164 HUMPHREYS: METEOROLOGICAL PARADOXES 



and, therefore, highly absorptive of earth radiation, to great 

 altitudes, especially as anticyclones with their extensive regions 

 of descending air are there unknown. Clearly, then, a large 

 part of the radiation through the stratosphere of this region 

 must come from the clouds and from water vapor that are very 

 high and correspondingly cold, and therefore its intensity, it 

 would seem, must be correspondingly feeble. The pent up heat 

 below can find an outlet through horizontal circulation and radia- 

 tion from lower and warmer levels in higher latitudes. 



This, perhaps, is at least the partial explanation of why the 

 minimum temperature of the stratosphere occurs over the trop- 

 ical regions — why the coldest air covers the warmest earth. 



AS THE DAYS GROW LONGER THE COLD GROWS STRONGER 



This old proverb paradox expresses the well-known fact that 

 our lowest temperatures do not occur at the time of the shortest 

 days, or when the heat supply from the sun is least, but some 

 time afterwards, 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 (repre- 

 senting the earth) suspended within a thermally opaque shell 

 (assumed the source of incoming radiation) whose temperature 

 is everywhere the same. For simplicity let the enclosed object 

 be a "black body," that is, a full radiator and a perfect absorber. 

 Let the absolute temperature of the shell be T and that of the 

 enclosed object T ^ t. Under these conditions the rate of heat 

 absorption by the suspended body is AKT"^, where A is its 

 "equivalent" area and K the "black body" coefficient, while 

 the rate of its emission is AK{T =t t)"^, if^ now, t is small in 

 comparison with T, the rate of net gain or loss of heat by the 

 enclosed object is 4AKTH, approximately, and the ratio of its 

 rate of temperature increase or decrease to the temperature dif- 

 ference, /, a constant inversely proportional to its heat capacity, 

 assuming high conductivity. The limiting temperature T 



