i8 7 3] STIRLING AND HEGEL 87 



a time the humble but perfectly truthful Vorstellungen 

 of the fluxional method, they might have spoken with 

 authority, and found willing hearers. But when Dr. 

 Stirling, disclaiming for himself &quot; all pretensions to the 

 position even of a student &quot; in mathematics, takes it upon 

 him to separate the dross from the pure gold of a Newton, 

 the incongruity between the humility of the disclaimer 

 and the arrogance of the enterprise is manifest to every 

 reader. And of course we find accordingly that Dr. 

 Stirling is not even able to reproduce the despised Vorstel- 

 lung with accuracy. He tells us that Newton himself 

 declares the quality independent of the quantity (p. 113). 

 Newton does no such thing. He tells us that a &quot; square 

 is a quantum ; but it may be conceived as increasing or 

 decreasing, and if it be so conceived, there can be con 

 ceived also to lie in it a principle that, whether there be 

 increase or decrease, is always the same infinite, then, 

 non-quantitative, qualitative only&quot; (p. 121). Newton 

 would have held up his hands in horror at such a caricature 

 of his view, and would have told his critic that, to say 

 nothing of other points, one great use of the moment was 

 to show, by changes in itself, whether the quantity of which 

 it is the moment is increasing, diminishing, or stationary. 

 Again, Dr. Stirling obviously misunderstands the sense 

 in which Newton says that Nature shows us the generation 

 of quantity by flow. &quot; Who ever saw lines flowing into 

 planes, planes into solids, or sides rotating into angles ? 

 And yet who has not seen sand and salt . . . and a 

 pocketful of marbles ? &quot; (p. no). Well, no one has ever 

 seen sides rotating into angles ; and Dr. Stirling would 

 not have imagined that Newton had said this, had he not 

 been hampered by his queer conception of mathematical 

 continuity, by which the continuum must always arise 

 out of the discrete the angle out of something that is not 

 angle. What Newton says is that when Nature presents 

 us with the process of measuring out quantity, the opera 

 tion is not performed by successive applications of foot- 



