114 Transactions of the South African Philosophical Society. 



The formula is essentially an equation to a curve, and can in fact 

 be applied to any pulsatory graph if a sutficient number of terms be 

 taken. It seems to have been claimed that the individual terms 

 represent separate physical processes ; but that, surely, is to strain 

 its applicability to undue lengths. If, for example, we imagine the 

 term involving 77^30 in the curve of maximum temperature to repre- 

 sent the direct solar effect, cleared of all secondary influences, then 

 obviously A^ should have a constant value equal to about 114° for all 

 places south of the tropics. But while this value of the angle is 

 closely approached in the interior of South Africa, we shall see 

 presently that the values for other places greatly reduce the 

 significance of the circumstance.* The virtue of the formula is 

 geometrical rather than physical ; it assigns interpolated terms to 

 any degree of accuracy, and it is most convenient for purposes of 

 comparison.! There is not a single term in it which can be proved 

 to epitomise any natural sequence of events with reference to their 

 cause, although it is not unlikely — and this is important — that a 

 comparison of a number of corresponding terms taken from the 

 equations referring to places having different geographical positions 

 and climates may suggest such an epitome. It is from this point of 

 view that the results collected here should be examined. 



In the Tables below will be found values of the coefficients and 

 angles in the respective formulae representing the pressures at 

 Kimberley, Umtata, and Durban, and the maximum, minimum, and 

 mean [ = (M + m)/2] temperatures of the same places, together 

 with those of Queenstown, Aliwal North, and Philippolis. There 

 are also given computed values of most of these, compared with 

 observation, at twenty-four equidistant intervals throughout the year, 

 say at the middle and end of each month. 



In the case of the barometric pressure the term of single annual 

 period is by far the most important, its amplitude being, in each 

 case, about twelve times as great as any of the following terms. The 

 ratios between one station and another, of this term, are — 



Durban : Umtata : Kimberley = 100 : 88 : 96. 



Thus Umtata, on the slopes, approximates to mountain conditions, 

 whereas Kimberley, which is at a much greater altitude on the 

 Table-land, does not. The phase-time of maximum for this term at 



* In corresponding latitudes in the interior of South America the constant angle 

 does not exceed 85''. 



t See, e.(j., its use at Greenwich to represent the diurnal march of the magnetic 

 elements. / 



