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To make the following new bye-law— 
~ Residents in Cambridge or the neighbourhood, not being 
graduates, may be elected Associates of the Society. 
Each one shall be proposed by three Fellows of. the 
Society, nominated by the Council, and elected by the 
Society. An Associate shall be elected for a period of 
three years, and if not then a graduate, shall be eligible 
for re-election. Associates shall have the privilege of 
attending the meetings and consulting the books in the 
Library of the Society. 
After an eloquent address from the President on the loss 
sustained by the death of Professor Sedgwick, whom he justly 
described as really the founder as well as the ardent promoter 
of the Society, it was moved by Professor MILLER, and seconded 
by Professor LivEIne, that an expression of the deep regret 
felt by the Society at the loss of Professor Sedgwick be recorded 
on the minutes. 
The following communications were made :— 
On the Proof of the Equations of Motion of a connected 
system. By Prof. Cuerx Maxwett. 
To deduce from the known motions of a system ne forces 
which act on it is the primary aim of the science of Dynamics. 
The calculation of the motion when the forces are known, 
though a more difficult operation, is not so important, nor so 
capable of application to the analytical method of physical 
science. 
__ The expressions for the forces which act on the system in 
terms of the motion of the system were first given by Lagrange 
in the fourth section of the second part of his Mécanique Ana- 
lytique. Lagrange’s investigation may be regarded from a 
mathematical point of view as.a method of reducing the dy- 
namical equations, of which there are originally three for every - 
