32 Report S.A.A. Advancement of Science. 



analysis, as it is called, is of considerable importance in many- 

 branches of physics. It is based on the principle that the summation 

 of any number of harmonic curves is a periodic curve. The task of 

 the meteorologist is the laborious inverse process : the separation of the 

 various periodic curves met with in meteorology into their harmonic 

 constituents as far as possible. Most of the diurnal meteorological 

 curves well repay analysis as far as the fourth harmonic, the curve of 

 diurnal barometric variation in particular. The periodic formula as 

 it is usually employed in meteorology is, for hourly observations, — 



a = p + Uj sin (Vj + n 15°) 



+ U2 sin (V2 + 2n 15°) 



+ U3 sin (V3 + 3n is'') 



+ 



where p is the mean value, 



Ui, U2, U3, the amplitudes, and 



Vi, Vg, V3, the epochs 



of the first, second, and third harm.onic terms respectively. 



Now, Hann has established that in the case of the barometric 

 pressure, up to latitude 48° at least, U2 is greater than Ui, and, 

 indeed, considerably the greater over the tropical oceans. Also that 

 the flood-time of the semi-diurnal barometric wave is very constant 

 over pretty well the entire globe. The flood-time of the diurnal wave, 

 however, varies widely according to the latitude and topography of the 

 station. 



Table 3 gives the various harmonic elements for the four 

 barometer curves of Fig. i, together with one or two others for 

 comparison. I have also added harmonic elements of vapour tension 

 for Kimberley, Lisbon, Cordoba, and Hong Kong. You will see from 

 these that the epoch of the semi-diurnal wave of pressure comes later 

 on the whole (i.e., the constant angle gets smaller) as the latitude 

 increases, saving in the case of the station near the Arctic Circle. 



Let me now quote a passage or two from a comparatively recent 

 paper by Hann as expressing some of his latest views : — 



" I was myself convinced that all the attempts to explain the 

 diurnal barometric oscillation by means of the daily variations 

 of the meteorological elements at any one place. . . . could lead 

 to no conclusion ; and I have published a series of papers giving 

 a precise description of the phenomenon as manifested over the 

 whole earth, at sea-level as well as at all elevations for which 

 observations exist, and I have endeavoured to give the results in 

 such a form as would be suited for the basis of a physico- 

 mathematical theory. With this object I have represented all the 

 results of observations in periodic functions. 



" I am of opinion that, speaking generally, the observed 

 daily variation of wind and temperature do not stand in as close 

 a relation to the diurnal barometric oscillation as has hitherto been 



assumed We had better deal with the action of the sun 



on the upper strata of the atmosphere, and treat this as the 

 principal cause. The actinometrical observations show us that 



