ATMOSPHERIC FRICTION. 
259 
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 
R — av 1,85 ..... 0). 
(3.) For smooth planes of variable length, l, and constant 
width and speed the friction is 
R = al * 93 .0). 
(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 velocity. 
The equation R=av n was found to express very accu¬ 
rately the resistance of all the shapes tested at speeds from 
five to forty feet a second. For normal planes, spheres, 
cylinders, and blunt bodies generally, except very small ones, 
n equals 2, very approximately; for thin, tapering bodies 
n may have any value from 2 to 1.85; but in every case, if 
the form and aspect of the model remain fixed, a and n are 
found to remain practically invariable for all the speeds em¬ 
ployed. This was manifested by plotting the speed and 
resistance on logarithmic cross-section paper and observing 
that the diagram was invariably a straight line for all the 
models tested. The statement cannot be true for a great 
range of speeds. 
Such were the results obtained in a wind of uniform 
velocity and direction. When, however, the current is tur¬ 
bulent a and n are found to vary considerably; but since 
the flow of a turbulent wind cannot be specified, the meas¬ 
urements obtained in one such current cannot well be ap¬ 
plied to determine the resistance in a different one. For 
that reason it seemed better to make the measurements in a 
