S. Kawai, one of the present authors, with Prof. T. Indow, in 1964, studied about optimal levels of illumination on the basis of easiness of reading a letter, namely the “readability”, by the method of successive intervals, without referring to the conventional threshold value.
The readability S was found to be a function of illuminance E, contrast C and size A of the letter, as expressed by the following empirical formula:
S=alogE+bA+e',
where a=11 and b=2 (as observed at 2 m apart) and 5 (as observed at 30cm apart), yet e', as a function of C, was not definitely determined.
The results were applied for revising the Japanese Industrial Standard JIS Z-9110 Recommended Levels of Illumination, in 1969.
Besides, the Tokyo Electric Power Company Inc., in 1970, consulted our Institute in regard to lighting for an overhead line work. Having known the threshold lying between 0.2 and 2lx, Prof. T. Tanabe, chairman of an ad hoc committee, recommended 200lx under an assumption of S=40.
The present authors studied on the relation between e' to contrast, as defined by the equation
C=((L_bgd-L_obj)/L_bgd)×100%,
that is “percent contrast”, and the distance D of observation.
A unified formula, including D as a parameter, was obtained as follows:
S=11logE+0.5 C+9 √D (A-1) +32,
where A and D are measured in centimeter.
The readability S implies:
0-unable to see,
12-threshold to read, which was found to be so in further study on the results, comparing them with those by Mr. T. Suda.
30-barely able to read,
50-practically able to read,
70-80-easy to read,
100-very easy to read.

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The glow-to-arc transition mechanism of the discharge lamps has been investigated using an idealibed temperature distribution model, wnich is characterized by the following conditions:
(1) The temperature of the active part of the electrode is assumed to be uniform.
(2) heat current continuity is fulfilled by assuming an appropriate layer (the area is S, the thickness is Δx) between the active part and the rest of the electrode.
(3) The transition occurs at the critical temperature T_c.
(4) The radiation loss is neglected.
The results are
(1)The minimum starting energy, which is defined by the electric energy to heat the cathode up to the temperature T_c in the infinitesimal time interval after ignition, is given by mC (T_c-T₀).
(2) The minimum starting power, which is defined by the electric power to heart the cathode up to the temperature T_c in the infinite time interval after ignition, is given by KS(T_c-T₀).
Where m and C are the mass and the specific heat of the active part, respectively. T₀ is the ambient temperature and K=kΔx, where k is the thermal conductivity of the layer material.
The value of mC (T_c-T₀) is about 280 joules and that of KS (T_c-T₀) is about 42 watts for the 400 watts metal halide lamp.
To start the lamp reliably in appropriate time interval more power than the minimum starting power is necessary. The ballast design criteria are
V_n²/πωL{βcosα+sinα-sin(α+β)-β²/2-Vg/_Vn}Vg/_Vn>KS(T_c-T₀)
where V_n is the peak value of the supplied vollage, L is the ballast inductance, V_g is glow discharge voltage, ω is angular velocity of the applied voltage, α and β are the starting and extinguishing phase angles of the glow discharge, respectively.

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