192 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1920. 



when the days have grown longer and the supply of solar heat has 

 increased. That is, over a considerable period the air grows colder 

 as the sun grows warmer. In the far interior of continents, especially 

 if arid, this lag may not be more than a couple of weeks, but on many 

 islands and along several coasts whose winds are prevailingly on- 

 shore, it is from one to two months. 



To understand this phenomenon consider an object (representing 

 the earth) suspended within a thermally opaque shell (assumed the 

 source of incoming radiation) whose temperature is everj^where the 

 same. For simplicity let the inclosed object be a "black body," that 

 is, a full radiator and a perfect absorber. Let the absolute tempera- 

 ture of the shell be T and that of the inclosed object T ± t. Under 

 these conditions the rate of heat absorption by the suspended body is 

 AKT 4 , where A is its "equivalent" area and K the "black body" 

 coefficient, while the rate of its emission is AK(T ± t)*. If, now, t 

 is small in comparison with T, the rate of net gain or loss of heat 

 by the inclosed object is 4AKT 3 £, approximately, and the ratio of its 

 rate of temperature increase or decrease to the temperature difference, 

 t, a constant inversely proportional to its heat capacity, assuming 

 high conductivity. The limiting temperature T would, therefore, 

 never be fully attained, but forever approached asymptotically. 

 Clearly, then, if the temperature of the shell were T and that of the 

 inclosed object T + 1, the latter would continue to grow colder 

 through any finite time unless, and until some time after, the tem- 

 perature of the shell were raised above the then temperature of the 

 inclosed object. 



The reasoning in this special case applies also to the normal daily 

 temperature of the atmosphere (substantially that of the surface of 

 the earth), provided, as will be assumed for the moment, that there 

 is neither circulation nor any thermal effects due to water trans- 

 formations — freezing, thawing, etc. It applies because the normal 

 daily loss of heat through radiation to space by any given region is 

 as though it were a full radiator at a certain temperature, and its 

 normal daily gain of heat from the outside as though it were com- 

 pletely canopied by another full radiator also at a certain (generally 

 different) temperature. 



During the autumn, therefore, while there is still stored in the 

 earth much of its summer gain of heat, and while the daily supply of 

 energy from the sun is growing less and less per unit area, the aver- 

 age 24-hour temperature of the surface, and of the surface air, 

 must be appreciably higher than that of equilibrium with the simul- 

 taneous incoming radiation — higher because of the additional supply 

 of heat by conduction from its reservoir beneath the surface — and 

 as the summer storage of heat in the earth is very large and also near 

 the surface (but little penetrating beyond a depth of 5 or 6 meters) 



