FLUIDS AND THE DETERMINATION OF THE CRITERION. 139 
heat-motions of matter so fundamental and general, that from the time these motions 
were first recognized the distinction has been accepted as part of the order of nature, 
and has been so familiar to us that its cause has excited no curiosity, cannot, if they 
have any effect at all, but cause effects which are general and important on the 
mean-motions of matter. It would thus seem that evidence of the general effects of 
such properties should be sought in those laws and phenomena known to us as the 
result of experience, but of which no rational explanation has hitherto been found ; 
such as the law that the resistance of fluids moving between solid surfaces and of 
solids moving through fluids, in such a manner that the general-motion is not 
periodic, is as the square of the velocities, the evidence covered by the law of the 
universal tendency of all energy to dissipation and the second law of thermo- 
dynamics. 
13. In considering the first of the instances mentioned, it will be seen that the 
evidence it affords as to the general effect of the properties, on which depends transforma- 
tion of energy from mean- to relative-motion, is very direct. For, since my experiments 
with colour bands have shown that when the resistance of fluids, in steady mean flow, 
varies with a power of the velocity higher than the first the fluid is always in a state 
of sinuous motion, it appears that the prevalence of such resistance is evidence of the 
existence of a general action by which energy of mean-mean-motion with infinite 
periods is directly transformed to the energy of relative-mean-motion, with finite 
periods, represented by the eddying motion, which renders the general mean-motion 
sinuous, by which transformation the state of eddying-motion is maintained, not- 
withstanding the continual transformation of its energy into heat-motions. 
We have thus direct evidence that properties of matter which determine the cause 
of transformation, produce general and important effects which are not confined to the 
heat-motions. ; 
In the same way, the experimental demonstration I was able to obtain, that 
relative-mean-motion in the form of eddies of finite periods, both as shown by colour 
bands and as shown by the law of resistances, cannot be maintained except under 
circumstances depending on the conditions which determine the superior limits to the 
velocity of the mean-mean-motion, of infinite periods, and the periods of the relative- 
mean-motion, as defined in the criterion 
DU,,/p = K, 
is not only a direct experimental proof of the existence of a discriminative cause which 
prevents the maintenance of periodic mean-motion except with periods greatly in excess 
of the periods of the heat-motions, but also indicates that the discriminative cause 
depends on properties of matter which affect the mean-motions as well as the heat- 
motions. 
