37] 



CLASSIFICATION OF REACTIONS. 



123 



and since in this case the work dissipated in unit time is 



F represents one -half the time rate of loss, or dissipation of energy. 

 F is called the Dissipation Function, or the Dissipativity. 1 ) It was 

 introduced by Lord Rayleigh, and is of use in the theory of motions 

 of viscous media, and in the dynamical treatment of electric currents. 

 Beside this case we have dissipative forces not capable of representa- 

 tion o/f by a dissipation function. 



We will now place our various reactions in a table showing 

 their grouping in various classes and sub -classes. 



Positional 



Reactions 



Inertial 



Motional 

 or Kinetic 



, T , ,( Accelerational 

 Momenta!] 



Non - accelerational F W 



Non- momental 

 or Centrifugal 



JT (8) 



Non- conservative 



Having Dissipation -function 

 Others 



The advantage of this complete classification is as follows. 

 Suppose that a certain system or apparatus is presented to us for 

 dynamical examination. Its parts are concealed from o%r view by 

 coverings or cases, but at certain points there protrude handles, cranks, 

 or other driving points, upon which we may operate v and which will 

 exert certain reactions. All that we can learn of the system will 

 become known to us by a study of the reactions. Maxwell 2 ) compares 

 such a system to a set of bell -ropes hanging from holes in a roof, 

 which are to be pulled by a number of bell ringers. If when one 

 rope is pulled none of the others are affected, we conclude that that 

 rope has no connection with the others. If however, when one rope 

 is pulled, a number of others are set in motion, we conclude that 

 there is some sort of connection between the corresponding bells. 

 What the connection is we can find out by studying the motions. 

 In general, if when we move one driving point, and let it go, it 

 remains where we put it, we conclude that it is not attached to 

 anything, but is a mere blind member. If when we push it, it 



1) A case of perhaps equal importance is one in which the dissipation 

 function contains the squares of differences of the velocities. 



2) Maxwell, Scientific Papers, Vol. II, p. 783. 



