THE UNIT DIAPHRAGM SCALE This diaphragm scale is different from all others in that it is a geometrical series of cone values starting with that of f/ 64 as unity. These diaphragms therefore do a certain work in more or less time as there are a lesser or greater number of units working and exposure problems are in this manner brought under the ordinary processes of reasoning. It is strongly recommended therefore that this unit scale be substituted on all lenses and shutters as a pre paratory step in learning the theory and practice of this system. In the scheme defining the unit cone (p. 25) the principle involved in the unit method of diaphragm numbering is fully explained.
In order to substitute the unit scale for that of the f or U. S. scale which is already applied to the lens, it is necessary only to substitute the equivalent unit scale numbers for those of the old scale. Find in the f or U. S. column (see table, p. 32) the numbers already on the lens and the equivalent unit number in each case will be seen on the right in the column headed " cone unit value." On request makers of lenses ought to supply unit scale plates interchangeable with those already attached to their lenses. The worker may easily make for himself however a thin, stiff card-board plate or even a metal one having the same form as the diaphragm plate on his lens or shutter and mark the intervals or lines on it in the same position as on the original plate but using the unit scale numbers. This plate should then be fastened in the position of the original one.
If preferred the diaphragms may be deter mined and the scale applied with practical accuracy by the following method. If the focal length of the lens be not known, find it with sufficient accuracy by measuring the distance from the diaphragm to the ground glass when distant objects are in focus. One sixteenth of I this distance gives the diameter of the stop which is numbered 16 in all the scales as will be seen ' in the table on page 32. It subtends in double lenses of popular construction, 16 cone units at a point on the plate since it has 16 times the solid angle of the unit cone and diaphragm.
Now multiply this diameter by 1.41 ( = 1.41 + ) which will give the diameter of the 32 unit diaphragm or number 32 of the unit scale. Then, doubling the diameter of diaphragm 16 gives consecutively the diameters of the unit scale numbers 64 and 256 and by halving it consecutively are obtained the diameters of diaphragms 4 and 1. Doubling the diameter of number 32 gives consecutively 128 and 512 and halving it, the numbers 8 and 2. There remains only to place the index or lever so that the openings assume these respec tive diameters and mark the position of the index with the corresponding unit scale number which is simply the unit value of the cone formed when the index is in that position. In
sizing the diaphragms as just described iris diaphragm shutters should be snapped open to get the size, instead of using the shutters open and approaching the size with the stop lever. This is advised in order to obviate errors due to any possible lost motion in the shutter mechan ism. The author has observed cases in which at the small openings an error of more than 100 per cent would be made by disregarding this advice. Of course if there is excessive false play the shutter should be repaired or discarded.
Multiplying the diameter of one diaphragm by 1.41 to obtain that of the next larger or the one having double the rapidity of the first is in compliance with the fact that circles having areas varying as the numbers, 1, 2, 4, 8, etc., have diameters which vary as the square roots of these numbers or as 1, 1.41 +, 2, 2.82 +, etc.
With regard to the small hand cameras of the Brownie and Buster Brown type, the "large," "medium," and "small" stops may best be con sidered in the unit scale 32, 16, and 4 respec tively. The single diaphragm in the still smaller or "one diaphragm" cameras may be considered as unit number 32.
The table which follows expresses the sphere value, the f number, the U. S. number and the cone unit value of all cones from f/ 64 to f/1 : At the beginning of the preceding discussion it was stated that a cone equal to 1/16 of a sphere was only approximately f/1, and it follows of course that the equivalent values in the above table are only approximate. The approximation however in the case of that which we have chosen as the cone unit is very close. As a matter of fact 1/65,536 of a sphere (that given as, 1/64M in the first column), is equivalent to f/ 63.99 + instead of 1 / 64. In the higher values the error is a much higher percentage of the whole quantity involved, but the allowable variation in photographic exposure time is so great as to make even these greater differences quite negligible in practice.
The author realizes the difficulties in the way of the general adoption of a new diaphragm scale, especially as many thousands of lenses and shutters are already in use graduated in one or another of the older systems. It must prove an attractive system indeed that will induce the photographic worker to rearrange the diaphragm scale of his lenses. Those who realize the advantages of a unit method in raising pho tography out of the chaotic state of its present practice, will do well to urge their respective societies to adopt this method unless a still more practical unit may be decided upon. Only in this manner will it be possible to interest the various National Bureaus of Standards and secure their aid in establishing an international unit and scale. (See beginning of Chapter IV, p. 49.)