588 Meeting of the British Association. [Oct., 



forms, — how did this originate ? In the accidental observation by 

 Eisenstein, some twenty years ago, of a single invariant (the 

 quadrin variant of a quartic), which he met with in the course of 

 certain researches just as accidentally and unexpectedly as M. Du 

 Chaillu might meet a goriUa in the country of the Fantees, or any 

 one of us in London a white Polar bear escaped from the Zoological 

 Gardens. Fortunately he pounced down upon his prey, and pre- 

 served it for the contemplation and study of future mathematicians. 

 It occupies only part of a page in his collected posthumous works. 

 This single result of observation (as weU entitled to be so called as 

 the discovery of globigerinae in chalk, or of the confocal ellipsoid 

 structure of the shells of the foraminifera), which remained in- 

 fructuous in the hands of its eminent author, has ser\ed to set in 

 motion a train of thought and propagated an impulse which have 

 led to a complete revolution in the whole aspect of modern analysis, 

 and will continue to be felt until mathematics are forgotten and 

 British Associations meet no more. 



The speaker continued : — " Were it not unbecoming to dilate on 

 one's own personal experience, I could tell a story of almost 

 romantic interest about my own latest researches (in a field where 

 geometry, algebra, and the theory of numbers melt in a surprising 

 manner into one another, like sunset tints, or the colour's of the 

 dying dolphin (the last still lovehest), a sketch of which has just 

 appeared in the ' Proceedings of the London Mathematical Society,' 

 which would very strikingly illustrate how much observation, 

 divination, induction, experimental trial and verification, 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 mathematician. In the face of these facts, which every analyst 

 in 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, nothiug 

 of causation ? ' " 



The speaker continued to say that he was not so absurd as to 

 maintain that the habit of observation of external nature will be 

 best, or at all, cultivated by the study of mathematics, at all events 

 as that study is at present conducted, and no one could desire more 

 earnestly than himself to see natural and experimental science 

 introduced into our schools as a primary and indispensable branch 

 of education ; that study and mathematical culture should go on 

 hand in hand together, and they would greatly influence each 

 other for their mutual good. He should rejoice to see mathematics 

 taught with that life and animation which the presence and example 



