Section A. 



U I « S A « Yi :xi| 



v:y 



ASTRONOMY, MATHEMATICS, PHYSICS, aND 

 MECHANICS. 



Address by the President, 

 W. H. BRAGG, M.A., 



Professor of Mathematics, Unh-ersltii Adi'lttide, S.A. 



Fifty years ago it was shown by Sir William Thomson 

 that there existed between the theory of electrostatics, at 

 that time in its infancy, and the theory of the conduction of 

 heat, then fresh from Fourier's hands, a very close analogy. 

 So exact was the analogy that the solution of any problem 

 in the one theory was at the same time the solution of a 

 problem in the other : it was only necessary to change the 

 meanings of the mathematical symbols. Some time after- 

 wards Sir William Thomson, enlai'ging his former statement, 

 showed that the analogy extended also to the theories of 

 magnetism and of the irrotational motion of a perfect liquid 

 through a porous solid. To these may be added the theory 

 of the steady flow of electricity through conductors. 



Nor is this list yet complete, for there may be added 

 certain other theories, to some extent imaginary, yet im- 

 portant in that they are simple to realise, and therefore of 

 great use in presenting to the mind an easy means of grasp- 

 ing the problems of their more difficult analogues. 



It is a matter of the greatest interest that there should 

 exist so wide and so perfect an analogy between these different 

 branches of Physics : and for this reason alone I feel that I 

 should be justified in making the analogy the subject of my 

 address to you this morning. But I have also other reasons 

 than that of inviting you to consider a curious mathematical 

 correlation between several theories. It is, I think, of the 

 greatest assistance to the student of Physics to follow up the 

 analogy, and examine carefully its nature. It is a common 

 remark that analogies are dangerous things, and the remark 

 is often true enough. But the danger Hes only in an im- 

 perfect knowledge of the extent to which reliance may be 



