PROBLEMS IN UNIT ACTINOMETRY To Find the Actinicity of Any Surface of Known Average Diameter and Known Distance from the Tinting Medium, t.e., of Known Cone Value.
To illustrate this problem suppose that the average actinicity of a common kerosene flame is desired. Measure or estimate the average diameter of the flame and take its time at a distance of (say) two of its diameters from it. Its impinging cone is therefore f / 2 in form. The time on the standard emulsion in the present case is found to be 8 seconds. Dividing this number by 4, the square of the f value gives a result 2, the seconds of first appearance time as though measured at f / 1 or with the meter. Now, 64 divided by this time gives 32, the aver age intensity of the flame in actinos.
Rule: Divide the standard emulsion first appearance time of the surface at whatever f value measured, by the square of that f value. The quotient will be the standard meter time at the convergence of f / 1 or as though measured with the standard meter. Its actinicity is now found in actinos according to the rule for using the standard meter, i.e., by dividing 64 by the meter time.
In the case of a flame its average actinicity would be found by the above method, and this is what must be known provided it is to be used as a source of illumination for some other surface which it is intended to photograph. Should one wish to know the actinicity of the brightest part of the flame or that part a little above the center, then the base of the impinging cone to be meas ured must necessarily be confined to that part. This might be accomplished by placing a piece of thin metal with an opening in it a little smaller than the uniformly intense part of the flame, in such a position that the opening will come oppo site and in close proximity to the flame. The measurement could then be made as before but on the basis of the diameter of this opening instead of that of the average diameter of the whole flame.
Although the preceding method is simplest in practice it is necessary to give another method based on the use of the cone units. The time was taken in the foregoing example at the con vergence of f / 2 and this cone is equal to 1M cone units. Then if 1M cone units will produce a least visible tint in 8 seconds one cone unit of that light source would require 1M times 8 seconds or 8M seconds. Now the standard time
of unit intensity with f / 1 is 64 seconds and with the one unit cone, which is only 1/4M of 1/ 1, it must be 4M times 64 seconds or 256M seconds. Then since the one cone unit time of the flame is 8M seconds the flame must be as many actinos in intensity as 8M is contained times in 256M which is 32 times. Therefore the intensity of the flame is found to be 32 actinos as before.
As another illustration, to measure the actin icity of the sun it is necessary as in any other case to confine its cone to a convenient f value and as the sun's total f value in relation to any point on the earth's surface is approximately f / 108 it is best to reduce it to the form of f / 128 to preserve the geometric series by 2. This may be accomplished simply by arranging to let it shine through any small opening while the tinting medium rests at 128 times the diameter of that opening distant from it. Let down the top sash of a window through which the sun is shining, sufficiently to allow the sun's rays to enter above it without passing through the glass and then cover all but one top corner of the window with a dark cloth. At this corner ar range a black paper, large enough fully to cover the opening, in such a position that a circular opening a half inch or 1 cm. in diameter will be at right angles to the sun's rays. Then on a slow tinting medium, say solio paper, take the first appearance time of the sun's light 64 inches or 128 cm. from the opening. This has been found by the author to be 1/2 second when the sun is at about 30° from the horizon and the atmosphere clear. Now this time is divided by 8, the tinting factor of solio to find the standard tint time, which is 1/16 of a second. Now pro ceeding by the first rule given, the tint time as found with the standard medium, 1/16 of a second, is divided by 16M, the square of 128, the f value of the cone employed, of a second, the time as though measured at f / 1 or with the meter. Then 64 divided by this time gives 16,000,000 (or 16MM), the intensity of the sun's surface in actinos. The reader should work this problem also by the unit cone method which is more truly a method of analysis. At the zenith the sun would show double this actinicity or 32 million actinos as already stated.