Air at Speeds helow One Thousand Feet a Second. 53$ 



Knowing the fall of the plate at the middle of each eclipse, 

 the time of transit from beam to beam is fixed with an 

 accuracy proportional to the precision of the engine-readings 

 and the freedom of fall of the plate. The error introduced 

 by assuming that the plate falls without any resistance 

 amounts to less than one twentieth per cent, of the time of 

 fall, since the resistance never exceeds one thousandth of the 

 weight of the plate and holder. The error due to want of 

 precision in the engine-readings may be one or two millionths 

 of a second ; for the plate, when the interruptions occur, has 

 a speed of about 2500 millim. a second, which divided into a 

 quantity less than 0*005 millim. gives a time error less than 

 two millionths of a second. 



The true projectile velocity midway between the sunbeams 

 is very accurately equal to the average velocity between them, 

 even for light wooden balls, because the beams are so near 

 together. It can be shown that for dry pine balls moving 

 500 feet a second, the average and mid velocities differ by less 

 than one fiftieth per cent. 



Having measured the distances h l9 Ji 2 , h 3 , through which 

 the plate has fallen when the ball is midway across each beam, 

 the times of fall, t l7 t 2 , f g -, are found by the formula t = (2h/cf)i T 

 for free fall in vacuo, which has been shown to be legitimate 

 for the chronograph used. From the times t 1} t 2i t 3 , are found 

 the projectile velocities, 



7 7 



l 2 — 1 1 H — &2 



at the middle of the first and second seven-foot stages. The 

 resistance may be obtained by writing the work done by the 

 ball equal to its loss of energy ; thus 7R=|??i(f 1 2 -i i 2 2 ), 

 whence H=^pn(v 1 + v 2 ) (v x — v 2 ), m being the mass of the 

 ball, R the retarding force. By using a seven decimal table 

 of logarithms and arranging all the work concisely, it is 

 possible, with ordinary skill, to compute t 1} t 2 , t 3 , v 1} v 2 , and R, 

 for one shot in about twenty minutes to half an hour, and 

 review the work ; which is about the time required to measure 

 the record on the dividing-engine. 



The accompanying table gives the essential data and the 

 computed velocity and resistance for a four-inch ball obtained 

 from ten records. The resistance values in the last column, 

 also those following the table, are given without correction 

 for the temperature and barometric pressure of the atmosphere; 

 but these corrections, if made for the mean conditions of tbe 

 experiment, would not materially alter the curve of resistance 



