26, 27] KINETIC REACTION. 65 



inertia. This is the only universal definition of matter now possible. .-> "") 

 (It is to be noticed that this definition includes the luminiferous , [ 

 ether.) 



We may then state d'Alembert's Principle in these words: The 

 impressed forces, together with the forces of inertia, form a system 

 in equilibrium. Thus the principle is not new, but merely expresses 

 Newton's third law of motion, embodying at the same time the other 

 two, in the expression of the forces. The great service done by 

 d'Alembert was in reducing the statement of a problem in motion 

 to that of a statical problem. 



A practical advantage frequently of great use in applications is 

 similar to that possessed by the principle of virtual work, namely, 

 that the reactions of the constraints do no work, and may therefore 

 be omitted from the equation 18), for it is evident that the reactions 

 due to all constraints between bodies act equally in opposite directions 

 on both, so that the work done in the motion of their common 

 point of application vanishes. 



As a simple example of the meaning of force of inertia consider 

 two locomotives pulling in opposite directions at the ends of a train, 

 the pulls being transmitted by spring dynamometers. If the train 

 remains at rest, the pull recorded on both dynamometers will be the 

 same. If now one locomotive be given more steam, so that the 

 train begins to move, the indications of the dynamometers will be 

 found to be unequal, the greater pull being that of the locomotive 

 on the side toward which the train is moving, the difference being 

 found to be exactly equal (disregarding friction) to fche product of 

 the mass of the train by the acceleration which it gains. Thus the 

 difference of pull is balanced by the force of inertia, or kinetic 

 reaction. 



Again, consider a person standing in a street -car, when the car 

 starts. An acceleration is impressed on his body in the direction of 

 the motion of the car. The kinetic reaction is thus directed horizont- 

 ally to the rear. The force of weight of the person being vertically 

 downwards, the remaining force, namely, the static reaction of the 

 floor of the car, must be such as to equilibrate these two, and is 

 found by the triangle of vectors to be directed upwards and inclined 

 forwards. Thus the person must lean forward in order to preserve 

 equilibrium. Similarly when the car stops, the acceleration being 

 directed the other way, he must lean backward. This application of 

 d'Alembert's Principle is a matter of common knowledge, where 

 electric railroads are common. 



27. Energy. Conservative Systems. Impulse. If in the 



equation of d'Alembert's principle, 18), we put for dx, dy, 82 the 



WEBSTER, Dynamics. 5 



