The author shows briefly:

The origins and the relations of the idea of the dynamic film to the classic results concerning viscosity. How one can pass from one idea to the other, and in the expressions Δu and Δv make the forces tangent and normal to the elements of films appear in the case of movement parallel to a plane.

The introduction and the significance of the curvature φ of rectangular trajectory to the filaments, which comes into the new expressions for Δu and Δv, together with the curvature ψ of the filaments.

The condition of rectangularity between filaments and trajectories gives a relation between ψ and φ and their partial derivatives following these curves. A very simple and new form for the component of the viscous force due to the velocity, with its new notations.

Discussion of results. Experimental study of simple slip—arrangement employed—influence of the proximity of the walls—inadequacy of the classical expressions concerning the forces due to convergence or divergence—plane films with forced uniform motion—schematic picture of actual lubrication in the case of considerable speed of rotation—the zone of crushing (Leslie pressure)—the two zones of viscous acceleration—the surface of zero velocity.

Test of an intrinsic method of rectangular system of coordinates with application to the dynamics of incompressible fluids. Use of the new functions
Φ′ = Φ∂s2/∂y; Ψ′ = Ψ∂s1/∂x
to define a system of curvilinear coordinates by the curves carries to the axes.

The potential of curvature and the factor of torsion. Representation of the expressions γx and γy.

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