vi LECTURES AND ESSAYS 



marked favour by Lord Kelvin, Professor Tait, and other 

 eminent men of science with whom he was then associated, 

 and the editors are permitted to print an estimate which 

 has been kindly furnished by the present Sadleirian Pro 

 fessor of Pure Mathematics at Cambridge who was 

 Smith s colleague and friend during his Cambridge 

 period. Professor Hobson writes : 



&quot; The three papers entitled Theory of Geometric 

 Reasoning/ Hegel and the Metaphysics of the Fluxional 

 Calculus/ and Dr. Stirling, Hegel, and the Mathe 

 maticians are of a controversial character, and relate to 

 the Philosophy of Mathematics. The incisive vigour with 

 which they are written, and the acuteness of the dialectic 

 therein displayed, are characteristic of Robertson Smith. 

 At the present time their interest is, however, mainly 

 biographical and historical. Much of the criticism of 

 Hegel s views relating to the Infinitesimal Calculus is no 

 doubt valid, but it is clothed in a form which implies 

 ideas of the foundations of Analysis which are not in 

 accord with the conceptions of mathematicians at the 

 present time. Robertson Smith s criticism of Mill s ideas 

 about the nature of geometric reasoning are made from 

 the point of view of a disciple of Kant in relation to the 

 space- problem. The study of the foundations of Geometry, 

 to which a vast amount of attention has been given 

 since the time of the publication of this criticism, has 

 resulted in revelations which make the ideas of Kant in 

 this regard no longer tenable, at least without very con 

 siderable modification. The paper On the Flow of 

 Electricity in Conducting Surfaces is not controversial, 

 and thus comes under a different category. It contains 

 detailed work which amounted to a distinct contribution 

 to the development of the subject of which it treats at the 

 time it was published, and was regularly consulted by 



