6 REPORT 1869. 



manner into one another, like sunset tints or the colom-s of the dying dolphin, 

 "the last still loveliest " (a sketch of which has just appeared in the Pro- 

 ceedings of the London Mathematical Societj'*), which would \erj strikingly illus- 

 trate how much observation, divination, induction, experimental trial, and verifica- 

 tion, causation, too (if that means, as I suppose it must, mounting from phenomena 

 to their reasons or causes of being), have to do with the work of the mathema- 

 tician. In the face of these facts, which eveiy analyst iu this room or out of it 

 can vouch for out of his own knowledge and personal experience, how can it be 

 maintained, in the words of Professor Huxley, who, in this instance, is speaking of 

 the sciences as they are in themselves and without any reference to scholastic 

 discipline, that Mathematics "is that study which knows nothing of observation, 

 nothing of induction, nothing of experiment, nothing of causation." 



I, of course, am not so absurd as to maintain that the habit of observation of 

 external natm-e will be best or in an}' degree cultivated by the study of mathematics, 

 at all events as that study is at present conducted ; and no one can desire more 

 earnestly than myself to see natiu'al and experimental science introduced into our 

 schools as a primary and indispensable branch of education : I think that that study 

 and mathematical cultm-e should go on hand in hand together, and that they would 

 gi-eatly influence each other for theu' mutual good. I should rejoice to see mathe- 

 matics taught with that life and animation which the presence and example of her 

 young and buoyant sister could not fail to impart, short roads preferred to long 

 ones, Euclid honourably shelved or buried " deeper than did ever plummet 

 sound " out of the schoolboy's reach, morphology introduced into the elements 

 of Algebra — projection, correlation, and motion accepted as aids to geometry — the 

 mind of the student quickened and elevated and his faith awakened by early initia- 

 tion into the ruling ideas of polarity, continuity, infinity, and familiarization with 

 the doctrine of the imaginary and inconceivable. 



It is this living interest in the subject which is so wanting in our traditional and 

 mediaeval modes of teaching. In France, Gei-many, and Italy, everywhere where 

 I have been on the Continent, mind acts direct on mind in a manner imknown to 

 the frozen formality of our academic institutions ; schools of thought and centres 

 of real intellectual cooperation exist : the relation of master and pupil is acknow- 

 ledged as a spiritual and a lifelong tie, connecting successive generations of great 

 thinkers A\dth each other in an unbroken chain, just in the same way as we read, in 

 the catalogue of our French Exhibition, or of the Salon at Paris, of this man or that 

 being the pupil of one gi-eat painter or sculptor and the master of another. When 

 followed out in this spirit, tliere is no study ui the world wliich brings into more 

 harmonious action all the facidties of the mind than the one of which I stand here 

 as the humble representati-Ne, there is none other which prepares so many agi-ee- 

 able surprises for its followers, more wonderfid than tlie changes in the transforma- 

 tion-scene of a pantomime, or, like this, seems to raise them, by successive steps 

 of initiation, to higher and higher states of conscious intellectual being. 



This accounts, I believe, for the extraordinary longevity of all the greatest masters 

 of the Analytical art, the Dii Maj ores of the mathematical Pantheon. Leibnitz, lived 

 to the age of 70 ; Eulerto7(j; Lagi'ange to 77; Laplace to 78; Gauss to 78; Plato, 

 the supposed inventor of the conic sections, who made mathematics his study and 

 delight, who called them the handles or aids to philosophy, the medicine of the 

 soul, and is said never to have let a day go by without inventing some new 

 theorems, lived to 82 ; Newton, the crown and glory of his race, to 85 ; Archi- 

 medes, the nearest akin, probably, to Xewton in genius, was 75, and might have 

 lived on to be 100, for aught we can guess to the contrary, when he Avas slain by 

 the impatient and ill-mannered sergeant, sent to bring him before the Roman 

 general, in the full ^-igour of his facidties, and in the very act of working out a 

 problem ; Pythagor;\s, in whose school, I believe, the word mathematician (used, 

 however, in a somewhat wider than its present sense) originated, the second 

 founder of geometry, the inventor of the matchless theorem which goes by his 

 name, the precognizer of the undoubtedly mis-called Copemican theoiy, the dis- 

 coverer of the regular solids and the musical canon, who stands at the very apex 

 of this pyramid of flame (if we may credit the tradition), after spending 22 years 

 * Under the title of " Outline Trace of the Theory of Reducible Cyclodes." 



