him to frame an antithesis between this relative 

 knowledge and a so-called absolute knowledge, and to point out our igno- 

 rance of the absolute position of a point as an instance of the limitation of 

 our faculties. Any one, however, who will try to imagine the state of a 

 mind conscious of knowing the absolute position of a point will, ever after, 

 be content with our relative knowledge." 



But, granting at once the truth of this remark, in what sense are 

 we to understand the First Law of Motion ? As Newton gives it, 

 it runs : — 



(i Corpus omne perseverare in statu suo vel quiescendi vel movendi unifor- 

 miter in directum, nisi quatenus illud a viribus impressis cogitur statum ilium 

 mutareP 



There are here two difficulties, one of which is double-headed : — 

 (1) The nature of Force (vis impressa) ; (2) Uniform motion in a 

 straight line, of which rest is merely one particular case. We will 

 defer, for a moment, the consideration of (1). As to (2), since we 

 can conceive of relative motion only, what must be the properties 

 of the system, relative to which a body unacted on by forces moves 

 uniformly in a straight line ? And this difficulty involves another, 

 which may be stated in either of two forms — What is uniform 

 motion? or, How can we compare intervals of time? The latter 

 difficulty is shown to have been fully overcome by D'Alembert, 

 though the first precise exposition of his method is due to Poisson. 



The reference-body (Fundamental-Korper) required for the 

 Galilei-principle is then shown to be any body, unacted on by force 

 and free from rotation. 



[Newton had shown, in the Principia, how to detect by physical 

 processes the existence, and the sense, of absolute rotation ; but his 

 hope that something similar might possibly be done for absolute trans- 

 lation seems to be quite unrealizable.] 



It is shown that any number of such bodies necessarily behave 

 Galilei-wise with regard to one another, and therefore that any one 

 of them may be taken as a reference-body ; while three lines, fixed 

 in it and mutually at right angles, supply the requisite system of 

 coordinates (Fundamental-System), There can be no doubt of the 

 accuracy of these results ; but they follow so directly from the mere 

 inspection of the differential equations, formed as a translation of 

 Newton's words, that the proof given by the author is unnecessarily 

 tedious. 



The author, however, seems to be the only one who has of late 

 years taken the trouble to master the history of this part of the 

 subject (save, perhaps, Diihring ; but all his writings show extrava- 

 gant bias) ; and, though we cannot estimate at quite so high a 

 value as he himself seems to put on them, the originality and the 



