LXXVIII. A Statistical Investigation of the Visibility of Red Light. By R. A. HOUSTOUN, Ph.D., D.Sc., Lecturer on Physical Optics in the University of Glasgow, and ERIC W. M. HEDDLE, M.A., B.Sc., Lecturer in Mathematics in the Royal Technical College, Glasgow

DUR

URING the past six years or so a statistical survey of the colour vision of some two thousand students has been carried out at the University of Glasgow. This survey has shown that some observers have better colour vision than the average and some worse, following the law of normal deviation, and that normal deviation almost covers everything so far as women are concerned. In the case of men, however, the colour blind and red and green anomalies occur scattered outside the normal curve.

Some observers see the red end of the spectrum much dimmer than others. The object of the present investigation was to see whether these observers were an extreme case of normal variation or not, and also to find to what extent they occurred. The investigation has also a bearing on the original Young-Helmholtz theory of colour vision, according to which the colour blind were divided into two well-defined classes, the red blind and the green blind, a view which Helmholtz himself afterwards abandoned.

§1. We find the most valuable previous data on the subject in a paper by Coblentz and Emerson †. By means of a flicker photometer they determined the relative visibility of the different colours of the spectrum for 125 different observers who were apparently a random distribution so far as colour vision is concerned; their results are exhibited in a table. The wave-length 665 up is the point nearest the red end of the spectrum for which every one of the 125 observers made a reading. The table gives the ratio of the visibility of this colour to the visibility of the most visible colour in the spectrum for each of the observers. The results vary from 252 to 822. The most visible colour in the spectrum is always in the green, though its position varies somewhat from one observer to another. The two numbers cited above, therefore, give the ratio of the brightness of the red to the brightness of the green, multiplied by a constant factor, for the two observers in question. If the logarithm of this ratio is taken, the 125 observers can be Communicated by the Authors.

"Relative Sensibility of the Average Eye to Light of Different Colours and Some Practical Applications to Radiation Problems," Bull. Bur. Standards, xiv. p. 167 (1918).

grouped in the following manner in terms of its value; in the table the characteristic of the logarithm is omitted:

The table is plotted in fig. 2. The number of observers is grouped against logarithm of ratio instead of against ratio for a reason that will be explained later in connexion with our own results. The distribution represented in fig. 2 is not far off the normal curve. Coblentz and Emerson subdivide their observers into various groups for convenience of handling, red sensitive, blue sensitive, &c., but these groups are arbitrary. There is nothing in the paper to show that we are not dealing with one homogeneous population.

§2. As we desired only to get one reading for each observer, the arrangement of Coblentz and Emerson would have been too elaborate for our purpose. We made three false starts before obtaining an apparatus to our taste.

(1) First of all an attempt was made with a speciallyfitted spectroscope to put the cross-wire on the red end of a continuous spectrum. We had never much hope of this method, and it failed owing to diffuse light in the instrument and variation of the reading with the state of dark adaptation of the observer's eye.

(2) A thin piece of copper with two very fine holes drilled in it was placed on the stage of a low-power microscope. Behind one of these holes was a piece of red glass; behind the other a wedge of neutral glass. On looking into the microscope the observer saw a red disk, something like a signal lamp at a hundred yards or so, and a grey disk beside it. By rotating a wheel which carried the wedge he adjusted the luminosity of the grey disk, until the two disks were equally bright. This method was abandoned, because the

"neutral" wedge had a green tint, because the range of adjustment was not great enough, and because a slight displacement of the piece of copper on which the holes were drilled had a great influence on the result.

(3) We next measured a red light against a white one by means of a Simmance-Abady flicker photometer. But the fact that this instrument gives more consistent readings than the grease-spot or shadow photometers when the colours are different was outweighed by its inconvenience and unfamiliarity to the observers. So it was abandoned in favour of the simple arrangement of the grease-spot type the plan of which is shown in fig. 1.

T is a tube about 18 cm. long and of 25 cm. diameter, with a small hole at the end of 4 mm. diameter into which the eye E of the observer looks. He sees a diamond shaped

E

T

B

Fig. 1.

A

opening D of 8 mm. side in a piece of paper which is stretched diagonally across a cubical box of 5 cm. side. Through this opening a ground-glass plate G is visible; this plate is illuminated by an 8 candle power carbon glowlamp A at a fixed distance of 2 metres. Light from a 16 candle-power carbon glow-lamp B falls on the front of the paper through the piece of clear red glass R. Consequently the observer sees a white diamond against a red background. The lamp B moves along a scale S 50 cm. long, and its position on this scale is adjusted so that the background has the same intensity as the diamond. The same lamps were used throughout the whole series of tests: they were mounted at about a height of 30 cm. above the table. There were screens, not shown in the diagram, to prevent direct light from the lamps reaching the eye of the observer. The red glass was a pure red of the kind used

for the signal lamps; it transmits from the red end of the spectrum to about 610 μ, and is much purer than Wratten and Wainwright's standard tricolour red, which contains some yellow.

The tests were carried out between April 1922 and June 1923, partly in the Natural Philosophy Department of the University and partly in the Natural Philosophy Department of the Technical College. Altogether 604 students were examined, 56 women and 548 men. Of these 373 were University students, arts, pure science, engineers, and medicals, and 129 were day and 102 evening students at the Technical College. They made the test during the optical laboratory course, simply leaving the optical bench or whatever it was they were working at and returning to it when the test was completed. The distribution was essentially a random one; the observers were not selected in any way, but simply taken as they came, and no one who was asked to make the test declined.

In order to have conditions exactly the same in each case instructions were not given orally, but by means of a written card, which stated that "the light on the right-hand side was to be moved backwards and forwards along the metre stick until the white diamond and the surrounding red appeared of the same brightness." Each observer made three settings; the first of these was intended only to give familiarity with the apparatus and was consequently not recorded, but the second and third were recorded and their mean taken. The apparatus, it should be stated, worked very satisfactorily; it was simple and straightforward, and all the observers understood at once what was wanted.

Most observers, of course, find it extremely difficult to say when a white surface and a red one are equally bright. Helmholtz himself had no confidence in his judgment on this point. But it is easy to arrange that first the red, and next the white, is the darker of the two and then leave the lamp midway between these two positions, and this is how the observers usually proceeded.

As the scale was calibrated by an auxiliary experiment, it was possible from each observer's settings to state what fraction of the total light of the glow-lamp the red glass in question transmitted for him. The results varied from 086 for the man who was most red sensitive to 0015 for the man who was least red sensitive. This fraction specifies the observer's red sensitiveness. Its reciprocal specifies red blindness. Now in drawing the frequency curve the shape differs according as we use the fraction or its reciprocal as

abscissa. In the one case the left-hand side will be crowded together and the right-hand side extended, while in the other case the opposite will happen. If, however, we were to use the logarithm of the fraction or of its reciprocal as abscissa, the shape of the curve would be the same in each case. As there is no particular reason for preferring the ratio to its reciprocal, or vice versa, we have stated the results in terms of the logarithm, and, in order to avoid negative characteristics, have chosen the logarithm of the reciprocal, or rather, for convenience in calculation, the logarithm of a number proportional to the reciprocal. The results are given in the following table, and are graphed in fig. 3, the women being shown in black. The 4 in the first column of the table means 4 and less than 5, the 5 means 5 and less than 6, etc.

The distribution is slightly asymmetrical, and there is one. very red-blind observer very far out by himself, but we cannot definitely say, owing to the asymmetry, since there is only one, that he does not belong to the main group. In the red-green test and Rayleigh tests, described in previous papers, 13 men out of 835 and 29 men out of 423 respectively fell outside the continuous distribution. As the number of men in the present case is 548, the similar

* Houstoun and Dunlop, Phil. Mag. xli. p. 186 (1921); Houstoun, Proc. Roy. Soc. A cii. p. 353 (1922).