100 MEMOIR OF AUGUSTUS DE MORGAN. 



1 83R. counterfeit knowledge, with which he was visibly possessed, 

 and which he had an extraordinary power of arousing and 

 Taylor's 67 sustaining in his pupils. The fundamental conceptions of 

 each main department of Mathematics were dwelt upon 

 and illustrated in such detail as to show that, in the judg- 

 ment of the lecturer, a thorough comprehension and mental 

 assimilation of great principles far outweighed in import- 

 ance any mere analytical dexterity in the application of 

 half-understood principles to particular cases. Thus, for 

 instance, in Trigonometry, the wide generality of that 

 subject, as the science of undulating or periodic magnitude, 

 was brought oat and insisted on from the very first. In 

 like manner the Differential Calculus was approached 

 through a rich conglomerate of elementary illustration, by 

 which the notion of a differential coefficient was made 

 thoroughly intelligible before any formal definition of its 

 meaning had been given. The amount of time spent on 

 any one subject was regulated exclusively by the import- 

 ance which De Morgan held it to possess in a systematic 

 view of Mathematical science. The claims which Uni- 

 versity or College examinations might be supposed to 

 have on the studies of his pupils were never allowed to 

 influence his programme in the slightest degree. He 

 laboured to form sound scientific Mathematicians, and, if 

 he succeeded in this, cared little whether his pupils could 

 reproduce more or less of their knowledge on paper in a 

 given time. On one occasion, when I had expressed regret 

 that a most distinguished student of his had been beaten, 

 in the Cambridge Mathematical Tripos, by several men 

 believed to be his inferiors, De Morgan quietly remarked 



that he "never thought likely to do himself justice 



in THE GREAT WRITING RACE." All cram he held in the 

 most sovereign contempt. I remember, during the last 

 week of his course which preceded an annual College exa- 

 mination, his abruptly addressing his class as follows : " I 

 notice that many of you have left off working my examples 

 this week. I know perfectly well what you are doing ; 



