96 BULLETIN OF THE 



where the theoretical condition of our formula, that no heat shall 

 be lost by conduction, was not perfectly fulfilled. 



A portion of the earth's surface, where the soil is dry and sandy, 

 having little conductivity for heat and exposed to the vertical rays 

 of the sun, would be a case similar to that of an isolated disk radi- 

 ating sensibly from one side only, and the temperature of such a 

 surface, so exposed, should stand at a very high temperature, but 

 of course not nearly up to the theoretical temperature, since much 

 heat would be conveyed away by the conduction and convection of 

 the air, and also some conducted down into the earth. The tem- 

 perature of sandy soils is often observed to be as high as 150° F. 

 and upwards, and the preceding theory explains these very high 

 temperatures and the great differences of temperature of different 

 bodies under the same circumstances. 



From equations (2), and (3), with the given values of A and B, 

 we get 



(5) K = .07232 /^V — r ' — 1) 



This is an actinometric formula, giving the amount of heat re- 

 ceived from the sun, in absolute heat units, from the observation of 

 the sunshine and shade temperatures. So far as the author's read- 

 ing extends no such formula has ever been given, but r — -' has 

 been regarded as a measure of the sun's relative intensity under 

 different circumstances. The formula not only gives the absolute 

 instead of the relative amount of heat received, but it shows that 

 r — t' is not proportional to K, and consequently not a correct 

 measure of the relative intensities of the sun's rays. With an ob- 

 served value t — t' = 35° and r' = 30° the formula gives K = 

 .02806; but with the same value of r — /, and with the value 

 of t' = 0°, it gives K = .02229. Hence the value of K is not 

 proportional to r — r', and differs considerably when the value of 

 r — T ', under different circumstances, is the same. Both these 

 values of /fare less than the value of A = .03046, as they should 

 be by equation (2). The greater the altitude the more nearly 

 should the value of p approximate to that of unity, and the more 

 nearly should the value of K approximate to that of A. 



If the value of p, according to Tyndal, as has been stated, de- 

 pends upon the hygrometric state of the atmosphere, then the value 

 of K, as given by the preceding formula, for any observed values 

 of r and r', must give the diathermancy, and consequently the 



