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|    NATURĘ OF VI SCO SITY

amorphous rings in the Debye-Scherrer X-ray j diagrams of liąuids in temporary molecular groups 1 o| tliis kind. He has called the phenomenon " Cybotaxis,” and the groups themselves " Cybo-rnas.” This treatment is really statistical, sińce one I must not consider the individual cybomas as I permanent entities. It is simply that the molecules are associated for longer than would be the case if I there were no fields of attraction (vide Houwink). I Ward considers that viscosity depends on the I number of molecules having enough energy to 1 convert applied shearing stress into configurational . j change. He uses the probability eąuation rj = Ag^B/^RT, in which A and B are constants. B is not, in fact, independent of temperaturę. Curves plotting log ij I against x/T should be linear, and are nearly so for water. There are deviations in both senses for other materials. Eyring and co-workers have developed a theory of viscosity based on the idea that the elementary process of shear consists in the passing of a single molecule from one eąuilibrium position to * another, over a potential barrier. The movement of molecules, relative to each other, is thus a process exactly similar to that involved in ordinary Chemical reactions. A complex mathematical theory has been evolved to relate viscosity to the distances between molecules in the piane, and at right angles to the piane of flow, to the partition functions of the 1 molecules, and to the activation energy for the flow process. Ewell is gradually applying these new conceptions to explain the anomalous viscous behaviour of such materials as resins and glasses.

For a generał account of the theory of liąuid structure, the reader is recommended to consult the Royal Society Discussion on this subject, published in 1937. Altar’s " theory of holes ” cannot be :

dealt with fully here, He not only considers the bchaviour of molecules of evaporatcd liąuid surrounded by gases, but with his co-workers he deals with the negative conception of the hole left in the liąuid by the departure of the molccule. For ordinary shear to take place, such holes must be formed by a process analogous to dilatancy (which will be dealt with later). The theory of holes in fluids may be considered in comparison with Smekal's i Lockerstellen | theory, which will be dealt with in connection with the theory of solids.

At this point it would be well to consider the naturę of a true fluid. Of the early work done on the flow of water through pipes, that of Bemouilli (1726) is the best known, but he excessively idealised his conditions. The first extensive experimental determination of the laws of flow is due to Poiseuille¹ (1846), who was interested in the flow of blood through arteries, veins and capillaries. He studies the flow of water through narrow tubes and estab-lishes laws of flow from his observations. Hagen first derived equations of flow from theoretical considerations; and it was not until Stokes (1845) re-introduced the Newton hypothesis of proportion-ality between stress and ratę of shear that even the simplest eąuation was finally derived in its entirety.

There are many ways in which viscosity can be measured and many physical processes into which it enters. The simplest case to consider is that of the flow of a fluid through a long, narrow tubę, and this was in fact the first case to be worked out, leading to the formulation of the Poiseuille-Hagen law. This law, which relates the ratę of flow of a fluid through a capillary tubę to the pressure applied and to the

¹ Hagen had published some quantitative experiments as early as 1839, i.e., before Poiseuille's work appeared.