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ZAHM. 
uniform wind, where, moreover, the instruments give steadier 
readings. 
On comparing the above results with those obtained by 
Dr. Froude for water, it is found that the equations are very 
similar. The exponents are nearly the same, and the co¬ 
efficients are to each other roughly as the densities of air 
and water. Using varnished friction-boards, Froude finds 
n = 1.85 for a surface 8 to 20 feet long, and n = 2.00 for a 
plane 2 feet long; I find n — 1.85 for all lengths from 2 to 
16 feet. By Froude’s measurements the friction varies as the 
power 0.83 of the length for varnished planes 2 to 20 feet 
long; I find it to vary as the power 0.93. With a varnished 
board 2 feet long, moving 10 feet a second, the ratio of our 
coefficients of friction for air and water is 1.08 times the ratio 
of the densities of those media under the conditions of the 
experiment. 
But in some respects Froude’s results are quite unlike mine. 
For several surfaces he finds the skin-friction to vary as the 
square of the velocity, or nearly so, which is the relation I 
observed in a turbulent current and when the friction-board 
was vibrating slightly. He finds the friction of calico about 
twice that of a varnished surface ; I find that glazed cambric 
has about the same friction as a varnished surface; but if 
the cambric is roughened, so as to expose a fine down, the 
friction is very much increased. 
The fact that for some surfaces the coefficients of friction 
for air and water are roughly as their densities is of consider¬ 
able interest. It is well known that the head resistances of 
the two fluids are directly as their densities, and if their fric¬ 
tion coefficients also bear that ratio, the total resistances must 
be approximately as the densities. Hence the data obtained 
from water-resistance measurements on such surfaces may be 
fairly well applied to estimate the air resistance on various 
shaped models. 
It is not, however, self-evident that the surface friction of 
any two fluids is proportional to their densities, and should 
not be taken for granted. It happens to be roughly true for 
