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1Q4 KANSAS UNIVERSITY QUARTERLY. 
longer it is in coming full in the wind and the greater the reduction 
of effective wind area and consequent loss of power. If the wheel 
would stay full in the wind up to, say thirty miles per hour, the 
curve CR would probably coincide with the parabola up to this 
value. 
The curves FS and HT are approximately parabolas, but the 
departure from the parabolic form increases as the load on the mill 
and wind velocity increases. 
MATHEMATICAL RELATIONS BASED ON THEORY AND. EXPERIMENT. 
Sir Isaac Newton, in his ‘‘Principia,” gave the first practical 
formula for finding the resistance of plates to the motion of a fluid 
against them. His genetal theoretical formula for the pressure 
when the plane of plate is at right angles to direction of motion of 
) 
the fluid is PeayA nai (pz) 
of 
P is the total pressure in pounds on the area, A the greatest area 
of plate, y the heaviness of fluid (pounds per unit volume), c the 
wind velocity and g the acceleration of gravity. 
This formula when modified to give ait pressure takes the form 
p OrO0e FeV Ae | 
; 2 
, (14 
(1+4-.003665t)B, 4) 
t is the temperature in centigrade degrees, B the reading of barom- 
eter at place of observation, B, the barometer reading at sea level 
and zero centigrade and c the velocity of the air in miles per hour, 
This purely theoretical formula has been tested by quite a num- 
ber of scientists and engineers and found to have a correct form, 
but to need a coefficient in order to give the measured pressure, 
The value of this coefficient, as found by these experimenters, 
varies in value from 1.3 to 1.8. . One of the latest and best of these 
values is 1.44, derived from Prof. S. P. Langley’s experiments. 
Introducing this value in (14) we have the formula 
p 0.00389 BA “a 
*G-f.003605t)B, 9) 
The wind velocity c is in miles per hour. 
Por ta=80 Cent, B==28.g ins, the standard conditions of the 
atmosphere when the test was made (15) reduces to 
P 
P, is in pounds per sq. ft., A in sq. ft. and cin miles Denon et 
3==0.00364Ac® (16) 
c is in ft. per second (16) takes the form 
P,==0.00169Ac? C17) 
