100 abbot: solar constant of radiation 



the curvature of the earth; second, the refraction of the beam 

 in air. These causes produce opposite effects, the first tending 

 to increase the angle of incidence, the second tending to dimin- 

 ish it as the beam approaches the earth's surface. Their com- 

 bined effect is dependent on the height to which the temperature 

 exercises absorption and on the distribution of density with the 

 height. But it is generally supposed that the absorption of the 

 air above 40 miles from the earth's surface is negligible, and, 

 remembering that the atmospheric density diminishes with the 

 height, it appears that for zenith distances less than 70" the 

 effect of change of the secant of the angle of the incident beam 

 from the outermost to the innermost layer of the atmosphere 

 will not introduce error greater than 1 per cent. Accordingly for 

 zenith distances less than 70° we may write approximately 



En = Eo{aia2 . . . . a„) « (2) 



The symbols ay, ao .... an denote constants (providing 

 no change of transparency occurs during the interval of time 

 in question), and their values are slightly less than unity. We 

 may substitute for their product a single constant, a, itself a 

 proper fraction, and remembering that En is the intensity at the 

 earth's surface, above denoted simply by E, we have 



E = Eoa-' (3) 



Limitations of formula. No mention is made in this expres- 

 sion, of the barometric pressure, but it is easy to see that an 

 alteration of barometric pressure would signify, under the con- 

 ventions adopted in deriving the formula, a change in the number 

 of layers, n. This would cause an alteration of the quantity a, 

 which is the continued product of the transmission coefficients 

 of the layers, by introducing additional multipliers a^ + u a„+2 



. ... or by the withdrawal of some a„_i, a„_2 Since 



we have no means of determining the value of the terms so 

 introduced or taken away, there is no means of correcting for 

 change of barometer in the use of the expression (3) and it would, 

 for instance, be impossible to compute, from knowledge of the 



