100 THE ROYAL SOCIETY OF CANADA 



and qualitatively for the intensity and distribution of sky-radiation 

 as far as the observations available at that time could be tested. As 

 a final test the Smithsonian results were reduced with a view to ob- 

 taining a value for the number of molecules per cm.^of a gas at standard 

 temperature and pressure: the result obtained by the writer/ Wo = 

 (2 • 78 ± • 01) X 10^^ and a later independent determination by Fowle,^ 

 no = (2 • 70 ± • 02) X 10^^ indicate that we may rely with confidence 

 on Rayleigh's Law in dealing with molecular extinction for wave- 

 lengths not too close to regions of selective absorption. 



In dealing with attenuation in a stellar distance x = A, the term 

 KA is so small that we may write to sufficient degree of approximation 

 KA= (Eo — E)/Eo, i.e. KA is the proportional loss of intensity in 

 travelling a distance A. Denoting by i^iA and X2A the proportional 

 losses of intensities corresponding to "photographic" and "visual" 

 light of average wave-lengths Ai and A2 respectively, we derive on 

 reducing to intensities the result obtained by Jones,^ [ (photographic) — 

 (visual)] losses=-f 0-00473 ±0-00035 magnitude, the relation (Ki- 

 X2) A = • 00435 ± - 00032, the distance A being 10 parsecs. (1 parsec 

 = distance corresponding to a stellar parallax of 1 =3-26 light-years 

 = 3-08XlO^Vm.). If it is assumed that the extinction is brought 

 about solely by molecular scattering, we also have the additional 

 equation Ki /K2 = (h/hY- 



Unfortunately it is somewhat difficult to assign with accuracy 

 the average wave-lengths corresponding to "photographic" and 

 "visual" light. A rough estimate by the writer from Parkhurst's 

 curves of spectral intensities corresponding to the plates and. filters 

 employed in the photographic and visual determinations yielded the 

 values Ai = 0-446/i and A2 = 0-533ju, so that we obtain KilK2 = 2-0S, 

 giving KiA = 0-00838 and K2A = 0-00403.1° In order to realize 

 more vividly the extremely small attenuation which these numbers 

 represent, it is easily verified that in order to lose one-tenth of its 

 original intensity radiation of these wave-lengths must travel for about 

 4 • 1 and 8 - 5 centuries respectively. 



^ King, L. v., "Nature," 93 (July 30, 1914), pp. 557-559. 



8 Fowle, F. E., Astrophysical J., 40 (Dec, 1914), pp. 435-442. 



'Jones' determination is in fair agreement with Kapteyn's final result, {Astro- 

 physical J., 30, p. 398) [(photographic)— (visual)[ losses = -^ 0"- 0031 + 0-0006. 

 The corresponding determintions by King (E. S.) of the coefficients of attenuation 

 for photographic and visual light give values about five times that of the text. 



10 The losses -|-0™- 0080 and -|-0"- 0033 estimated by Jones for "photographic" 

 and "visual" light lead to the values XiA = 0-0073 and X2A = 0-0030 (wave-lengths 

 not stated). Kapetyn's (corrected) estimate for wave-length Xi = 0-43lM is KjA 

 = 0-00507, leading to the value w = 0-68XlO'^ hydrogen molecules per cm^, 

 which is of the same order of magnitude as the determination already made. E. S. 

 King's results (footnote 1) increases the estimate of the text about five-fold. 



