Section A. 



ASTRONOMY, MATHEMATICS, 

 AND PHYSICS. 



ADDRESS BY THE PRESIDENT : 



PROFESSOR H. S. CARSLAW, Sc.D. 



THE RELATION BETWEEN PURE AND APPLIED 

 MATHEMATICS. 



I propose to-day to speak of the intimate relation between Pure and 

 Applied Mathematics at the present time, and to refer to some common 

 but mistaken views on the nature of the Science of Mathematics as a 

 whole. But before I pass to the subject of my address, I pause to 

 express in a few words our sense of the loss the world has suffered 

 within the last few months by the death of Sir George Darwin, tlie 

 great mathematical astronomer, and of M. Henri Poincare, . the 

 greatest mathematician of our time. 



Sir George Darwin, by his contributions to science, has worthily 

 maintained the traditions of his name, and his tenure of the Plumian 

 Prof essorship . of Astronomy at Cambridge recalls the days when the 

 other astronomical chair at that University was filled by Adams, who 

 shares with Leverrier the honour of the discovery of the planet Neptune. 

 There is probably no part of Applied Mathematics in which the refine- 

 ments of Analysis can be employed with greater effect than in the 

 domain of Mathematical Astronomy. Laplace and Lagrange were 

 consummate matJiematicians. To almost every branch of Mathematics 

 known in their time they made important contributions. And to come 

 to our own day, Newcomb was a mathematician of the first rank. 

 Darwin belonged to the same band. His researches on the past history 

 of the earth-moon system and on the practical and theoretical tidal 

 problems which the oceans present, could only have been carried to a 

 successful issueby one with a wide knowledge of Pure Mathematics. 



Here in this room it is but fitting that we should recall the services 

 he so fully and gladly rendered to the British Association for the 

 Advancement of Science, the parent of this our Australasian Associa- 

 tion. President of Section A in 1886, he attained the honour of the 

 presidency of the Association itself in 1905, And we had looked forward 

 to his taking an active part in the meetings of the Association next 

 year in Australia. 



