Table I
Factors for 7-term polynomial representation.
k | λk (micron) | C0k (Factor for K0) | C1k (for K1) | C2k (for K2) | C5k (for K3) | C4k (for K4) | C5k (for K5) | C6k (for K6) |
---|
0 | 0.40 | +3003. | 0000 | −3205 | 4.333 | +1419 | 02.22 | −3336 | 50.00 | +4388 | 88.88 | −3066 | 66.66 | +8888 | 8.888 |
1 | 0.45 | −1601 | 6.000 | +1754 | 05.33 | −7944 | 13.33 | +1906 | 533.3 | −2553 | 333.3 | +1813 | 333.3 | −5333 | 33.33 |
2 | 0.50 | +3603 | 6.000 | −4026 | 70.00 | +1859 | 116.6 | −4542 | 783.3 | +6190 | 000.0 | −4466 | 666.6 | +1333 | 333.3 |
3 | 0.55 | −4368 | 0.000 | +4960 | 26.66 | −2327 | 777.7 | +5778 | 666.6 | −8004 | 444.4 | +5866 | 666.6 | −1777 | 777.7 |
4 | 0.60 | +3003 | 0.000 | −3455 | 68.33 | +1644 | 433.3 | −4139 | 883.3 | +5823 | 333.3 | −4333 | 333.3 | +1333 | 333.3 |
5 | 0.65 | −1108 | 8.000 | +1290 | 16.00 | −6213 | 46.66 | +1584 | 133.3 | −2260 | 000.0 | +1706 | 666.6 | −5333 | 33.33 |
6 | 0.70 | +1716. | 0000 | −2015 | 5.333 | +9808 | 5.555 | −2530 | 16.66 | +3655 | 55.55 | −2800 | 00.00 | +8888 | 8.888 |
Note.—When the same integer appears two or more times at the end of a number, a repeating decimal is indicated.
Table II-A
Coefficients for analytic representation by power functions, illuminant A′ (T=2842°K).
m | X/Km=(Gm)x | Y/Km=(Gm)y | Z/Km=(Gm)z |
---|
0 | 97871. | 15758 | 89030. | 43140 | 31808. | 15913 |
1 | 58213. | 74203 | 50837. | 46164 | 14679. | 55636 |
2 | 34829. | 43400 | 29177. | 27551 | 6793.0 | 99875 |
3 | 20947. | 43173 | 16831. | 41425 | 3152.1 | 50622 |
4 | 12657. | 68727 | 9759.1 | 27328 | 1466.6 | 72173 |
5 | 7681.4 | 56236 | 5687.4 | 24315 | 684.30 | 47043 |
6 | 4680.2 | 08759 | 3331.4 | 62027 | 320.15 | 45319 |
7 | 2862.3 | 19093 | 1961.4 | 16866 | 150.19 | 88913 |
8 | 1756.8 | 13078 | 1160.7 | 08641 | 70.660 | 06836 |
9 | 1082.0 | 08061 | 690.39 | 71133 | 33.333 | 81029 |
10 | 668.63 | 69908 | 412.76 | 55677 | 15.768 | 95051 |
−1 | 16565 | 1.6324 | 15671 | 4.4008 | 69110 | 11449 |
−2 | 28255 | 1.4794 | 27726 | 5.0264 | 15056 | 3.2492 |
−3 | 48630 | 2.7495 | 49305 | 6.2803 | 32890 | 2.7208 |
−4 | 84580 | 6.4444 | 88127 | 6.0923 | 72041 | 6.9499 |
−5 | 14891 | 32.965 | 15832 | 14.636 | 15822 | 13.994 |
−6 | 26589 | 54.108 | 28587 | 58.385 | 34842 | 41.456 |
−7 | 48244 | 93.973 | 51882 | 60.618 | 76932 | 50.787 |
−8 | 89119 | 85.292 | 94638 | 73.335 | 17032 | 056.03 |
−9 | 16787 | 571.28 | 17350 | 592.23 | 37807 | 393.57 |
−10 | 32285 | 593.57 | 31970 | 742.95 | 84146 | 454.83 |
Table II-B
Coefficients for analytic representation by power functions, illuminant B′ (T=7000°K).
m | X/Km=(Gm)x | Y/Km=(Gm)y | Z/Km=(Gm)z |
---|
0 | 18412 | 947.38 | 19073 | 137.52 | 22737 | 457.35 |
1 | 10366 | 452.66 | 10600 | 594.17 | 10310 | 063.44 |
2 | 59183 | 99.463 | 59226 | 11.023 | 46877 | 25.665 |
3 | 34198 | 54.940 | 33263 | 89.454 | 21372 | 12.357 |
4 | 19965 | 89.838 | 18780 | 67.280 | 97705 | 9.5833 |
5 | 11759 | 82.397 | 10659 | 28.458 | 44790 | 4.6469 |
6 | 69791 | 7.3894 | 60816 | 8.6704 | 20589 | 4.3912 |
7 | 41692 | 6.4500 | 34881 | 8.0869 | 94907. | 64391 |
8 | 25050 | 5.2082 | 20111 | 8.7997 | 43869. | 11915 |
9 | 15128 | 6.6549 | 11656 | 9.4955 | 20333. | 91569 |
10 | 91790. | 40904 | 67919. | 73482 | 9451.2 | 85022 |
−1 | 33232 | 976.53 | 34497 | 397.90 | 50280 | 623.83 |
−2 | 61071 | 574.79 | 62721 | 927.71 | 11148 | 9617.3 |
−3 | 11447 | 4305.3 | 11463 | 4984.9 | 24787 | 9164.2 |
−4 | 21916 | 1863.9 | 21060 | 7976.6 | 55260 | 4344.9 |
−5 | 42887 | 7903.1 | 38894 | 3716.8 | 12352 | 47828 |
−6 | 85787 | 5031.2 | 72201 | 5985.7 | 27685 | 75112 |
−7 | 17527 | 87105 | 13472 | 49964 | 62218 | 25423 |
−8 | 36531 | 57127 | 25268 | 73644 | 14019 | 597341 |
−9 | 77528 | 87777 | 47637 | 06843 | 31674 | 253851 |
−10 | 16719 | 723481 | 90266 | 04971 | 71750 | 894821 |
Note.—The superscripts refer to the number of zeros before the decimal point. For example, 14019 59734
1=14,019,597,340.
Table III
Direct integration method. Values of Fk, to be used in Eq. (10).
k | λ | For X | For Y | For Z |
---|
0 | 0.40μ | 273.95 | 75.019 | 1102.9 |
1 | 0.45 | 3994.1 | −334.56 | 22,033.7 |
2 | 0.50 | 537.14 | 11,173.9 | 8887.2 |
3 | 0.55 | 16,853 | 37,303.5 | −123.04 |
4 | 0.60 | 56,501 | 34,274.6 | −181.43 |
5 | 0.65 | 18,530 | 5685.9 | +96.956 |
6 | 0.70 | 1161.5 | 834.58 | −16.608 |
Table IV
Example of direct computation of X, Y, Z, No. 151 green ceramic tile, Planckian radiation (T=2842°K).
k | λk | ρ(λk)/ρ0 | ρ(λk)Fk/ρ0 For X | ρ(λk)Fk/ρ0 For Y | ρ(λk)Fk/ρ0 For Z |
---|
0 | 0.40μ | 0.220 | 60 | 16 | 242 |
1 | 0.45 | 0.381 | 1521 | −127 | 8394 |
2 | 0.50 | 0.542 | 291 | 6056 | 4816 |
3 | 0.55 | 0.601 | 10128 | 22419 | −73 |
4 | 0.60 | 0.527 | 29776 | 18062 | −95 |
5 | 0.65 | 0.430 | 7967 | 2444 | +41 |
6 | 0.70 | 0.370 | 429 | 308 | −6 |
| | | X=50175 | Y=49181 | Z=13320 |
X+
Y+
Z=112676,
x=0.44530,
y=0.43648,
z=0.11822,
ρ/
ρ0=49181/89030.4=0.5524.
By selected ordinates,
x=0.4455,
y=0.4364,
ρ/
ρ0=0.552.