1888. | NEW YORK ACADEMY OF SCIENCES. 103 
milligrammes on each limb. The seven vibrations divided by 
the rate of the fork gives directly the 4, of a second as the time 
required by the shutter to fly 4.75 cm., which is the actual 
distance traversed by the shutter, though the distance between 
the vertical lines is a millimetre or two greater, owing to the 
expansion of the film. From these data the velocity of the 
shutter is easily calculated. The time of exposure, which is 
another matter, may be found quite as easily by methods which 
vary in different cases. 
As an illustration, take first the case of ashutter of inconsider- 
able thickness, having an opening of 1.905 cm., and passing 
close behind an exposing aperture of the same diameter. First 
must be determined the distance the shutter must traverse to 
open and close the aperture. That this distance is in this case 
3.81 cm. or twice the diameter of the aperture is shown by the 
diagram, Fig. 3. 
A. The shutter. 2B. The exposing aperture. To complete 
Fic. 3. 
an exposure the side A of the shutter opening must move from 
a to b, twice the diameter of the aperture. 
In order, therefore, to determine the time of exposure in this 
case, measure 3.81 cm. upon the film Fig. 2, by taking 1.905 
em., plus half the gain by expansion in each direction from a 
point midway between the vertical lines. 4.75 waves can be 
fairly counted in the 3.81 cm. so located, and these divided by 
331.25 vibrations, the rate of the fork, give =; of a second as the 
time of exposure. 
If, however, the shutter be not of inconsiderable thickness, or 
not close against the exposing aperture, other considerations are 
involved. Suppose, for instance, we have an exposing aper- 
ture of 1.27 cm. before a simple achromatic lens, and a shutter 
opening of 1.9050 cm., but have the shutter so far behind the 
diaphragm, as shown in Fig. 4, that when the openings are su- 
perposed the diverging rays entering the aperture just fill the 
shutter opening. The case seems practically the same as before, 
because the shutter must still move 3.81 cm. from the beginning 
