72 LECTURES AND ESSAYS [1869- 



&quot; observations in regard to the show of mathematical 

 proof &quot; (put forth by mathematicians) &quot; in matters 

 known from experience alone,&quot; takes delight in the 

 felicitous home-thrusts delivered to Newton and others 

 (p. 381), and above all, finds that in a criticism of the 

 process by which the second lemma of the second book of 

 the Principia determines the fluxion of a product, &quot; Hegel 

 has succeeded in striking his harpoon into that vast 

 whale Newton &quot; (p. 363). These utterances were virtu 

 ally a challenge to mathematicians, and the challenge 

 became express and personal when Dr. Stirling, anim 

 adverting in the Edinbiirgh Evening Courant on allusions 

 to Hegel made by Professor Tait in a University lecture, 

 called that gentleman s attention to the &quot; harpoon &quot; 

 passage just cited, and asked him &quot; whether or not even 

 in his opinion Hegel is right and Newton wrong ? 

 This challenge appeared December 21, 1868. On 

 February i, 1869, Professor Tait and Sir William Thomson 

 found opportunity to allude to the matter in a discussion 

 in the Royal Society of Edinburgh, and without entering 

 into detail, showed by concrete examples of varying 

 velocity, such as are offered by railway trains and steam 

 boats, that Newton s process was that which was naturally 

 suggested by his physical conception of a fluxion, and 

 that Hegel s criticism was based on an unnatural (and 

 therefore incorrect) view of the problem. It seemed, 

 however, to be desirable to take up the matter more fully ; 

 and on May 17 Professor Tait laid before the Society a 

 paper on &quot; Hegel and the Metaphysics of the Fluxional 

 Calculus,&quot; written by me. The publication of this paper 

 elicited a newspaper controversy between Dr. Stirling and 

 myself, in which neither party gave way on any point ; 

 and then the discussion slumbered for three years, to be 

 again awakened by the publication of Dr. Stirling s recent 

 book. 1 Of this book about forty pages are devoted to 



1 Lectures on the Philosophy of Law. Together with Whewell and 

 Hegel, and Hegel and MY. W. R. Smith, a Vindication in a Physico- 

 Mathematical Regard (1873). 



