The previous studies on the optimal levels of illumination [1, 2, 3] have been based on the data of the threshold. But the threshold itself has no connection with the optimal levels of illumination. This study purports to construct a scale for easiness of reading a letter (which we shall hereafter call “readability”) without referring to the threshold data, and express the “readability” as a function of the size, contrast and brightness of the letter.
The objects used in the experiments (Exp. I and Exp. II) were Chinese characters with various sizes (Table 1) and contrasts (Table 2). Here the contrast was defined by the logarithm of the ratio of the brightness of the object to that of the background. In Exp. II Chinese characters printed on a newspaper and a dictionary were also used. Subjects (4 persons) observed the object under various levels of illumination (Table 3) from the distance of 2 m in Exp. I and from the distance of 30 cm in Exp. II. The experiments were designed so that every letter might be observed under every level of illumination. The subjects were required to evaluate the “readability” of each letter by categories shown as follows.
0 cannot see it at all.
1 can see something but cannot read it.
2 can guess the letter.
3 can read with effort.
4 can read but cannot see the fine structure of the letter.
5 can read and see the fine structure of the letter but feel tiresome to read a number of such letters for a long time.
6 can read easily but not easily enough.
7 can read very easily and feel just right.
8 feel too much brightness and/or too much contrast.
9 feel unpleasant because of too much brightness and/or too much contrast.
By the method of successive intervals [4] the subjective scale of “readability” was constructed from the data obtained. The principle of the method may be outlined as follows. The “readability” is assumed to be one-dimensional continuum S. In Fig. 3, S is represented on the abscissa. Then, the probability distribution of the “readability”S for a given level of illumination E, for all the possible grades of size, contrast and complexity of the object will look like the solid curve below E in Fig. 3. In the present paper the distribution is assumed to be normal.
Now the categories mentioned before are assumed to correspond to nine consecutive and nonoverlapping intervals, -L₀-L₁-L₂-...L₈-, on the S-axis. The determination of the location of these intervals on the S-axis will lead to establishing a scale of “readability”. For this purpose the location (and hence the lengths) of the intervals were adjusted so that the probability distribution of S might become normal for all levels of Ei (i=1-7).
The results and consideration. The method of successive intervals described in the preceeding paragraph can be applied to the data of the present experiment very well as is shown in Fig. 5. One can, therefore, define a scale of “readability” as follows. The “readability” 0 corresponds to the situation where one can not read the object. The “readability” 100 corresponds to the situation where one can read the object very easily and feels just right. The intermediate values of the “readability” are defined by dividing the distance between 0 and 100 on the abscissa of Fig. 5 into 100 equal parts. Actually, the origin of the scale is arbitrary since the scale is a so called interval scale, hence, only the difference of “readability” is meaningful.

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From the colorimetric considerations the following two theorems are proved mathematically.
A. The maximum luminous efficiency for any colored light is achieved from the appropriate combination of two spectrum colors.
B. The mixture of two spectrum colors, which gives the maximum luminous efficiency for a colored light, also gives the maximum luminous efficiency for all the colors which can be produced with combinations of these spectrum colors.
A new type fluorescent lamp, named fresh white, which has a slightly greenish color has been developed on the basis of these theorems. The high output 110 W lamp of this type is as efficient as 91 1m/W. Because of its moderate color rendering property this lamp is suitable for street lighting.

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