Examination will at once justify this view. Thus we find a great many systems which are adequately described in terms of two variables, pressure and temperature, in that a function of _p_ and _t_ can be found such that its differential equals _dQ_ + _dW_. There are other systems in which the six components of stress and _t_ completely fix the internal condition in the sense that they determine a _dE_. In other systems the specification of a magnetic field may be necessary, or an electric, or a gravitational field. No case is known which cannot be handled in terms of the action of external forces of the proper kind, but there is no general procedure, and the first law owes its generality to the exhaustive cataloging of special cases. We may now return to the question left in abeyance above of the ambiguity in _dQ_ + _dW_. In all the cases in which the specific variables can be found which define _dE_, _dQ_ and _dW_ also have meaning. Consider, for example, a gas, the internal condition of which may be characterized in terms of _t_ and _p_. The mere fact that the internal condition can be specified in terms of two variables, one a mechanical variable, shows that the substance is mechanically homogeneous. Being mechanically homogeneous, we do not have the possibility of ambiguous values of _dW_ varying with the scale of the measuring instruments, and in fact we know that dW = p dv. Similarly the gas being homogeneous and at rest as a whole allows unique values for _dQ_. Of course this cannot obscure the physical fact that even in such a gas, when we go to a small enough scale, we find inhomogeneities arising from the Brownian movement, etc. Practically our statement means that the inhomogeneities are so fine grained that over a very wide range of scale of the measuring instruments we find the same definite results. The same sort of considerations apply to more complicated systems. If _dE_ is a complete differential in terms of _t_ and six stress components, this means again that the body is homogeneous, its condition is determined by temperature and stress, which are the same throughout the body, and again there is no possible ambiguity from the scale of the instruments which measure _dW_ and _dQ_. It seems in general, then, that if the body allows operations by which _dE_ acquires meaning, at the same time _dQ_ and _dW_ are provided for. In working out this idea in full detail, some care must be given to the question of order of differentials. _dQ_, for unit time and unit volume, is strictly equal to k∇^2 t, where _k_ is thermal conductivity, so that in determining _dQ_ the second derivatives of temperature are involved. If the body is obviously not homogeneous, it is still a matter of experience that it can be divided into small pieces, each of which are by themselves sufficiently homogeneous, and the first law in its usual form may be applied to each of the pieces.