MATHEMATICAL PHYSICS. 5°7 



THE MATHEMATICAL PHYSICS OF THE NINETEENTH 



CENTURY. 



By Professor HORACE LAMB, LL.D., D.Sc, F.R.S., 



PRESIDENT OF THE MATHEMATICAL AND PHYSICAL SECTION OF THE BRITISH ASSOCIATION. 



f I ^HE losses sustained by mathematical science in the past twelve 

 -*- months have perhaps not been so numerous as in some years, but 

 they include at least one name of world-wide import. Those of us who 

 were students of mathematics thirty or forty years ago will recall the 

 delight which we felt in reading the geometrical treatises of George 

 Salmon, and the brilliant contrast which they exhibited with most of 

 the current text-books of that time. It was from him that many of us 

 first learned that a great mathematical theory does not consist of a 

 series of detached propositions carefully labeled and arranged like 

 specimens on the shelves of a museum, but that it forms an organic 

 whole, instinct with life, and with unlimited possibilities of future 

 development. As systematic expositions of the actual state of the sci- 

 ence, in which enthusiasm for what is new is tempered by a due respect 

 for what is old, and in which new and old are brought into harmoni- 

 ous relation with each other, these treatises stand almost unrivaled. 

 Whether in the originals, or in the guise of translations, they are ac- 

 counted as classics in every university of the world. So far as British 

 universities are concerned, they have formed the starting point of a 

 whole series of works conceived in a similar spirit, though naturally 

 not always crowned by the same success. The necessity for this kind 

 of work grows, indeed, continually; the modern fragmentary fashion 

 of original publication and the numerous channels through which it 

 takes place make it difficult for any one to become initiated into a new 

 scientific theory unless he takes it up at the very beginning and follows 

 it diligently throughout its course, backwards and forwards, over rough 

 ground and smooth. The classical style of memoir, after the manner 

 of Lagrange, or Poisson, or Gauss, complete in itself and deliberately 

 composed like a work of art, is continually becoming rarer. It is there- 

 fore more and more essential that from time to time some one should 

 come forward to sort out and arrange the accumulated material, reject- 

 ing what has proved unimportant, and welding the rest into a con- 

 nected system. There is perhaps a tendency to assume that such work 

 is of secondary importance, and can be safely left to subordinate hands. 

 But in reality it makes severe demands on even the highest powers ; and 

 when these have been available the result has often done more for the 



