24 



EXPERIMENTS IN AERODYNAMICS. 



The values in the tables are subject to a correction resultins,- from a flexure 

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

 that the trace of the plane sot at 90° did not coincide with the horizontal (/. e., 

 the perpendicular to the vertical) line marked on the trace, but was uniformlv 4° 

 or 5° below it; so that the angle between the vertical and the trace of the plane 

 did not measure 90°, as had been assumed, but uniformly 94° or 95°, the average 

 being 94°.6. This result was found to be due to the bending biickward 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 wliich 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°, 35°, 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,-j- 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 



* The ratios given by the " corrected curve " of the diagram have been tabulated for angles of every 5° and 

 then compared with all the exiseriments and forniulfe with which I am acquainted. Only since making these 

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

 whose valuable memoir puljlished by the French War Department, Manorial ck VArtiUerie No. V, I regret not 

 knowing earlier. The following taljle presents my values, the values given by Duchemin's formula, and a column 

 of differences: 



Rdlhi iifthe total pressure (Pa ) on an inclined square plane to the pressure (Pgo) on a normal 

 ]>lane moved in the air until the same velocity. 



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



