88 FLUIDITY AND PLASTICITY ' nearly additive as the flow progresses and the mixture becomes more and more nearly complete. This result takes place further- more irrespective of the original arrangement of the parts of the mixture. Some one may object that a perfectly homogeneous mixture — in itself a contradiction of terms — is not made up of layers such as we have considered in these greatly simplified cases. There can be no doubt whatever of the existence of layers during the process of mixing. N"o "one has watched the drifting of tobacco smoke in his study without noting how it is drawn out into gossamer-like layers.1 Since the fluidity is least \vhen fluidities are additive, there would have to be a sudden drop in fluidity as the mixture became perfect, if the fluidities were no longer additive. This is not supported by any experimental evidence. We have already noted that when there is no chemical action between the components of a mixture, the viscosity-concentration curves are usually but not always sagged. Dunstan (1913) has put it: "It can therefore safely be predicted that wherever the two components show little tendency for chemical union a sagged curve, or one departing but slightly from linearity, will be found." If the fluidities of such mixtures are additive, these facts ought to be accounted for by the theory, peculiar as they may seem to be. We shall first prove that according to the theory that fluidities are additive, we should expect the viscosity- concentration curves to be sagged. Equations (25) and (24) represent the two assumptions that fluidities are additive and that viscosities are additive respectively but for convenience we shall assume that only two components are present in the mixture. From Eq. (23) we get that or b'. For all intermediate values of a and b we desire to learn