Friction on Even Surfaces. 63 
Some measurements were made with the four-toot friction- 
board covered with various materials, to observe the effect of 
quality of surface upon the tangential resistance. Practi- 
cally the same friction was observed whether the board was 
covered with dry varnish or wet sticky varnish, or sprinkled 
with water, or covered with calendered or uncalendered 
paper, or glazed cambric, or sheet zinc, or Old English 
draughting paper, which feels rough to the touch. But 
when the piane was covered with coarse buckram, having 
sixteen meshes to the inch, the friction, at 10 feet a second, 
was ten to fifteen per cent. greater than for the uncovered 
surface; and the friction increased as the velocity raised to 
the power 2°05, or approximately as the square of the speed. 
The fact that such a variety of materials exhibit practically 
the same friction seems to indicate that this is a shearing 
force between the swiftly gliding air and the comparatively 
stationary film adhering to the surface, or embedded in its 
pores. If, as seems to be true, there is much slipping, this 
means that the internal resistance of the air is less at the 
surface than at a sensible distance away. As the shearing 
strength of a gas is due to the interlacing of its molecules, 
owing to their rapid motion normal to the shearing plane, 
it may be that the diminution of shearing resistance near a 
boundary surface is due to the dampening, within the film, 
of the component of molecular translation normal to the 
surface. 
To summarize the results attained thus far it may be said 
that, within the ascribed limits of size and wind-speed : 
(1) The total resistance of all bodies of fixed shape and 
aspect is expressed by an equation of the form 
Jo OC KA MOSM I A Sy RES Ree i aeeeny (4) 
R being the resistance, v the wind-speed, a, n numerical 
constants. | 
(2) For smooth planes of constant length and variable 
speed the tangential resistance may be written 
Bene ney a hiiay) p< suche) ss) C8) 
(3) For smooth planes of variable length / and constant 
width and speed the friction is 
ae SN I a ak 8 () 
(4) All even surfaces have approximately the same co- 
efficient of skin-friction. 
(5) Uneven surfaces have a greater coefficient of skin- 
friction, and the resistance increases approximately as the 
square of the veiocity. 
