132 HEAT. 



are sufficiently close together to act very considerably on each other, and 

 work has to be done to alter their arrangements in any way, as is shown 

 by the elasticity of solids. 



In liquids, we must suppose that the molecules are not only agitated 

 but are travelling about, though only progressing slowly, for the pheno- 

 mena of liquid-diffusion show that the molecules take some time to 

 travel any considerable distance in a liquid. We may suppose that the 

 molecules possess on the average sufficient energy to do the work needed 

 to get away from their neighbours, but that they are still so near 

 together that they readily become entangled again. Their great resist- 

 ance to compression and their cohesion show, too, that the molcules 

 are near enough to act very considerably upon each other. 



The existence of viscous solids, such as pitch, intermediate between 

 solids and liquids substances which will flow like liquids if a sufficiently 

 long time is given to them seems to show that in these solids there 

 is a certain amount of travelling about of the molecules. We may, 

 perhaps, suppose that a given molecule will, in its excursions about its 

 mean position, come within the sphere of action of its neighbours in 

 such a way as to receive from them continual supplies of kinetic energy 

 which enables it to increase the extent of its excursion until it can 

 break away and travel on to some new position of less constraint. It 

 is quite possible that exactly the same process takes place in every liquid, 

 only on a much greater scale, many of the liquid molecules vibrating 

 about a mean position like solid molecules for a time, but ultimately, 

 by the action of neighbouring molecules, becoming detached and travelling 

 about till they become entangled by new surroundings. 



We may probably explain, by the aid of this supposition, the viscosity 

 of a liquid. If a liquid is in motion in one direction, but in such a 

 way that each layer moves slightly faster than the one below it, then 

 there is a tangential action between the layers proportional to the change 

 of velocity per unit length perpendicular to the layers. 



If, for example, the successive layers A,B,0,D, Fig. 76, are all moving 

 in the direction AX, but A moves v per second more than D at a 



distance d from it, the tangential 



. V force per square centimetre 



* exerted by each layer on the 



next is -, where n is the co- 

 c d 



efficient of viscosity. Now each 



D element of the liquid is being 



FIG. 76. sheared by the relative motion 



of the successive layers, and we 



may suppose that for a short time after the shearing the element resists 

 the shear just as a solid element would, but that the resistance rapidly 

 dies away, owing to the breaking loose of the molecules from their old 

 positions and their adjustment in new positions. The strain producing 

 the tangential stress is not the whole strain of the element since the 

 beginning of motion, but only that part of it in which the particles have 

 not yet had time to rearrange themselves. It is easy to see that if rate 

 of decay of strain is proportional to the strain, then if the relative 

 velocity per unit length v is doubled, this effective strain is doubled, and 



