THE SPECIAL NEED OF UNIT DIAPHRAGM NUMBERS On seeing the f as well as the unit system employed in the problems in the following chap ter, some reader may justly ask why the author should find the former so unfit for the number ing of lens stops. This has been explained but should be discussed more fully.
Suppose a simple exposure problem: If, under certain conditions, stop f/16 is found to require an exposure of 4 seconds what exposure will stop f/8 require? The rule with the f system is that the exposures vary as the squares of the f numbers and therefore the following proportion: is to 8' as 4 is to 1, gives the exposure with f/8 as 1 second.
The trouble with this rule is that it does not disclose the reason for the answer which it secures. The nature of the computation re quires for its intelligent working, a knowledge of the relation of cone values as involved in the f system and a knowledge of the geometric truths which concern the relation of the circum ference of a circle to its diameter, including the extraction of the square root of numbers.
A small boy with a pile of wood to deposit in the wood-house is well aware that if he can get another boy to help him they can do it together in half the time. Just so one would analyze immediately the truth involved in stops if they were marked with their values only and could be thought of the same as "one boy" and "two boys" at work. The truth is that with the f or any markings other than of simple solid angle values, the above rather advanced mathe matical problems must be comprehended in order to perform a computation which does not disclose at any step the basic principles involved.
Why is the exposure with f/8 1 second when it is 4 seconds with f/16? In the analysis of this problem of simple cause and effect the "exact science" of mathematics admits of but one line of reasoning: "Stop f/8 requires one quarter the exposure of stop f/16 because it has four times the working dimension or solid angle of f/16. There is no other way of reasoning
to be found for the problem and although the f or the U. S. numbers may be employed, or even though we might distinguish the stops from each other with the names of great mathe maticians or of mythological gods, when we analyze the problem, we must come down to the same simple reasoning as that used by the boy with the wood to carry.
With stop numbers then, we may evaluate solid angle in simple units, and use them in computing exposure as we use the "dollar," and "grain" in computing problems of value, length and weight, or we may not do so and whether we do so or not is the one impor tant matter in stop numbering.
The problem of the wood, calculated so easily by the small boy, can not be simplified and that of calculating exposures with the help of solid angle unit values is exactly the same in char acter. By fixing this unit the requirements of science would be complied with, in that "the unit would be of the same character as the thing measured." Also it would be to the advantage of all who practise photography, even though they be children or people of little or no education, since only the simplest reasoning is involved.
Since a unit of actinicity can not be fixed without first fixing that of solid angle it may be truly said that the whole train of lamentable conditions in photography relative to exposure are due to the failure to recognize this solid angle dimension as a simple quantity value and fix a unit of it for use both in and out of lenses.
It will be well to group here the most impor tant of these conditions: Probably three quarters of the cameras in the world have been made and are still being made without stop numbers. If the use of stops were understood generally the public would demand that all lens stops be numbered.
The people who use these cameras as a rule simply guess at exposures and finally learn, through their failures; to confine their "shoot ing" to sunlighted subjects.