The Barometer in South Africa. hi 



Table i shows that in the mean the lowest barometer occurs in 

 March and the highest in July. The means can be represented by a 

 Fourier series. As the calendar months are of varying lengths, we 

 should not assume that the mean of any month is the mean of the 

 corresponding one-twelfth of the year. The introduction of a rational 

 calendar is probably out of the question. Such a one is as follows : — 



or 31 days in leap year. 



This calendar would coincide with the present one on Jan. ist, 

 April I St, June ist, and from August ist to the end of the year. The 

 quarters and half-years would compare as follows : — 



Rational. 



ist quarter 90 or 91 days. 



2nd ,, 92 ,, 



3rd ,, 91 ,, 



-Ith ,, 92 ,, 



ist half-yeai 182 or 183 ,, 



2nd ,, 183 ,, 184 ,, 



With this rational calendar, the derivation of the co-efficients 

 of a Fourier series by the assumption that each month is a twelfth of 

 a year would be sufficiently exact for all purposes. 



In taking monthly rneans, some meteorologists transfer the last 

 day of January and the first of March to February. 



But if we keep to the means of the calendar months, we can 

 make use of the formulae developed by INIons. A. Angot in the 

 Annales du Bureau Central Meteorologique de France, 1887., Vol. I., 

 pp. B227-B236. This course has not been followed here, as it would 

 be a refinement not warranted bv the material at our disposal, and, 

 indeed, we did not know of Angot 's formulae when the computations 

 were made. Where Q is measured from the middle of January, we 

 find that the e;xpression 



28.2210 — 544 cos ^ — 190 sin Q. 



-h 198 cos 2Q -\- 7 sin iQ. 

 — 21 cos 3^- 47 sin 3^. 



