120 



Anniversary Meeting. [Nov. 30, 



functions of real variables, to the considerations of conver- 

 gence and divergence of series and products, and to the 

 theory of bilinear and quadratic forms. 



(ii.) His contributions to the general theory of functions of complex 

 variables. This subject he has developed from its founda- 

 tions, and has re-established on a new basis, so that much 

 of it is his creation. The extensions which he has made to 

 this theory have of themselves proved sufficient to secure fcr 

 him the distinction of an acknowledged master. 



(iii.) His work in the theory of periodic functions. In particular, 

 the advances made by him in the theory of Abelian trans- 

 cendents, mark the chief algebraical development since the 

 time of Abel and Jacobi, and they have stimulated others to 

 further developments. Also the valuable advances made by 

 him in the theory of elliptic functions have been fruitful and 

 suggestive as the starting points for researches by a number 

 of distinguished mathematicians. 



(iv.) His work in the calculus of variations, the best known pub- 

 lished part of which relates to the theory of minimal sur- 

 faces. 



Not least remarkable among his claims to originality is the method 

 of proof which he has introduced in his investigations ; he has 

 associated a vigour and a strictness with the minutest details of his 

 proofs that have not merely led to the sound establishment of pro- 

 positions, but have indicated limitations and have suggested new ideas. 



Eotal Medal. 

 Dr. John Murray. 



To Dr. John Murray one of the Royal Medals is awarded for his 

 energetic and successful editorship of the Report of the " Challenger " 

 Expedition, and for his own large contributions to the work of the 

 expedition and to the scientific papers embodied in ohe Report. In 

 this matter Dr. Murray's labours are recognised universally as having 

 been of extreme value to zoological science. His own contributions 

 to the elucidation of the material brought home by the " Challenger " 

 have been of great importance and originality. His researches on 

 the deep sea, deposits, and his general discussion of the oceanographic 

 results of the expedition, are recognised as being of first-rate quality. 



Dr. John Murray has already received the " Prix Cuvier " of the 

 French Academie des Sciences, and it is right that the corresponding 

 body in this county should take the first opportunity available to it, 

 after the completion of the " Challenger " Reports, to express its 

 appreciation of their value. 



