Ixxxvi REPORT — 1871. 



cially in meteorology, by the harmonic analysis. It is purely by an appli- 

 cation of this principle and practical method, that the British Association's 

 Committee on Tides has for the last four years been, and sliU is, working 

 towards the solution of the grand problem proposed forty-eight years ago by 

 Thomas Young in the following words : — 



" There is, indeed, little doubt that if we were provided with a sufficiently 

 " correct series of minutely accurate o'jservations on the Tides, made not merely 

 " with a view to the times of low and high water only, but ratlicr to the heights 

 " at the intermediate times, we might form, by degrees, with the assistance 

 " of the theory contained in this article * only, almost as perfect a set of tables 

 " for the motions of the ocean as we have already obtained for those of the 

 " celestial Ijodies, which are the more immediate objects of the attention of 

 " the practical astronomer." 



Sir John Herschel's discovery of a right or left-handed asymmetry in the 

 outward form of crystals, such as quartz, which in their inner molecular 

 structure possess the heli^oidal rotational property in reference to the plane 

 of polarization of light, is one of the notable points of meeting between 

 Natural History and Natural Philosophy. His observations on " epipoHc di- 

 spersion ". gave Stokes the clue by which he was led to his great discovery of 

 the change of periodic time experienced by light in fiiUiug on certain substances 

 and beiug dispcrsively reflected from them. In respect to pure mathematics 

 Sir John Herschel did more, I believe, than any other man to introduce into 

 Britain the powerful methods and the valuable notation of modern analysis. 

 A remarkable mode of symbolism had frcslily appeared, I believe, in the 

 works of Laplace, and possibly of other French mathematicians ; it certainly 

 appeared in Fourier, but whether before or after Herschel's work I cannot 

 say. "With the French writers, however, this was rather a short method of 

 writing formuhe than the analytical engine whicli it became in the hands 

 of Herschel and British followers, especially Sylvester and Gregory (com- 

 petitors with Green in the Cambridge Mathematical Tripos struggle of 1837) 

 and Boole and Cayley. This method was greatly advanced by Gregory, who 

 first gave to its working-power a secure and pliilosophical foundation, and so 

 prepared the way for the marvellous extension it has received from Boole, 

 Sylvester, and Cayley, according to which symbols of operation become the 

 subjects not merely of algebraic combination, but of differentiations and in- 

 tegrations, as if they were symbols expressing values of varying quantities. 

 An even more marvellous development of this same idea of the separation of 

 symbols (according to which Gregorj* separated the algebraic signs 4- and — 

 from other symbols or quantities to be chai-acterized b}- them, aud dealt with 

 them according to the laws of algebraic combination) received from Hamilton 

 a most astonishing generalization, by the invention actually of new laws of 

 combination, and led him to his famous " Quaternions," of which he gave 

 his earliest exposition to the Mathematical and Physical Section of this As- 

 sociation, at its meeting in Cambridge in the year 1845. Tait has taken up 

 the subject of quaternions ably and zealously, and has carried it into phy- 

 sical science with a faith, shared by some of the most thoughtful mathematical 

 naturalists of the day, that it is destined to become an engine of perhaps 

 hitherto uuimagined power for investigating and expressing results in 

 Natural Philosophy. Of Herschel's gigantic work in astronomical observa- 

 tion I need say nothing. Doubtless a careful account of it will be given 

 in the ' Proceedings of the Eoyal Society of London ' for the next anniver- 

 sary meeting. 



* Young's; written in 1823 for the Supplement to ti:e ' Encyclopjifdia Eritannica.' 



