It seems fairly evident in the first place that we shall have to rule out systems in which there is large scale mechanical motion; the simple notion of temperature does not apply to a system moving with respect to us. Only when the two thermometers A and B move with the same velocity as the stream do we have three-fold equilibrium between the stream, A and B. We may state this in another way by saying that the temperature of a moving body must be measured on a thermometer stationary with respect to the body, but this is only a matter of words, and properly speaking the temperature concept applies only to a certain aspect of the relation between two bodies mutually at rest. We here entirely neglect relativity questions such, for example, as the proper way of correcting for the change of dimensions of moving thermometers. If now the body whose temperature we are measuring does not move with the same velocity in all its parts, we may still give a meaning to local temperature by dividing the body into parts so small that the velocity of each part is essentially uniform, and measuring the temperature of each part with a thermometer stationary with respect to it. We are now confronted with the question of how far to carry the process of subdivision. Suppose we have a fluid whose motion is completely turbulent when measured with instruments of the ordinary scale of magnitude. For such a fluid the fundamental equilibrium proportions hold between two measuring bodies A and B and the fluid, provided that the bodies A and B are so large that the motion is completely turbulent on their scale of magnitude. We may then define the temperature of the turbulent fluid from the standpoint of these large scale bodies. But we may also define the temperature from the small scale point of view as the average of the temperatures recorded by sufficiently small thermometers, each moving with the velocity of a local bit of the fluid. These two temperatures will in general be different, and we must more or less arbitrarily select one which we define as the true temperature. It would seem that the small scale temperature is the better one to choose, because there is a certain degree of arbitrariness in specifying the scale from which the motion shall be judged completely turbulent But on the other hand, there are difficulties in the small scale definition, because the turbulence may become more and more fine grained, until we end with the motion of the molecules themselves, when the operations certainly fail which give meaning to the temperature concept. In this case of molecular turbulence, we are driven back to the large scale definition, which obviously corresponds to ordinary physical practice.