VISIBILITY IN METEOROLOGY 93 
extinction coefficient used, which was introduced by 
Duntley, is that pertaining to diffused radiation. The 
present writer believes that this is correct. The only 
portion of the light from an object which goes to form 
an image of it is that which reaches the eye from the 
direction of the object and it would seem logical to use 
the extinction coefficient for directed light m such a 
discussion. It seems probable that the choice of the other 
quantity was conditioned by a desire to explain some 
results of Douglas and Young [17] which suggested that 
the value of « determined by the photometry of a 
projector is slightly less than that calculated from 
(8). The author has recently shown [87] that the dis- 
crepancy may arise from other causes. It would never- 
theless be a comfort to have a long series of simultaneous 
measurements of « by the two methods, especially in 
fog. 
The Relevant Properties of the Eye 
If we are to use equations such as (7) to determine 
the visual range of objects, it is obvious that we need to 
know the least value of contrast that the eye can 
appreciate. Similarly, if we are interested in the visual 
range of light signals, we need data on the threshold 
illuminance H#;, at the eye. This can easily be trans- 
formed into a contrast limen, so that one set of data is 
really sufficient for both problems. 
The eye can exist in two states of adaptation, known 
as the dark-adapted and light-adapted conditions, the 
transition taking place at a field luminance of about 
2 X 10~ candles m~. The reader may be referred to 
Stiles, Bennett, and Green [45] for a discussion of the 
properties of the eye in the two states and we shall only 
note here that color vision is restricted to the light- 
adapted state. 
It has been known for a long time that the threshold 
of contrast creases at low values of luminance and for 
objects of small angular subtense. In meteorology it has 
become a sort of convention to adopt a value « = 
=-E0.02 for ordinary objects in the daytime; but there 
is no doubt that this is frequently far from the truth. 
During World War IJ a very extensive investigation was 
made at the Louis Comfort Tiffany Foundation, and re- 
ported by Blackwell [4]. This report covers 450,000 
observations of circular objects ranging from 0.6 to 360 
minutes of arc in angular diameter, and over a very wide 
range of background luminance (5 X 104 to 4 X 102 
candles m ~~); Fig. 2 shows one set of curves interpolated 
from some of the results. Note the straight portions of 
the curves; over this range of visual angle the product 
of the area and the luminance of a stimulus (7.e., its 
candlepower) is a constant; this is the range in which 
the signal can be considered a ‘“‘point source,’ and 
values of threshold illuminance may easily be derived 
from the curves. 
These curves refer to the contrast required for 50 
per cent probability of detection by an observer using 
both eyes under natural conditions. For almost certain 
detection the values of contrast should be multiplied 
by 2 or at most by 3. 
A recent field investigation by Blackwell [5] makes 
it highly probable that these laboratory values will 
also apply under field conditions, provided that the 
factors of attention and search do not enter. Other 
experiments [2, 11] indicate that vision through binocu- 
lars follows the same laws, provided that allowance is 
made for the reduction of contrast by the optical 
system. 
The factors of attention and search remain to be 
investigated, as does the enormously complicated phe- 
nomenon of recognition, which also brings in the question 
of visual acuity, and is a matter worthy of the interest 
of any number of extremely able psychologists. 
There have been many investigations of the threshold 
illuminance of lights and its dependence on field lumi- 
nance (see [45]). While satisfactory absolute values can 
be derived from the Tiffany data, “practical”? values 
have been sought, with the general result of about 0.2 
lumens km for fixed, achromatic sources on a moonless 
night. If the light is flashing, a somewhat greater 
illuminance is required for equal conspicuity, depending 
+3 
+ 
wy 
aE 
10° * CANDLES/ M2 
LOG. DIAM, OF OBJECT (MINUTES) 
=3 = -1 te) +1 +2 +3 
LOG € 
Fig. 2.—Threshold of contrast of circular objects, from the » 
Tiffany data. Each curve refers to the background luminance 
marked. 
on the time of the flash; this has been investigated by 
various authors (see [45]). Threshold illuminance varies 
with the color of the point source, and there are some 
papers [24, 25, 34] dealing with the recognition of 
colored lights. The general result of these investigations 
is to show that only red and blue-green are “‘safe’’ colors 
near their threshold illuminance. 
The Calculation of the Visual Range 
We are now in a position to combine the results of 
the last three sections and calculate the visual range 
of objects or of lights. For either computation we must 
know the extinction coefficient o, and in the case of an 
inclined path of sight we must also know or estimate its 
variation in the vertical. We must know the contrast 
threshold appropriate to the angular size (and probably 
the shape) of the object and to the field luminance; or 
the threshold illuminance for a light of the charac- 
teristics concerned, against the existing background. 
There is really no fundamental difference between the 
