34 LECTURES AND ESSAYS [1869- 



it hardly possible to criticise our author fairly. Luckily, 

 we can see that Hegel is leaning entirely on Lagrange, and 

 that &quot; the series in which the function of a motion is 

 developed must therefore mean the series which ex 

 presses space in ascending powers of time. And this 

 enables us to ask, secondly, What reason Hegel has for 

 supposing that it is in this series that we are to find the 

 basis for a truly philosophical view of kinetics ? It was 

 Hegel s misfortune to live at a time when, among other 

 fruits of the &quot; Aufklarung,&quot; Lagrange s &quot;formal and super 

 ficial &quot; method of treating physics was in great repute ; 

 and surely it was a cruel fate that the great enemy of the 

 &quot;Aufklarung&quot; should, through a defective mathematical 

 education, be made a willing captive to a mathematical 

 &quot; Aufklarung/ which has, from its intrinsic weakness, 

 fallen as fast as it rose. In details, it is true, Hegel is 

 keen enough in detecting the unsatisfactory character 

 of Lagrange s standpoint (see, for example, a note at this 

 very point) ; but that the whole method was artificial he 

 could not see, not for want of mental power, but because, 

 having never studied the subject, he knew nothing what 

 ever about it had not even mastered its technicalities. 

 Then, again, if it is true that successive differential co 

 efficients have a qualitative difference, how can that be 

 brought out except in virtue of the relations established 

 in mathematics between quantity and quality, relations 

 which are not reached by pure analysis, but only in 

 Newton s way, i.e. by intuition ? And would not these 

 relations be violated, and all mathematics rendered absurd, 

 if the term that is qualitatively important could be 

 quantitatively negligible ? And, last of all, let me 

 challenge Hegel to bring forward any proof on his own 

 principles, that the third term relates to the resistance of 

 forces ; or for that matter, to show that this statement 

 has any real meaning whatever. 



But most men, I imagine, have now had enough of 

 Hegel s criticisms criticisms which simply show that the 



