354 Obitwry Notices of Fellows deceased. 



and admiration when he found that Salmon had missed no point in the 

 long debate, had assimilated everything, and was explaining his views 

 with an incredible wealth of homely illustration, with abundant wit, 

 and with matured common sense. 



For many years Salmon was greatly attracted by the theory of 

 numbers. He said it almost amounted to a disease with him, and he 

 regarded his work on it as frivolous or useless. Having nearly com- 

 pleted a book on the subject, he burned it for some unknown reason. 

 In addition to the intrinsic fascination of the subject, he may have 

 found that this work relieved him of boredom, or it may have served 

 as an anodyne ; and one may hazard the suggestion that the destruc- 

 tion of his book was a kind of penance. In his latest years he ceased 

 working on the theory. 



Salmon's first paper was published in 1844, ' On the Properties of 

 Surfaces of the Second Degree which correspond to the Theorems of 

 Pascal and Brianchon on Conic Sections,' (" Phil. Mag.," 24) ; the last of 

 his forty-one mathematical papers was * On Periods in the Reciprocals of 

 Primes ' (" Messenger of Mathematics," 1873, pp. 49-51). The majority 

 of his papers have reference to numerical characteristics relating to 

 curves and surfaces, and many of these results are summarised in the 

 great chapter " On the Order of Restricted Systems of Equations " in 

 his " Modern Higher Algebra." It would be most unfair to Salmon to 

 judge of his contributions to mathematics by his papers alone. He had 

 a great dislike to the physical trouble of writing ; he modestly commu- 

 nicated his discoveries to friends, or reserved them for incorporation in 

 his books, so that it is a matter of extreme difficulty to say how much 

 is his. Apart from the discovery of new facts, the methods employed 

 in his books must have been of tremendous service in promoting the 

 advance of mathematics. His style was characterised by complete 

 absence of pedantry and by profound common sense. By a few words, 

 by some geometrical illustration, he dispensed with pages of trouble- 

 some analysis. At times the great condensation of his diction may 

 conceal from the casual student the width and the depth of his conclu- 

 sions, but on referring to an original memoir from which he quotes one 

 is amazed to find that every essential point is reproduced, and that 

 frequently some brilliant addition has been made and left unclaimed 

 by him. 



It must not be supposed that Salmon shared the characteristic 

 attributed to MacCullagh of shirking analysis and trusting to his 

 great geometrical insight. On the contrary, he seemed to revel in 

 analysis so tedious and so intricate that it would be distasteful to most 

 mathematicians. He says : *" By means of the differential equation I 

 * " Treatise on Modern Higher Algebra," Art, 260. 



