480 PROCEEDINGS OF THE AMERICAN ACADEMY 



fork between the starting-point and the points observed is denoted by 

 t^ and t.,, and the acceleration of gravity during one vibration by (/. 

 The distance Sj in general did not much exceed a centimeter, and the 

 retardation of the atmosphere for tliis distance could for a first approxi- 

 mation be neglected. The theoretical distance S,-^ traversed by the ball 

 will equal 



Substituting s^ for S^ , we get an approximate value of *S, , from 

 which S^ may be calculated, and substituted in the above formula. A 

 small correction to the observed distances had to be made, owing to 

 the angular motion of the spot of light on the ball, but this did not 

 exceed two millimeters in any case. From the measurement of five 

 photograjAs taken on three diiferent days, and with two different ar- 

 rangements of the ball and scale, it was found that a ball of the above- 

 mentioned size and weight was retarded proportionately to the distance 

 traversed ; and that the retardation amounted to exactly .03 of the 

 distance. The maximum fall measured was one meter. This retarda- 

 tion would be proportional to the square of the diameter of the ball, 

 and inversely as its weight ; hence we have the equation : 



„ , . .03 X 25 rf2 .0435 rf2 



Retardation r = — ^ ,.., — = . 



4.1o- to w 



It will therefore be seen that *for drop-shutter exposures where an 

 accuracy of three per cent is entirely out of the question, we may 

 neglect the retardation of the air entirely, or, better still, counteract 

 it by placing the ball just in front of the scale to be photographed, at 

 .03 of the distance between it and the lens. 



Apparatus for Measuring Instantaneous Exposures. 



The apparatus which I have adopted as the most convenient for 

 measuring drop-shutter exposures of .05 sec. or less consists simply 

 of a box filled with cotton wool, to the back of which is nailed a verti- 

 cal slat, 50 cm. in height, painted black, on wliich, at the intervals 

 given below, are painted fine white horizontal lines, numbered from 

 up to 30. The apparatus is placed in the sunlight, and a glass ball 

 hung by a silk thread is suspended at such a height that when focused 

 in the camera the spot of light upon its surface shall coincide with the 



