Table I
Values of constants for best-fitting solutions of Eqs. (8), (11), and (1) predicting the relation between ΔIt and τ at threshold. Standard deviations (SD) are in units of logΔIt.
Equation | | Graham and Kemp | Keller | Herrick |
---|
| n | >30 | >47 | 16 |
| τ0′ | > 5.00 | > 2.300 | 0.104 |
8 | k5 | ⋯ | ⋯ | 0.106 |
| ΔVnB/w1 | ⋯ | ⋯ | 0.0079 |
| SD | < 0.119 | < 0.059 | 0.079 |
| n | 6 | 7 | 5 |
11 | ΔVmax/A | 116·10−10 | 55·10−11 | 188·10−9 |
| SD | 0.195 | 0.215 | 0.164 |
| k1 | 0.115 | 0.105 | 0.085 |
1 | k2 | −3.109 | −2.940 | −2.747 |
| SD | 0.101 | 0.042 | 0.118 |
Table II
Best-fitting solutions for Eq. (6) describing the relation between I and τ for experiments on luminance discrimination in man by Graham and Kemp, Keller, and Herrick. The data of Rushton–Fuortes are from the eye of Limulus. τ0′ is measured dark-adapted membrane resistance for Limulus, best-fitting value of dark-adapted critical duration for man. Standard deviations (SD) are in units of logI.
| Graham and Kemp | Keller | Herrick | Rushton–Fuortes |
---|
n | 7 | 8 | 8 | 9 |
τ0/′ | 0.169 | 0.136 | 0.103 | 5.5·106 |
k5 | 0.934 | 0.632 | 0.291 | 1.96 |
B | 0.009 | 0.069 | 17.73 | 0.259 |
SD | 0.074 | 0.070 | 0.103 | 0.019 |
Table III
Values of constants for best-fitting solutions of Eqs. (10), (12), and (14) predicting the relation between ΔIt and I at threshold. Standard deviations (SD) are in units of logΔIt for Eq. (10), logI for Eqs. (12) and (14). Although B is not a constant in Eq. (10), it was necessary to use Eq. (5) to obtain a relation between I and Vn for use in treating Eq. (10); hence a best-fitting value of B had to be found.
Eq. | | Graham and Kemp | Keller | Herrick |
---|
| n | 8 | 9 | 10 |
10 | ΔVn/w1 | 17·10−5 | 30·10−5 | 17·10−5 |
| B | 92 | 68 | 53 |
| SD | 0.073 | 0.088 | 0.037 |
| n | 6 | 8 | 6 |
| k5 | 0.500 | 0.800 | 0.550 |
12 | ΔVmax/A′ | 156·10−4 | 117·10−4 | 762·10−5 |
| B | 56.26 | 5.62 | 13.23 |
| SD | 0.166 | 0.177 | 0.085 |
| n | 39 | 8 | 17 |
14 | k6/w1 | −0.231 | −4.298 | −0.552 |
| k7/w1 | 0.052 | 1.263 | 0.165 |
| B | 256 | 177·10−5 | 10.75 |
| SD | 0.176 | 0.080 | 0.025 |
Table IV
Results of fitting three systems of theoretical equations to luminance discrimination data of Graham and Kemp, Keller and Herrick. The table provides values for constants listed in the second column which yielded best fit to a criterion requiring that the sum of the standard deviations of error in prediction of a set of data for the three equations of a system shall be a minimum. The standard deviations of the error in predicting a set of data by the three equations of a system are provided in the rows below the rows displaying the values of the constants; for example, the row in which SD(8) is in the second column contains the standard deviations of error in predicting the three sets of data from Eq. (8) when evaluation of the system of Eqs. (6), (8), and (10) employs the above-mentioned criterion.
| | Eqs. (6), (8), (10) | Eqs. (6), (11), (12) | Eqs. (6), (1), (14) |
---|
Relation | | Graham and Kemp | Keller | Herrick | Graham and Kemp | Keller | Herrick | Graham and Kemp | Keller | Herrick |
---|
| n | 8 | 9 | 8 | 6 | 7 | 5 | 7 | 8 | 10 |
| τ0′ | 0.102 | 0.095 | 0.103 | 0.130 | 0.140 | 0.104 | 0.130 | 0.133 | 0.152 |
| k5 | 0.490 | 0.358 | 0.291 | 1.20 | 0.90 | 0.50 | 0.846 | 0.624 | 0.197 |
| B | 19.00 | 9.00 | 17.73 | 0.065 | 0.021 | 10.53 | 0.140 | 0.090 | 2.900 |
| ΔVn/w1 | 461·10−6 | 786·10−6 | 310·10−6 | | | | | | |
| ΔVmax/A | | | | 118·10−10 | 55·10−11 | 175·10−9 | | | |
| k1 | | | | | | | 0.115 | 0.105 | 0.085 |
| k2 | | | | | | | −3.109 | −2.940 | −2.747 |
τ to I | SD(6) | 0.293 | 0.217 | 0.103 | 0.083 | 0.074 | 0.150 | 0.078 | 0.070 | 0.240 |
| SD(8) | 0.187 | 0.103 | 0.119 | | | | | | |
ΔIt to τ | SD(11) | | | | 0.195 | 0.215 | 0.167 | | | |
| SD(1) | | | | | | | 0.101 | 0.042 | 0.118 |
| SD(10) | 0.211 | 0.237 | 0.092 | | | | | | |
ΔIt to I | SD(12) | | | | 0.309 | 0.285 | 0.123 | | | |
| SD(14) | | | | | | | 0.253 | 0.082 | 0.038 |
Table V
Results of fitting Eq. (20) to data of experiments in luminance discrimination (Graham and Kemp, Keller, Herrick) and flicker (Lloyd, Lloyd and Landis). Best fitting values of constants were those for which the coefficient of variation was minimum.
| n | ΔVmax/(g/c)n | Coef. of Var. |
---|
mean | SD |
---|
Graham and Kemp | 8 | 12.6·10−16 | 27.7·10−17 | 0.22 |
Keller | 8 | 53.7·10−17 | 11.9·10−17 | 0.22 |
Herrick | 6 | 13.0·10−12 | 5.7·10−12 | 0.44 |
Lloyd | 7 | 27.1·10−14 | 27.2·10−14 | 1.00 |
Lloyd and Landis | 9 | 15.5·10−18 | 20.7·10−18 | 1.33 |