Mathematics and General Physics. 405 



Secretary of the Section, who will communicate them to the coun - 

 cil of the society. The Secretary can also furnish copies of the 

 prospectus issued on the formation of the society, its regulations, 

 and an imperfect list of the present members. 



EVENING — George's street assembly rooms. 



The reports of the different Sections having been read by 

 the Presidents, Sir Thomas Brisbane requested Dr Lardner to 

 explain the principle of Mr Babbage's celebrated calculating 

 machine. The learned Professor explained, in as far as possi- 

 ble without exhibition of models or the machine itself, its var- 

 rious properties. The meeting adjourned till next evening. 



Thursday, Wth September. 



MORNING — UNIVERSITY. 



Section A. — Mathematics and General Physics. 



The Rev. Mr Whewell having taken the Chair, Mr Rennie gave 

 the second part of his report on Hydraulics, containing the applica- 

 tion of the principles of that science to the subject of rivers. 



Professor Hamilton then gave an account to the meeting of a 

 new method in Dynamics. After a brief review of the several 

 leading steps which had been successfully made in the advance- 

 ment of dynaminal science, and more particularly the labours 

 of Galileo, Newton, aud Lagrange, Professor Hamilton proceeded 

 to the consideration of the problem to be solved, which may be 

 stated to be the determination of the three co-ordinates of each 

 point by the moving system, as a function of the time ; and 

 after attending to the limitations of the solutions of the problem, 

 as hitherto given, he proceeded to explain his own method, and to 

 shew that the solution may be made to depend upon a certain func- 

 tion of the initial cind final configurations, analogous to that which 

 he has denominated a characteristic function in optics. In this 

 mode of treating the subject, the whole problem is reduced to the 

 research of this function. The author concluded by stating the de- 

 gree of success which had attended his own investigations respect- 

 ing the form of this function, in the case of a binary system in the 

 problem, by the determination of the orbit of a comet from the ini- 



