CRI TI CTS MS BY BRITISH WRITERS 261 



infinitesimals smaller than the * moonshine's wat'ry 



beams,' and more numerous than 



' Autumnal leaves that strow the brooks 

 In Vallombrosa.' (Milton, Par. Lost^ i, 302.) 



**The contemporaries and partizans of Newton 

 were men infinitely inferior to him in genius, but 

 they had zeal, and were resolved to defend his 

 opinions and judgments. Hence they undertook the 

 vindication of fluxions, according to the principles 

 and method of its author ; although it may be fairly 

 inferred, from the dififerent explanations given of 

 that doctrine by Newton in dififerent parts of his 

 Works, that Newton himself was not perfectly satis- 

 fied of the stabiHty of the grounds on which he 

 had established it." 



The reviewer quotes (p. 497) from Lacroix's 

 preface : 



**These notions [velocities, motions], although 

 rigorous, are foreign to geometry, and their appHca- 

 tion is difficult. . . . Properly speaking, fluxions 

 were to him [Newton] only a means of giving a 

 sensible existence to the quantities on which he 

 operated. The advantage of the method of fluxions 

 over the differential calculus in , point of meta- 

 physics, consists in this ; that, fluxions being finite 

 quantities, their moments are only infinitely small 

 quantities of the first order, and their fluxions are 

 finite ; by these means, the consideration of in- 

 finitely small quantities of superior orders is avoided. 

 ... I can only mention a method which Landen 

 gave in 1758, to avoid consideration of infinity of 



