Ill 



tained was so long that he suppressed it in his published paper. Ampere 

 by sheer labour had worked out a direct analytical demonstration, and 

 published it in the 'Annales de Chimieetde Physique'*, where it occupies 

 thirty-two pages, and presents so repulsive an aspect that few mathemati- 

 cians would be pleased to face the task of going through it. With these 

 antecedents, Archibald Smith's investigation, bringing out the desired re- 

 sult directly from Fresnel's postulates by a few short lines of beautifully 

 symmetrical algebraic geometry, constitutes no small contribution to the 

 elementary mathematics of the undulatory theory of light. It was one 

 of the first applications in England, and it remains to this day a model 

 example, of the symmetrical method of treating analytical geometry, 

 which soon after (chiefly through the influence of the * Cambridge Mathe- 

 matical Journal') grew up in Cambridge, and prevailed over the un- 

 symmetrical and frequently cumbrous methods previously in use. 



In 1836 he took his degree as Senior Wrangler and first Smith's Prize- 

 man, and in the same year he was elected to a Fellowship in Trinity 

 College. 



Shortly after taking his degree, he proposed to his friend Duncan 

 Farquharson Gregory, of the celebrated Edinburgh mathematical family, 

 then an undergraduate of Trinity College, the establishment of an 

 English periodical for the publication of short papers on mathematical 

 subjects. Gregory answered in a letter of date December 4th, 1836, 

 cordially entering into the scheme, and undertaking the office of editor. 

 Being, however, on the eve of the Senate-House examination for his 

 degree, he adds, "But all this must be done after the degree; for l business 

 before pleasure,' as Bichard said when he went to kill the king before 

 he murdered the babes." The result was, the 'Cambridge Mathematical 

 Journal,' of which the first number appeared in November 1837. It 

 was carried on in numbers, appearing three times a year under the 

 editorship of Gregory, until his death, and has been continued under 

 various editors, and with several changes of name, till the present time, 

 when it is represented by the l Quarterly Journal of Mathematics ' and 

 the ' Messenger of Mathematics.' The original ' Cambridge Mathe- 

 matical Journal' of Smith and Gregory, containing as it did many 

 admirable papers by Smith and Gregory themselves, and by other able 

 contributors early attracted to it, among whom were Greatheed, Donkin, 

 Walton, Sylvester, Ellis, Cayley, Boole, inaugurated a most fruitful 

 revival of mathematics in England, of which Herschel, Peacock, Babbage, 

 and Green had been the prophets and precursors. 



It is much to be regretted that neither Cambridge, nor the university 

 of his native city, could offer a position to Smith, enabling him to make 

 the mathematical and physical science, for which he felt so strong an 

 inclination, and for which he had so great capacity, the professional 



* Volume for 1828. 



62 



