294: 
The whole theory of the equations of motion is no doubt 
familiar to mathematicians. It ought to be so, for it is the 
most important part of their science in its application to matter. 
But the importance of these equations does not depend on their 
being useful in solving problems in dynamics. A higher func- 
tion which they must discharge is that of presenting to the 
mind in the clearest and most general form the fundamental 
principles of dynamical reasoning. 
In forming dynamical theories of the physical sciences, it 
has been a too frequent practice to invent a particular dy- 
namical hypothesis and then by means of the equations of 
motion to deduce certain results. The agreement of these 
results with real phenomena has been supposed to furnish a 
certain amount of evidence in favour of the hypothesis. 
The true method of physical reasoning is to begin with the 
phenomena and to deduce the forces from them by a direct 
application of the equations of motion. The difficulty of doing 
so has hitherto been that we arrive, at least during the first 
stages of the investigation, at results which are so indefinite 
that we have no terms sufficiently general to express them 
without introducing some notion not strictly deducible from 
our premisses. 
It is therefore very desirable that men of science should 
invent some method of statement by which ideas, precise so 
far as they go, may be conveyed to the mind, and yet suffi- 
ciently general to avoid the introduction of unwarrantable details. 
For instance, such a method of statement is greatly needed 
in order to express exactly what is known about the undulatory 
theory of light. 
(2) On a problem in the Calculus of Variations in 
which the solution is discontinuous. By Prof. CuerK 
MaxweELt. 
The rider on the third question in the Senate-House paper 
