+Efficiency in Lighting.+--One very simple problem is concerned with efficiency in lighting. We see by reference to Fig. 16, that in the radiation from the electric arc very little of the energy is in the visible part of the spectrum even though the temperature in the arc is the highest yet obtained on the earth, whereas the energy in the visible part of the spectrum from a gas flame is almost wholly negligible. The problem of efficient lighting is to get as big a proportion as possible of the energy into the visible part of the spectrum, and therefore the higher the temperature the greater the efficiency. This is the reason of the greater efficiency of the incandescent gas mantle over the ordinary gas burner, for the introduction of the air into the gas allows the combustion to be much more complete, and therefore the temperature of the mantle becomes very much higher than that of the carbon particles in the ordinary flame. The modern metallic filament electric lamps have filaments made of metals whose melting point is extremely high, and they may therefore be raised to a much higher temperature than the older carbon filaments. The arc is even more efficient than the metallic filament lamps, because its temperature is higher still; and we must assume that the temperature of the sun is very much higher even than the arc, since its maximum of energy lies in the visible spectrum. +Temperature of the Sun.+--The actual temperature of the sun may be calculated approximately by means of Stefan's fourth power law. We will first assume that the earth and the sun are both full radiators, and {53} that the earth is a good conductor, so that its temperature is the same all over. The first assumption is very nearly true, and we will make a correction for the small error it introduces; and the second, although far from true, makes very little difference to the final result, for it is found that the values obtained on the opposite assumption that the earth is an absolute non-conductor differ by less than 2 per cent. from those calculated on the first assumption. We will further assume that the heat radiated out by the earth is exactly equal to the heat which it receives from the sun. This is scarcely an assumption, but rather an experimental fact, for experiment shows that heat is conducted from the interior of the earth to the exterior, and so is radiated, but at such a small rate that it is perfectly negligible compared with the rate at which the earth is receiving heat from the sun.