X.—Reduction of the Observations.
By eliminating W from the equations above by means of the standard equation, we obtain equations involving each of the fourteen selected colours of the spectrum, along with the three standard colours; and by transposing the selected colour to one side of the equation, we obtain its value in terms of the three standards. If any of the terms of these equations are negative, the equation has no physical interpretation as it stands; but by transposing the negative term to the other side it becomes positive, and then the equation may be verified.
The following table contains the values of the fourteen selected tints in terms of the standards. To avoid repetition, the symbols of the standard colours are placed at the head of each column:—
Table VI.
| Observer (K.) | (24) | (44) | (68) |
| 44·3 (20) = | 18·6 | + 0·4 | + 2·8 |
| 16·1 (28) = | 18·6 | + 5·8 | - 0·1 |
| 22·0 (32) = | 18·6 | + 19·3 | - 0·1 |
| 25·2 (36) = | 12·2 | + 31·4 | - 0·8 |
| 26·0 (40) = | 3·3 | + 31·4 | - 0·2 |
| 35·0 (46) = | - 1·2 | + 31·4 | + 0·3 |
| 41·4 (48) = | - 2·6 | + 31·4 | + 3·5 |
| 62·0 (52) = | - 3·4 | + 31·4 | + 17·5 |
| 61·7 (56) = | - 3·1 | + 21·0 | + 30·5 |
| 40·5 (60) = | - 1·9 | + 7·7 | + 30·5 |
| 33·7 (64) = | - 1·1 | + 1·1 | + 30·5 |
| 32·3 (72) = | + 0·6 | + 0·2 | + 30·5 |
| 44·0 (76) = | + 1·1 | + 0·7 | + 30·5 |
| 63·7 (80) = | + 0·3 | - 1·8 | + 30·5 |
Mr. James Simpson, formerly student of Natural Philosophy in my class, has furnished me with thirty-three observations taken in good sunlight. Ten of these were between the two standard colours, and give the following result:—
33·7 (88) + 33·1 (68) = W.
The mean errors of these observations were as follows:—
Error of (88) = 2·5; of (68) = 2·3; of (88) + (68) = 4·8; of (88) - (68) = 1·3.
The fact that the mean error of the sum was so much greater than the mean error of the difference, indicates that in this case, as in all others that I have examined, observations of equality of tint can be depended on much more than observations of equality of illumination or brightness.
From six observations of my own, made at the same time, I have deduced the “trichromic” equation—
22·6 (104) + 26 (88) + 37·4 (68) = W (2)
If we suppose that the light which reached the organ of vision was the same in both cases, we may combine these equations by subtraction, and so find
22·6 (104) - 7·7 (88) + 4·3 (68) = D (3)
where D is that colour, the absence of the sensation of which constitutes the defect of the dichromic eye.
The sensation which I have in addition to those of the dichromic eye is therefore similar to the full red (104), but different from it in that the red (104) has 7·7 of green (88) in it which must be removed, and 4·3 of blue (68) substituted. This agrees pretty well with the colour which Mr. Pole[A] describes as neutral to him, though crimson to others. It must be remembered, however, that different persons of ordinary vision require different proportions of the standard colours, probably owing to differences in the absorptive powers of the media of the eye, and that the above equation (2), if observed by K., would have been
23 (104) + 32 (88) + 31 (68) = W (4)
and the value of D, as deduced from these observers, would have been
23 (104) - 1·7 (88) - 1·1 (68) = D (5)
in which the defective sensation is much nearer to the red of the spectrum. It is probably a colour to which the extreme red of the spectrum tends, and which differs from the extreme red only in not containing that small proportion of “yellow” light which renders it visible to the colour blind.
[A] Philosophical Transactions, 1859, Part I., p. 329.
From other observations by Mr. Simpson the following results have been deduced:—
Table A.
| (88) | (68) | (88) | (68) | ||
| (99·2 +) = | 33·7 | 1·9 | 100 (96) = | 108 | 7 |
| 31·3 (96) = | 33·7 | 2·1 | 100 (92) = | 120 | 5 |
| 28 (92) = | 33·7 | 1·4 | 100 (88) = | 100 | 0 |
| 33·7 (88) = | 33·7 | 0 | 100 (84) = | 61 | 11 |
| 54·7 (84) = | 33·7 | 6·1 | 100 (82) = | 47 | 21 |
| 71 (82) = | 33·7 | 15·1 | 100 (80) = | 34 | 33 |
| 99 (80) = | 33·7 | 33·1 | 100 (78) = | 22 | 47 |
| 70 (78) = | 15·7 | 33·1 | 100 (76) = | 10 | 59 |
| 56 (76) = | 5·7 | 33·1 | 100 (72) = | 1 | 92 |
| 36 (72) = | 0·3 | 33·1 | 100 (68) = | 0 | 100 |
| 33·1 (68) = | 0 | 33·1 | 100 (64) = | 0 | 83 |
| 40 (64) = | 0·2 | 33·1 | 100 (60) = | 3 | 60 |
| 55·5 (60) = | 1·7 | 33·1 | |||
| (57 -) = | 0·3 | 33·1 |
In the table on the left side (99·2 +) means the whole of the spectrum beyond (99·2) on the scale, and (57 -) means the whole beyond (57) on the scale. The position of the fixed lines with reference to the scale was as follows:—
A, 116; a, 112; B, 110; C, 106; D, 98·3; E, 88; F, 79; G, 61; H, 44.
The values of the standard colours in different parts of the spectrum are given on the right side of the above table, and are represented by the curves of [Fig. 9], Plate II., where the left-hand curve represents the intensity of the “yellow” element, and the right-hand curve that of the “blue” element of colour as it appears to the colour blind.
The appearance of the spectrum to the colour blind is as follows:—
From A to E the colour is pure “yellow,” very faint up to D, and reaching a maximum between D and E. From E to one-third beyond F towards G the colour is mixed, varying from “yellow” to “blue,” and becoming neutral or “white” at a point near F. In this part of the spectrum the total intensity, as given by the dotted line, is decidedly less than on either side of it, and near the line F, the retina close to the “yellow spot” is less sensible to light than the parts further from the axis of the eye. This peculiarity of the light near F is even more marked in the colour blind than in the ordinary eye. Beyond F the “blue” element comes to a maximum between F and G, and then diminishes towards H, the spectrum from this maximum to the end being pure “blue.”
The results given above were all obtained with the light of white paper, placed in clear sunshine. I have obtained similar results when the sun was hidden, by using the light of uniformly illuminated clouds, but I do not consider these observations sufficiently free from disturbing circumstances to be employed in calculation. It is easy, however, by means of such observations, to verify the most remarkable phenomena of colour blindness, as, for instance, that the colours from red to green appear to differ only in brightness, and that the brightness may be made identical by changing the width of the slit; that the colour near F is a neutral tint, and that the eye in viewing it sees a dark spot in the direction of the axis of vision; that the colours beyond are all blue of different intensities, and that any “blue” may be combined with any “yellow” in such proportions as to form “white.” These results I have verified by the observations of another colour-blind gentleman, who did not obtain sunlight for his observations; and as I have now the means of carrying the requisite apparatus easily, I hope to meet with other colour-blind observers, and to obtain their observations under more favourable circumstances.