FLUIDS AND THE DETERMINATION OF THE CRITERION. 137 
sensible size. But, as heat is by no means the only state of relative-motion of matter, 
if the heat-motions are relative to all mean-motions of matter, whatsoever their periods 
may be, it follows—that there must be some discriminative cause which prevents the 
existence of relative-motions of matter other than heat, except mean-motions with 
periods in time and space of greatly higher orders of magnitude than the corres- 
ponding periods of the heat-motions—otherwise, by equations (84), (8B), heat-motions 
could not be to a high degree of approximation relative to all other motions, and we 
could not have to a high degree of approximation, 
du du du a) 
Pre Ty + Pyx ly + Pex 7B 
dv dv dv ad 
(ae Bog, Page = ag ee 2 pe 8 2. IO) 
dw dw dw 
Piz ihe + Pyz dy Pz iB J 
where the expression on the right stands for the rate at which heat is converted into 
energy of mean-motion. 
Transformation of Energy of Relative-mean-motion to Energy of Heat-motion. 
10. The recognition of the existence of a discriminative cause, which prevents the 
existence of relative-mean-motions with periods of the same order of magnitude as 
heat-motions, proves the existence of another general action by which the energy of 
relative-mean-motion, of which the periods are of another and higher order of 
magnitude than those of the heat-motions, is transformed to energy of heat-motion. 
For if relative-mean-motions cannot exist with periods approximating to those of 
heat, the conversion of energy of mean-motion into energy of heat, proved by Jouts, 
cannot proceed by the gradual degradation of the periods of mean-motion until these 
periods coincide with those of heat, but must, in its final stages, at all events, be the 
result of some action which causes the energy of relative-mean-motion to be trans- 
formed into the energy of heat-motions without intermediate existence in states of 
relative-motion with intermediate and gradually diminishing periods. 
That such change of energy of mean-motion to energy of heat may be properly 
called transformation becomes apparent when it is remembered that neither mean- 
motion nor relative-motion have any separate existence, but are only abstract 
quantities, determined by the particular process of abstraction, and so changes in the 
actual-motion may, by the process of abstraction, cause transformation of the 
abstract energy of the one abstract-motion, to abstract energy of the other abstract- 
motion. 
All such transformation must depend on the changes in the actual-motions, and so 
MDCCCXCV.—A. T 
