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CAMERA APPLIANCES 137
a minimum useful size. He gave a formula by which this minimum size can be calculated. It is as follows : aperture = 0008 Jd. Thus suppose d = 10 inches, then Vl0 = 316, and 3*16 x0'008=0'025 + . So that in this case the least diameter of the hole giving good results would be -fa" about. (Compare the three results which are obtained by different formulae and have been worked out.)
In practice it is not necessary to provide different apertures for each different focal distance, on account of the wide range over which good results can be obtained.
The pinholes should be circular in section, and could be made with suitable needles in thin metal sheets, the rough edges being filed off, if the holes are punched. The great disadvantage of this photographic apparatus is the very long exposure which it is necessary to allow.
To find the length of exposure the / value may be calculated from tt-7 — — i ; thus, if aperture =A/" and
distance of screen r
distance of screen = 10", the /ratio is 1/40/10 =//400.
Now suppose it is found that //8 requires ^ second, then //400 will require ^V x2500 seconds = 125 seconds, i.e. 2 minutes 5 seconds.
In such a camera there is, of course, no distortion, but only fixed objects can be photographed by means of it.
It is, of course, very difficult to see the image on the screen ; perhaps the best means of judging the amount to expect on the plate is to have a slightly larger hole to replace the pinhole (one about J" diameter will do) ; then turn the camera round, remove the screen and look through the new aperture. The amount now visible when the eye is close to the hole will be approximately that included in the picture. A good idea of the amount included may also be obtained by calculation (see p. 135) if the distance of the object is known.
In our further consideration of the camera it will