Mr. R. F. Muirhead on the Laws of Motion. 487 



cal theories. This is the standpoint adopted by Biemann in his 

 epoch-making paper, " Ueber die Hypothesen welche der Geometrie 

 zu Grunde liegen." That space is infinite and that one and only 

 one parallel to a straight line can be drawn through any point, are, 

 it is true, the simplest hypotheses which serve to express our ex- 

 perience ; but, as Helmholtz points out in his tract Ueber die 

 Erhaltung der Kraft, at page 7, the task of theoretical science is 

 only completed when we have proved that our theories are the 

 only ones by which the phenomena can be explained. "Dann 

 ware dieselbe als die nothwendige Begriffsform der Naturauffas- 

 sung erwiesen; es wiirde derselben alsdann also auch objective 

 Wahrheit zuzuschreiben sein." 



In his critique of the second edition of Thomson and Tait's 

 treatise on Natural Philosophy (' Nature,' vol. xx. p. 213), Clerk 

 Maxwell clearly indicates the hypothetical nature of abstract Dy- 

 namics. On p. 214 we read : — " Why, then, should we have any 

 change of method when we pass on from Kinematics to abstract 

 Dynamics ? Why should we find it more difficult to endow moving 

 figures with mass than to endow stationary figures with motion ? 

 The bodies we deal with in abstract Dynamics are just as completely 

 known to us as the figures in Euclid. They have no properties 



whatever, except those which we explicitly assign to them 



We have thus vindicated for figures with mass, and, therefore, for 

 force and stress, impulse and momentum, work and energy, their 

 place in abstract science beside form and motion." 



" The phenomena of real bodies are found to correspond so 

 exactly with the necessary laws of dynamical systems that we can- 

 not help applying the language of Dynamics to real bodies," &c. 



It will be seen that, so far as they go, the above extracts are in 

 complete harmony with the views in this Essay. It is to be re- 

 gretted that these views are not consistently followed out in Clerk 

 Maxwell's book ' Matter and Motion.' In that book, while there are 

 very many clear expositions of particular points, the arrangement is 

 in many parts highly illogical. This has been pointed out to a 

 certain extent by Streintz in his aforementioned book, and the 

 reader of the foregoing Essay will have little difficulty in making 

 further criticisms. 



One point in Maxwell's book (' Matter and Motion ') calls for 

 special notice, viz., his a priori proof of the first law of Motion. 

 This proof rests on the assumption of the impossibility of defining 

 absolute rest. " Hence," he says, " the hypothetical law is with- 

 out meaning unless we admit the possibility of defining absolute 

 rest and absolute velocity." But it is obvious that if the " hypo- 

 thetical law " spoken of (velocity diminishing at a certain rate) 

 corresponded with experience, we should then have, by that very 

 fact, a conception of absolute rest and absolute velocity which 

 would be perfectly intelligible, so that the assumption " absolute 

 rest unintelligible " would not be justified. Thus, Maxwell's con- 

 clusion, " It may thus be shown that the denial of Newton's law is 

 in contradiction to the only system of consistent doctrine about 



