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particle of the system, to a number equal to that of the degrees 
of freedom of the system. In other words it is a method of 
eliminating certain quantities called reactions from the equations. 
The aim of Lagrange was, as he tells us himself, to bring 
‘dynamics under the power of the calculus, and therefore he had 
to express dynamical relations in terms of the corresponding 
relations of numerical quantities. 
In the present day it is necessary for physical enquirers 
to obtain clear ideas in dynamics that they may be able to 
‘study dynamical theories of the physical sciences. We must 
therefore avail ourselves of the labours of the mathematician, 
and selecting from his symbols those which correspond to con- - 
- ceivable physical quantities, we must retranslate them into the 
language of dynamics. 
In this way our words will call up the mental image, not 
of certain operations of the calculus, but of certain character- 
istics of the motion of bodies. 
The nomenclature of dynamics has been greatly developed 
by those who in recent times have expounded the doctrine of 
the Conservation of Energy, and it will be seen that most of 
the following statement is suggested by the investigations m 
Thomson and Tait’s Natural Philosophy, especially the method 
of beginning with the case of impulsive forces. 
I have applied this method in such a way as to get rid 
of the explicit consideration of the motion of any part of the 
system except the co-ordinates or variables on which the motion 
of the whole depends. It is important to the student to be 
able to trace the way in which the motion of each part is 
determined by that of the variables, but I think it desirable 
that the final equations should be obtained independently of 
this process. That this can be done is evident from the fact 
that the symbols by which the dependence of the motion of 
the parts on that of the variables was PEER, are not found 
in the final equations. ; 
