Smithsonian miscellaneous collections . 55 which is deduced in a manner similar to that of Bunsens law ofabsorption. After substituting this value then the solution of thedifferential equation offers no difficulty and the equation of thecurve of the pencil of light is easy to find. As to the constant exponent m, that is best found from oneaccurate determination of the refraction. I will hereafter checkthe value of m thus found against the diminution of temperaturewith the altitude, since I hope to be put in possession of the neces-sary observational material through the kindness of a physicist
Smithsonian miscellaneous collections . 55 which is deduced in a manner similar to that of Bunsens law ofabsorption. After substituting this value then the solution of thedifferential equation offers no difficulty and the equation of thecurve of the pencil of light is easy to find. As to the constant exponent m, that is best found from oneaccurate determination of the refraction. I will hereafter checkthe value of m thus found against the diminution of temperaturewith the altitude, since I hope to be put in possession of the neces-sary observational material through the kindness of a physicist,a relative, who expects to remain several years in the tropics. In accord with my previous efforts I also believe that I shall suc-ceed in obtaining from the observation of the twilight colors materialfor the direct demonstration of the diminution of the refractingpower and the determination of the constants. Let cm in fig. 7 be the earths radius and ca the horizon of theobserver at c. At t and / hours after sunset the sun is at s ami. FIG. 7. s \ the altitudes of the reflecting strata of air are a c = h anda c = h \ the corresponding angles of incidence and reflectionare e and e. We easily find 1 ,-fl-?- h 24 / v> 2 24 (1 - sin e) R h = (1 - sin e) R 56 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 and according to equation (8) the intensity of the reflections fromthese layers h and h whose indices of refraction are n and nwill be given by 2 cos2 e J \ 2 cos2 e If by means of a good photometer we measure the intensities Jand J, then the diminution of the refracting power between thetwo neighboring layers at the altitudes h, h, h can be computedfrom the equations 3 ri = 2 cos2 * Vj7,d n 2 cos2 e V ]».etc VII ON THE PATHS OF PARTICLES MOVING FREELY ON THEROTATING SURFACE OF THE EARTH AND THEIRSIGNIFICANCE IN METEOROLOGY BY DR. A. SPRUNG (Dated Hamburg, June, 1881) [Published (August 1881) in Wiedemanns Annalen der Physik und ChemieNew series, Vol. XIV, 1881, pp. T
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