LU THE ROYAL SOCIETY OF CANADA 



E. Gilmore, M.Sc. Presented by Dr. Alfred Stansfield, F.R.S.C. 



On the p — adic theory of the algebraic numbers. By Professor 

 J. C. Fields. 



Numerical divisors of the form a^ + /3^ / o; + /3. By Professor 

 J. C. Fields. 



Direct derivation of the Complementary Theorem. By Pro- 

 fessor J. C. Fields. 



Derivation of the Complementary Theorem from the Riemann- 

 Roch Theorem. By Samuel Beatty, Ph.D. Presented by Professor 

 J. C. Fields. 



The inversion of an analytic function. By Samuel Beatty, Ph.D. 

 Presented by J. C. Fields. 



A Demonstration of the existence of the branches of an algebraic 

 function. By J. R. Pounder. Presented by Professor J. C. Fields. 



Algebraic Proof of the Existence Theorem for the branches of 

 an algebraic function of one variable. By Professor J. C. Fields. 



On the motion of Dr. Shutt, seconded by Dr. Plaskett, the report 

 of Section III was adopted. 



Report of Section IV 



Section IV begs to submit the following report. 



Four sessions of the section were held. Twenty-nine Fellows 

 were in attendance. They were: — Sir James Grant, Dr. Walker, 

 Dr. A. H. MacKay, Dr. Huntsman, Dr. Bailey, Professor Prince, Dr. 

 Knight, Professor Buller, Dr. Adams, Mr. McConnell, Mr. Dresser, 

 Mr. J. B. Tyrrell, Dr. Harrison, Dr. Willet Miller, Dr. Coleman, 

 Dr. Ami, Dr. Thomson, Mr. Lambe, Dr. Hewitt, Dr. Willey, Pro- 

 fessor Lloyd, Mr. Dowling, Dr. Macallum, Mr. White, Dr. Mc- 

 Murrich, Dr. Burgess, Dr. MacKenzie, Mr. Faribault, Mr. Mclnnis. 



Two Fellows of the section are on active service, viz.. Colonel 

 J. G. Adami and Lt.-Col. Brock. Two new Fellows were added to 

 the membership of the Section, Dr. Huntsman and Dr. Thomson. 



The following officers were elected for the year 1917-18: — 



President— Mr. R. G. McConnell. 



Vice-President — Dr. F. C. Harrison. 



Secretary — Professor J. J. MacKenzie. 



Professor Coleman and Professor Harrison were appointed to 

 represent the Section on the Nomination Committee of the Society, 



Professor Harrison, Mr. Dowling and Dr. Hewitt were appointed 

 the Sectional Printing Committee. Of these Mr. Dowling and Dr. 

 Hewitt are nominated to act upon the printing Committee of the 

 Society. 



