62 Dr. A. F. Zahm on Atmospheric 
law of its variation with length of surface. To that end 
the values in Table IL. were plotted on logarithmic cross- 
section paper, as shown in fig. 3. The diagram is a straight 
line whose equation is : 
PO 0 Oy Bs 
in which f is the average friction in pounds per square foot 
Fig. 4.—Relation between Length of Board and Average Friction. 
-0006 
at a speed of 10 feet per second, and / is the length of sur- 
face in feet. At one foot per second, therefore, the coefficient 
is 0-000551 + 10**°=0-00000778. Hence at any speed, x feet 
per second, the average friction per square foot is : 
f=0:00000778 [oO Sw we CB) 
Assuming the two laws thus far derived to be true for the 
planes and wind-speeds employed, we may readily express 
the total friction on a plane of any length, from 2 to 16 feet, — 
moving at any speed from 5 to 40 feet per second. Thus, by 
equation (@) the total friction I, on a surface one foot wide 
and / feet long is :— 
F =/1=0-00000778 19,18, (v= ft./sec.). 
Of course this value of F must be doubled for a material plane 
of length /, since a material plane has two sides. 
lt may now be inquired what other circumstances alter the 
surface-friction. Perhaps the chief of these are the atmo- 
spheric changes of density and the unevenness of surface. 
No effort was made to determine the relation between the 
density and skin-friction of the air, partly for want of time, 
partly because too great changes of density would be needed, 
with the apparatus in hand, to reveal such relation accurately. 
Doubtless the friction increases with the density, since it is 
due to the inertia of the fluid near the friction surface. Of 
course in steady motion at low velocity, such as studied by 
Maxwell, the conditions are different. He found that when 
one plane moves edgewise near and parallel to another plane, 
at a constant speed below one twelfth of an inch per second, 
the friction is independent of the pressure, and proportional 
to the absolute temperature, for such atmospheric conditions 
as prevail near the earth’s surface. 
