76 SMITHSONIAN MISCELLANEOUS COLLECTIONS [vOL. 45 



is found to be a maximum for all wave-lengths, and the height falls 

 off as the sun declines in altitude, slowly in the infra-red region of 

 the spectrum, but more and more rapidly as we examine further and 

 further toward the violet, or still more rapidly if we note the 

 great atmospheric absorption bands due to water vapor. 



It is assumed that the atmospheric transmission for a very narrow 

 portion^ of spectrum may be expressed by the relation — 



where c and Cq are the intensities of light of this wave-length at the 

 earth's surface and outside the atmospheric respectively, a the frac- 

 tion transmitted by the atmosphere for zenith sun, m the air mass, 

 or ratio of the length of the transmitting column of air to that for 

 zenith sun, and /9 and /?(, the observed and standard barometer 

 readings respectively. Upon the holograph the height d corre- 

 sponding to any given wave-length is directly proportional to the 

 amount of energy of that wave-length. Accordingly we may intro- 

 duce a factor k constant for the single wave-length in question 



^=kc^/cc/"'^o (2) 



and hence 



log d= mj- log a + log (/v„) (3) 



ro 



x\s the last term of equation (3) is to be supposed constant during 

 the day's observations, the expression is in the form of the equation 

 of a straight line, and if the logarithms of the deflections at the given 

 wave-length on the successive holographs be plotted as ordinates 

 with the quantities (;;//9//?p) as abscissse, the several points so deter- 

 mined should fall on a straight line of which the tangent of the 

 inclination is the logarithm of the transmission coefficient (a) for 

 the given wave-length. 



Mr. Langley has stated that the attempted measures of the 

 solar constant from a station near sea-level like Washington are sub- 

 ject to great uncertainty from the necessity of the very large and 

 doubtful extrapolation for atmospheric absorption. Without in the 

 least questioning this, and while calling special attention to the 

 great interest which would attach to a repetition of the experiments 

 at high altitudes, I incline to the belief that the closeness with which 

 the plotted points determined as above described lie upon a straight 

 line for wide ranges of air mass is a reasonably sure criterion of 



' In our practice less than the width between the D hnes. 



