400 Prof. L. Natanson on the 



be =j j j dx dy dzpf. Then, generally speaking, F is suscep- 

 tible of three kinds of variation, and dF/dt is the sum of three 

 terms : — 1. A surface- integral relating to the action between 

 the body and the exterior world through the boundary of the 

 body; 2. A volume-integral expressing " action at a distance " 

 between the body and the exterior world ; and 3. A volume- 

 integral representing " coercion," i. e., that intimate action 

 whose constant tendency it is to attenuate and finally to efface 

 inequalities and disturbances, if there is no extraneous action to 

 maintain or to excite them ; and whose ultimate nature is, of 

 course, unknown to us. It would not be difficult to translate 

 our statement into symbols. Let us adopt, for instance, that 

 general Molecular Theory due to Maxwell, which we have 

 called (on a former occasion) "Kinematical Molecular 

 Theory." Let u + f, v + 17, iv + ? denote the components of 

 the velocities of individual molecules, / a function of the 

 ( w + £)> (v-r^), and («? + £), / the mean value of /within an 

 element, and D/Dt the rate of " coercion." Then 



hence 



= fff d$p{%f cos (nx) + rjf cos (ny) -f {/ cos (nz) } 



The three terms on the right-hand side refer to the three 

 kinds of variation as above stated. 



The assumption we propose to examine is that the third, or 

 coercive term DF/D^ is always proportional to the value 

 of F. Thus, writing t for a constant period of time, 



DF 2F 



w=~v w 



This equation, we shall find, is general ; in the neighbour- 

 hood of states of equilibrium at least it is exactly fulfilled. 

 The period of time r was first considered by Clerk-Maxwell ; 



