Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/1



I. Transmission of Sunlight through the Earth's Atmosphere.

By, C.B., D.C.L., F.R.S.

Received April 7,—Read May 5, 1892.

PART II.—

Introductory.

XXII.—In a previous communication (‘Phil. Trans.,’ vol. 178, 1887, A., pp. 251–283) the results of the absorption of sunlight by different thicknesses of atmosphere near sea level were found from measurements of the luminosity of the entire spectrum. The method used was that devised by General and the Author, as detailed in the Bakerian Lecture in 1886. The absorption coefficient for the different thicknesses of atmosphere at sea level was found by measurements made principally at South Kensington, and these were compared with measures taken at the Riffel, above Zermatt, at a height of about 8000 feet. It was shown that when the air thicknessis represented by $$x$$, the minimum intensity for each ray of the spectrum can be fairly represented by $$\mathrm{I}^\prime = \mathrm{I}\epsilon^{-.013x\lambda^{-4}}$$, and the average intensity by $$\mathrm{I}^\prime = \mathrm{I}\epsilon^{-.017x\lambda^{-4}}$$, $$\mathrm{I}^\prime$$ and $$\mathrm{I}$$ being the transmited and original intensifies, and $$\lambda$$ the wave length.

Further, it was shown that even if the absorption of each ray was very different from the above, the integral absorption was very accurately expressed by $$a^{-z}$$, $$z$$ being the air thickness, and $$a$$ a constant. This corresponds to $$a^{-\sec\theta}$$ corrected for refraction, when $$\theta$$ is the zenith distance.

This result was arrived at by taking the areas of the curves of luminosity as formed from the actual observations as a measure of the luminosity of the total white light which was decomposed into a spectrum. This was admissible, for in the paper already referred to, it was proved that the sum of luminosities of different rays is equal to their luminosity when compounded.

XXIII.—Objections to the Use of the Formula.

The formula involving $$\lambda^{-4}$$ is the formula theoretically deduced by Lord for the scattering of light by small particles, and its adoption in this research is open MDCCCXCIII.—A.