The Number of Particles in the Path of a Ray of Light Traversing the Earth's Atmosphere

It is useful in several astronomical problems to have some knowledge of the number of particles of a gas in the earth's atmosphere, that are encountered by a ray of light proceeding from a stellar source and reaching the observer. For instance, in stellar photometry, it is necessary to know the diminution in the intensity of light from a star due to absorption by the earth's atmosphere; this is easily found, if the number of particles of the absorbing gas and its coefficient of absorption are known. Or again, to deduce the laws of intensity-distribution of the telluric lines in a spectrum such as that of the sun, the number of particles of the gas producing those lines needs to be ascertained. The following is an attempt to arrive at an approximate formula for the number of such particles; which, while taking account of atmospheric refraction, is simple enough for ready calculation.