24 



EXPERIMENTS IX AERODYNAMICS. 



The values in the tallies are subject to a correction resulting from a flexure 

 in the balance-arm am! its support. It was observed (see note in Table III) 

 that the trace of the plane set at !»ll did not coincide with the horizontal (/. e., 

 the perpendicular to the vertical) line marked en tin- trace, hut was uniformly 4° 

 or •") below it ; so that the angle between the vertical and the trace of the plane 

 did net measure 90°, as had been assumed, but uniformly 94 c or 95°, the average 

 beiiii> - 94°. (J. This result was found to be due to the bendins; backward of the 

 balance-arm and its support by the pressure of the wind, while the recording 

 board and plumb-line presented only a thin edge to the wind, and consequently 

 remained relatively fixed. During motion, therefore, the plane actually had an 

 inclination to the horizon about 5° greater than the angle at which it was set when 

 at rest. This flexure seemed to obtain for all angles of experiment, but with 

 indications of a slightly diminishing effect for the smaller ones; consequently 

 the pressure ratios above given for angles of 45°, 30°, 20°, etc., really apply to 

 angles of about 50°, 3o c , 25°, etc. After making this correction the final result of 

 the experiments is embodied in the line of Fig. 1 designated "corrected curve."* 



At the inception of the experiments with this apparatus it was recognized 

 that the Newtonian law,f which made the pressure of a moving fluid on an 

 inclined surface proportional to the square of the sine of the angle between the 

 surface and the current, is widely erroneous, though it is still met in articles 

 relating to fluid pressures, and vitiates the results of many investigations that 



*Thc ratios given by the "correcte 1 curve" of tin- diagram have been tabulate 1 for angles of every 5' and 

 thru compared with all the experiments and formulae with which I am acquainted. Only since making th 

 experiments my attention has been called to a close agreement of my curve with the formula of Duchemin, 

 whose valuable memoir published bj the French War Department, Memorial <>< VArtilleru No. V, 1 regret not 

 knowing earlier. The follow ing table presents mj values, the values given by Duchemin's formula, ami a column 

 of differences 



Ratio of th total pressun [Pa an inclined squan plant totlu pre» ■ P 



plant mom d in th a> ity. 



t Implicitly contained in the Principia, Prop. XXXIV, Book II. 



