We have here a proof that the succession of phenomena is caused by a scattering of the shorter wave-lengths of light, and that the shorter the waves are the more they are scattered. It has been found theoretically by Lord Rayleigh that the scattering takes place in inverse proportion to the fourth power of the wave-length; thus, if two wave-lengths, which may be waves in the green and violet, are in the proportion of three to four, the former will be scattered as 1/3⁴ to 1/4⁴, or as 256 to 81, which is approximately as three to one. Consequently if the green in passing through a certain thickness of a turbid medium loses one-half the violet in passing through the same thickness will lose five-sixths of its luminosity. The inverse fourth powers of the following wave-lengths, which are within the limits of the whole visible spectrum, are shown below. +------+------+------+------+------+ | λ | 7000 | 6000 | 5000 | 4000 | +------+------+------+------+------+ | 1/λ⁴ | 1 | ·504 | ·260 | ·107 | +------+------+------+------+------+ Supposing λ7000 by the scattering of small particles loses one-tenth of its luminosity, then λ6000 would have ·454 of its original brightness; λ5000, ·234; and λ4000, ·095; that is, whilst λ7000 would lose one-tenth only of its luminosity, λ4000 in the violet would retain not quite one-hundredth of its brightness. During the years 1885, 1886, and 1887, the writer measured the luminosity of the solar spectrum at different times of the year, and at different hours of the day (see _Phil. Trans._ 1887: "Transmission of Sunlight through the Earth's Atmosphere"), and from the results he found that the smallest coefficient of scattering for one atmosphere at sea-level for each wave-length was ·0013, when λ⁻⁴ was for convenience sake multiplied by 10¹⁷ (thus λ6000⁻⁴ on this scale was 77·2), and that the mean was ·0017. The following table shows the loss of light for the rays denoted by the principal lines given at page 26, using this last coefficient for different air thicknesses. This is equivalent to giving the intensity of the rays of sunlight when the sun is at different altitudes.