# Method for Constructing the Natural Scale of Pure Color

Bulletin of the Bureau of Standards, Vol. 6, 89-93 (1909) Scientific Paper 118 (S118)
DEPARTMENT OF COMMERCE AND LABOR
Bulletin
OF THE
Bureau of Standards
S. W. STRATTON, Director
Volume 6
1909-10
[Seal omitted]
WASHINGTON
GOVERNMENT PRINTING OFFICE
1910
A METHOD FOR CONSTRUCTING THE NATURAL SCALE OF PURE COLOR.
By P. G. Nutting.
The color sensation is known to vary far from uniformly with the wave length of the exciting radiation. In a normal spectrum the variation is much more rapid in the yellowish-orange and bluish-green regions than in the midgreen or in the extreme red and violet. Hence, a color scale of say one unit for each 10 μμ difference in wave length would represent far from equal color steps. The difference in wave length just perceptible as a difference in color is roughly 5 μμ in the two most sensitive regions, 15 μμ in the midgreen, and much greater in the violet and red. The method here described makes use of data on this difference limen.
Given the least perceptible difference (difference limen) for an eye throughout the visible spectrum, the reciprocal will be proportional to color sensibility as a function of wave length. But sensibility is the derivative of a scale-reading curve, in this case the color scale desired. A method based on this principle will be applied to some of the best recent data on difference limen to illustrate the construction of a color scale.
Steindler has recently published data on the difference limen of twelve subjects having normal color vision. The characteristics of the color limen curve are shown in the figure. It has two deep minima at about 490 μμ and 580 μμ, a maximum in the green at 535 and a slight maximum and minimum at either end. The location and heights of these seven maxima and minima are given for each of the twelve subjects in the following table: ​
| | First Minima | First Minima | First Maxima | First Maxima | Second Minima | Second Minima | Second Maxima | Second Maxima | Third Minima | Third Minima | Third Maxima | Third Maxima | Fourth Minima | Fourth Minima |
| | λ | δλ | λ | δλ | λ | δλ | λ | δλ | λ | δλ | λ | δλ |
| Dr. O.St | 435 | 23.6 | 454 | 37.6 | 495 | 11.6 | 535 | 32.8 | 585 | 7.6 | 626 | 40.0 | 638 | 31.0 |
| Dr. E | 434 | 25.7 | 450 | 38.0 | 488 | 11.0 | 532 | 36.4 | 587 | 8.0 | 630 | 47.0 | 651 | 34.5 |
| Prof. E | 430 | 14.5 | 444 | 18.0 | 480 | 5.0 | 523 | 34.2 | 586 | 9.0 | 624 | 34.2 | 637 | 28.6 |
| Dr. Sch | 435 | 16.0 | 462 | 21.6 | 498 | 12.0 | 535 | 20.4 | 582 | 12.4 | 612 | 26.0 | 628 | 24.0 |
| Dr. A. St | 446 | 26.0 | 465 | 34.0 | 494 | 25.5 | 540 | 49.5 | 585 | 22.4 | 620 | 38.0 | 637 | 32.0 |
| Dr Ma | | | | | 488 | 15.9 | 520 | 22.0 | 572 | 9.1 | 622 | 24.0 | 638 | 17.2 |
| Dr.Me | 436 | 13.8 | 448 | 24.2 | 478 | 5.2 | 545 | 37.2 | 598 | 11.2 | 630 | 36.0 | 646 | 20.0 |
| Dr. Bi | 447 | 18.0 | 462 | 24.0 | 505 | 12.0 | 540 | 22.2 | 583 | 11.2 | 608 | 21.2 | 614 | 19.2 |
| Hr. B | 454 | 30.4 | 462 | 35.5 | 492 | 19.6 | 530 | 46.0 | 568 | 24.0 | 605 | 44.0 | 618 | 43.0 |
| Frl. M | 442 | 14.0 | 468 | 24.4 | 490 | 16.0 | 540 | 32.0 | 572 | 20.0 | 633 | 60.0 | 642 | 45.5 |
| Dr H | 450 | 51.0 | 460 | 54.6 | 497 | 7.6 | 530 | 46.0 | 583 | 19.2 |
| Dr. G | 437 | 39.3 | 435 | 39.3 | 501 | 22.4 | 536 | 22.1 | 571 | 12.8 | 625 | 42.4 | 640 | 34.6 |
| Means | 440 | 24.7 | 455 | 29.3 | 492 | 13.6 | 534 | 33.4 | 581 | 13.9 | 621 | 37.5 | 635 | 30.0 |
​While variations from the mean positions of the maxima and minima are not excessive they are so large that a simple average of all the curves would be smoother than any of them. Adjusting the positions of the maxima and minima of each curve to the means, the following data were obtained for the properties of average (of these twelve) eyes.
TABLE II.
| Wave Length (μμ) | Color Limen (μμ) | Sensibility | Ordinate Area | Color Scale |
| 420 | 41.0 | 244 | 5.45 | 21.96 |
| 425 | 36.0 | 278 |
| 430 | 30.0 | 333 | 7.51 | 21.41 |
| 435 | 26.1 | 384 |
| 440 | 24.7 | 405 | 7.55 | 20.66 |
| 445 | 26.3 | 380 |
| 450 | 28.5 | 351 | 6.90 | 19.91 |
| 455 | 29.3 | 341 |
| 460 | 28.8 | 347 | 8.00 | 19.22 |
| 465 | 24.6 | 407 |
| 470 | 20.6 | 485 | 11.60 | 18.42 |
| 475 | 17.0 | 588 |
| 480 | 15.2 | 13.12 | 17.26 |
| 485 | 14.0 | 714 |
| 490 | 13.7 | 14.44 | 15.95 |
| 495 | 13.7 | 730 |
| 500 | 14.5 | 690 | 12.04 | 14.50 |
| 505 | 16.5 | 607 |
| 510 | 19.4 | 515 | 8.70 | 13.30 |
| 515 | 22.9 | 436 |
| 520 | 27.4 | 365 | 6.56 | 12.43 |
| 525 | 30.9 | 324 |
| 530 | 32.7 | 306 | 6.04 | 11.77 |
| 535 | 33.4 | 300 |
| 540 | 32.5 | 308 | 6.60 | 11.17 |
| 545 | 30.3 | 330 |
| 550 | 27.1 | 369 | 8.80 | 10.51 |
| 555 | 22.7 | 440 |
| 560 | 19.2 | 520 | 11.72 | 9.63 |
| 565 | 17.1 | 588 |
| 570 | 15.4 | 650 | 13.90 | 8.46 |
| 575 | 14.3 | 700 |
| 580 | 13.9 | 720 | 14.00 | 7.07 |
| 585 | 14.1 | 709 |
| 590 | 15.2 | 658 | 11.36 | 5.67 |
| 595 | 17.3 | 578 |
| 600 | 22.2 | 450 | 7.32 | 4.53 |
| 605 | 28.2 | 355 |
| 610 | 22.8 | 305 | 5.58 | 3.80 |
| 615 | 35.6 | 281 |
| 620 | 37.5 | 267 | 5.48 | 3.24 ​ |
| 625 | 36.9 | 271 | | |
| 630 | 33.5 | 298 | 6.48 | 2.69 |
| 635 | 30.1 | 332 | | |
| 640 | 30.3 | 330 | 6.24 | 2.04 |
| 645 | 32.0 | 313 | | |
| 650 | 35.6 | 281 | 5.21 | 1.42 |
| 655 | 38.6 | 259 | |
| 660 | | | 9.00 | 0.90 |
The ordinates of the curve of color as a function of wave length are given in the last column. They were obtained by integration of the sensibility curve, the partial areas (divided by two on the scale of the figure) being given in the fourth column. Bach number in the last column is the sum (divided by lo) of the ordinate areas of the fourth column added from the bottom to and including that wave length. The color-wave length curve is plotted in the figure.
A difference of one unit in the color scale represents a difference in color that is just easily perceptible, hence forms a convenient natural unit, although any other subdivision might be used. In Fig. I , each unit of the color scale is indicated on the wave-length axis and just above are indicated roughly the positions of six spectral hues.
To test the theoretical color curve, a normal spectrum was projected on a black screen in which had been cut slits spaced according to the wave lengths of the color units, the slits being covered with ground glass. No departure from uniformity in the color steps could be detected by the ten or more individuals who carefully examined them.
The wave lengths of each of these color steps is given in Table III.
These computations have been carried through merely to illustrate the method. They may easily be made for any eye for which the sensibility curve is known.
If the sensibility curves of a large number of subjects were known, the properties of an average normal human eye might be deduced and a scale of color constructed and adopted. ​
TABLE III.
| Color | Wave Length | Wave Length |
| 1 | 420 | Violet |
| 2 | 435 |
| 3 | 449 |
| 4 | 463 | Blue |
| 5 | 474 |
| 6 | 483 |
| 7 | 490 |
| 8 | 497 |
| 9 | 504 |
| 10 | 514 |
| 11 | 527 | Green |
| 12 | 543 |
| 13 | 556 |
| 14 | 566 |
| 15 | 574 |
| 16 | 580 | Yellow |
| 17 | 588 |
| 18 | 595 |
| 19 | 606 | Orange |
| 20 | 626 |
| 21 | 641 |
| 22 | 658 | Red |
There is a widespread demand for reference standards of color in terms of which other colors may be specified. Such standards may easily be prepared of any desired hue or shade, but the great difficulties are in choosing rational and uniform divisions on the one hand and in obtaining dyes and pigments that are permanent on the other. Both difficulties would be largely obviated by the adoption of a fixed rational chromatic scale for use as a primary standard.
Washington, April 27, 1909.
2192—No. I—09——7
* ↑ This Bulletin 5, p. 266, 1908.
* ↑ Sitz. Ak. Wiss. Wien, 115, IIa; Jan., 1906.
This work is in the public domain in the United States because it was published before January 1, 1929.
This work may be in the public domain in countries and areas with longer native copyright terms that apply the rule of the shorter term to foreign works.
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