﻿6 SMITHSONIAN MISCELLANEOUS COLLECTIONS [vol. 47 



D = a mS (3) 



or 



log D = md log a (4) 



log D and being then used as the variables. The values of a in 

 equations (2) and (4) are not identical but are related as indicated 

 in equations 1 5 I and 1 6 i below. 



FIRST METHOD OF DETERMINING THE TRANSMISSION COEFFICIENT 



The treatment of the observations for finding the transmission 

 coefficient of water vapor may thus follow two independent pro- 

 cedures. In the first method the sun is observed at various altitudes 

 (Hi the same day. thus altering the amount of the absorbent by 

 changing the length of the path of the beam through it, while the 

 density, d, of the absorbent remains constant. The effect of diminish- 

 ing proportionately the path of the ray in every one of the horizontal" 

 layers of the earth's atmosphere containing the absorbing medium is 

 thus followed, and from the knowledge so gained it may be possible 

 to pass by extrapolation to the case where each layer is zero and there 

 is no absorption. In the case of high and low sun measures at a 

 single station, the exact vertical distribution of the absorbent is imma- 

 terial to the legitimacy of Bouguer's formula, provided the distri- 

 bution is constant during the observations, and uniform, at equal 

 altitudes, over moderate horizontal air layers. The unit layer of 

 water vapor would have the same distribution of density that exists 

 in the actual vertical atmospheric column. 



It may be objected that the water vapor in the air is too fluctuating 



for any such treatment, yet it seems from the spectroscopic evidence, 



which follows, that there are days when conditions are fairly constant, 



lom during the morning hours, but more often during afternoon. 



< (ftentimes a month may pass without such days in this locality. 



In plates 11 and 111 are shown some of the data plotted according 

 to this method. The abscissae are " atmospheres " and the ordinates 

 the logarithms of the galvanometer deflections. These plots, accord- 

 in- to Bouguer's formula, should be linear, and generally are so. 

 A still further test, however, may be applied. For each date and 

 wavelength two series of points are plotted. The lower points corre- 

 spond to the ordinates at the bottom of the deflections, the upper to 

 nooth curves drawn across the tops of the bands, representing 

 what the ordinates would have been had there been no absorption 

 from the gas or vapor under consideration. If the absorption were 



