3 REPORT — 1869. 



to thinking than to speaking (to making mathematics than to talking about them), 

 and partly and more especially by a feeling of my inadequacy to satisfy the expecta- 

 tions that would be raised in the minds of those who had enjoyed the privilege of 

 hearing or reading the allocution (which fills me with admiration and dismay) of 

 my gifted predecessor, Dr. Tyndall, a man in whom eloquence and philosophy 

 seem to be inborn, whom Science and Poetry woo with an equal spell*, and 

 whose ideas have a faculty of arranging themselves in forms of order and beauty 

 as spontaneously and unfailingly as those crystalline solutions from which, in a 

 striking passage of his address, he drew so vivid and instructive an illustration. 



From this lotos-eater's dream of fancied security and repose I was rudely 

 awakened by receiving from the Editor of an old-established journal in this city a 

 note containing a polite but peremptory request that I shoidd, at my earliest con- 

 venience, favour him with a " copy oi' the address I proposed to deliver at the 

 forthcoming Meeting." To this invitation, my first impulse was to respond very 

 much in the same way as did the " Needy knife-grinder " of the ' Antijacobin,' 

 when summoned to recoimt the stoiy of his vn-ongs to his republican sympa- 

 thizer, " Story, God bless you, I have none to tell, Sir ! " " Address, Mr. Editor, 

 I hav-e none to deliver." 



I have found, however, that increase of appetite still grows with what it feeds 

 on, that those who were present at the opening of the Section last year, and 

 enjoyed my friend Dr. Tyndall's melodious utterances, woidd consider them- 

 selves somewhat ill-treated if they were sent away quite empty on the present oc- 

 casion, and that, failing an address, the Members would feel very much like the 

 guests at a wedding-breakfast where no one was willing or able to propose the health 

 of the bride and bridegroom. 



Yielding, therefore, to these considerations and to the advice of some officially 

 connected with the Association, to whose opinions I feel bound to defer, and 

 unwilling also to countenance by my example the too prevailing opinion that 

 mathematical pursuits unfit a person for the discharge of the common d uties of 

 life and cut him ofl' from the exercise of Man's highest prerogative, " discourse 

 of reason and facidty of speech divine," — rather, I say, tlian favour the notion 

 that we Algebraists (who regard each other as the flower and salt of the earth) are a 

 set of mere calculating-machines endowed with organs of locomotion, or, at best, 

 a sort of poor visionary dumb creatures only capable of communicating by signs and 

 symbols with the outer world, I have resolved to take heart of grace and to say a 

 few words, which I hope to render, if not interesting, at least intelligible, on a 

 subiect to which the larger part of my life has been devoted. 



"f he President of the Association, Prof. Stokes, is so eminent alike as a mathe- 

 matician and physicist, and so distinguished for accuracy and extent of erudition 

 and research, that I felt assured I might safely assume he would, in his Address to 

 the Association at large, take an exhaustive survey, and render a complete ac- 

 coimt of the recent progress and present condition and prospects of Mathematical 

 and Physical Science. This consideration narrowed very much and brought almost 

 to a point the ground available for me to occupy in this Section ; and as I cannot 

 but be aware that it is as a cultivator of pure mathematics (the subject in which 



* So it is said of Jacobi, that he attracted the particular attention and friendship of 

 Bockh, the director of the philological seminary at Berlin, by the zeal and talent lie dis- 

 played for philology, and only at the end of two years' study at the University, and after a 

 severe mental struggle, was able to make his final choice in favour of mathematics. The 

 relation between these two sciences is not perliaps so remote as may at first sight appears, 

 and indeed it has often struck me that metamorphosis runs like a golden thread through 

 the most diverse branches of modern intellectual culture, and forms a natural link of 

 connexion between subjects in their aims so unlike as Grammar, Ethnology, Eatioual 

 Mythology, Chemistry, Botany, Comparative Anatomy, Physiology, Physics, Algebra, 

 Music, all of which, under the modern point of view, may be regarded as Iiaving morphology 

 for their common centre. Even singing, I have been told, the advanced German theorists 

 regard as being strictly a development of recitative, and infer therefrom that no essentially 

 new melodic themes can be invented until a social cataclysm, or the civilization of some 

 at present barbaric races, shall have created new necessities of expression and called into 

 activity new forms of impassioned declamation. 



