120 Transactions of the South African Philosophical Society. 



Over the centre of the Table-land of South Africa the equational 

 correction will, in most cases, be small. What it will be elsewhere 

 remains to be seen. We shall apply the equation (3) to the tem- 

 peratures observed at other places in the country, using the local 

 values previously found for a^, a^, a^, ... in evaluating the equa- 

 tion (4) ; Aj, A2, A3, . . . being assumed constant for all and 

 having the numerical magnitudes assigned in (2). This amounts, 

 in fact, to an assumption that the unperturbed maximum tempera- 

 tures considered as proceeding directly from the action of the sun 

 will everywhere evolve the same phase-times in Bessel's equation, 

 while the amplitudes will vary with geographical position. Hence, 

 obviously, final success must depend upon the initial accuracy of the 

 angles determined in equation (2). 



It is known that, generally speaking, the highest and lowest mean 

 maximum temperatures of the year come some time after the epochs 

 of the sun's greatest and least meridian altitude at noon. This is 

 easily perceived to depend in some way upon the balance that 

 is being struck continuously between the heat received from the sun 

 and that radiated again by the earth into space. It is commonly 

 spoken of as though it must be a magnified presentment of the 

 diurnal lagging of maximum temperature : the diurnal maximum 

 falling about a twelfth of a day after midday, while the annual 

 maximum falls about a twelfth of a year after midsummer. Or as 

 an authority puts it : " While the sun stands farthest north or south 

 of the equator in June or December, the greatest migration of the 

 heat equator northward or southw^ard is found in July or August and 

 January or February ; just as the hottest part of the day is an hour 

 or two after noon."''' It is difficult, however, to see that the two 

 phenomena are so closely analogous. At Kimberiey the hottest time 

 of the day is some time after XIV., like other places. But the 

 hottest time of the year is not far from Christmas Day — just after 

 the solstice. At Kimberiey, moreover, the temperature of the 

 surface layers of the soil reaches its highest degree during the day 

 an hour or more earlier than the air does ; while at Cordoba the 

 observations of a number of years seem to indicate an annual 

 maximum just beneath the surface some ten days earlier than 

 that of the air. These facts compared seem to imply that the 

 lagging of the hottest time of the day depends upon the vertical 

 temperature gradient. When this is steep, i.e., when the super- 

 incumbent layers aie relatively very cold, the lower layers will tend 

 to ascend ; })ut when sufficient heat has been communicated to the 



* Davis, FAenioitary Meteorology. 



