Some Besults from the Periodic FormulcB. 121 



former by the latter there will be equilibrium in accordance with 

 certain thermodynamical principles that are not difficult to under- 

 stand. And then the lower layers of air will run up a temperature 

 nearly equal to what it would have been at noon had there been no 

 upper layers to warm. But the annual lag seems to depend largely 

 upon conditions of circulation manifested upon a much larger scale, 

 in which Kimberley, with its lack of a prevailing wind setting in 

 from elsewhere, does not participate. That is to say, the tempera- 

 tures of most places are in part determined elsewhere, whereas that 

 of the Table-land of South Africa, from its simplicity, almost reaches 

 the character of the result of a laboratory experiment — determined on 

 the spot. It is this nearly universal lagging of temperature that 

 makes it so difficult of representation by a physical formula. The 

 formula (3), however, enables us to eliminate some of the complica- 

 tion, and to deduce monthly series which are fairly good linear 

 functions of the sun's altitude at noon — giving, moreover, the same 

 annual mean maximum, and much the same values of y (though of 

 course different values of x) for the condition expressed by dy/dx = 0, 

 as the original observed series. 



The results for four different stations are given in Table 8, in 

 which under the name of the station will be found : — 



Col. 1. The monthly mean observed maximum temperature, M; 



Col. 2. The correction E computed by means of the series given 

 in the formula (3) ; 



Col. 3. The series D deduced from M by the addition or sub- 

 traction of E ; 



Col. 4. The series T deduced from a consideration of the sun's 

 altitude and distance, but in which the constants A and B 

 of formula (1) are indicated by Col. 3 ; 



Col. 5. The differences T - D. 



East London was added to the Table more as an afterthought 

 because of the very small variation of its mean maximum tempera- 

 ture month by month, and the lateness of its spring period. Only the 

 amplitudes and phase-times of the maximum curve have been 

 computed. They are — 



J29, - -f 3-4204 gi = + 1-3207 



2), = -f -5250 {Za = - -1010 



^3 = -0000 ^3 = - -2000 



2), = - -1083 (l4 = — -3608 



