332 Mr. S. Skinner on the Occurrence 
same, and that the viscosity of the central layer is very much 
less. Let PQ represent a line in the layers when AB and 
CD are at rest. If now AB moves with a velocity QQ’, 
then the relative velocities of the particles in parallel layers. 
will be represented by the displacement of PRSQ to PR’S’Q%, 
RR’ and SS’ representing the velocities at the boundaries of 
the central layer. If, as we have supposed, the viscosity of 
the central layer is very small compared with that of the 
other layers, the inclination of R/S’ will be great, whilst 
PR’ and 8’Q’ will be nearly parallel to RQ. In words, the 
tangential force opposing the motion of AB will be almost 
entirely due to the thin central layer of very slightly viscous. 
fluid. 
Next we consider the case where CD makes an angle with 
AB, and EF and GH represent as before the boundaries of 
the three liquid layers. It is shown by O. Reynolds (Joc. eit.) 

that when one of two plates, at an angle with one another, 
and having viscous liquid between them, AB is moved in 
the direction AB a tension is produced tending to draw the 
plates together. The line PRSQ becomes PR’/S’Q’. If 
AB moves in the direction BA this tension becomes a pres- 
sure. Let us suppose that the ends of the lines EF and GH 
are joined, and then we shall have a cavity filled with less 
viscous fluid in a mass of viscous fluid between the two 
plates. Cases similar to this are treated in this paper. 
$6. In figs. 3 and 4 (Pl. XVII.) is represented a cylindrical 
lens lying ona plane surface with some fuchsin-glycerine solu- 
tion between them. In fig. 3 everything is at rest, and the line 
of nearest approach of the surfaces is shown by the absence 
of colour, i. e. the bright band down the centre. In fig. 4 
the cylindrical surface is being rolled by the fingers from 
left to right, and the transparent line of nearest approach is 
