2(3 Art. 1. - T, Terada: 



-data. Since the necessary materials were, however, not at our 

 disposal, we were compelled to resort to a provisory assumption : 

 That the mean a for a given zone of latitude as the function of lonyitbde 

 is proportional to the mean annual amplitude of the temperature for the 

 same zone. 



The latter assumption may appear at first sight utterly un- 

 justifiable, since the daily amplitude generally decreases with 

 latitude, whereas the annual amplitude increases with the distance 

 from the equator. If we, however, confine our attention to a given 

 narrow belt of latitude and consider the dependency of the ampli- 

 tude on the longitude, it will be rather plausible to assume for the 

 purpose of rough approximation, as is aimed at throughout the 

 present investigation, a parallelism between the two amplitudes, 

 since both depend on the nature of the earth's surface in a similar 

 way, in spite of the difference in the periods of the periodic heating 

 and cooling.'^ 



]) Avhen Ave consider the average daily fluctuation of temperature, we may consider the 

 sun at the equator. Then the solar radiation per unit area of the surface will be proportion- 

 al to cos </>, where (f is the latitude. The temperature amplitude of the earth's surface 

 depends not only on the intensity of the radiation, but largely on the nature of the surface. 

 Assume it to be proportional to F(X). Then the daily amplitude will be roughly of the form 

 Fcos </■. 



On the other hand, the annual amplitude is determined by the difference of insolation 

 in different seasons which will be proportional to 



cos (9 — Sj) — cos (cp + Sj) = 2 sin 9 sin 5j, 



where 5^ = 23.5°. Hence, the annual amplitude may be put 



F' (X) sin cp sin Sg- 



The ratio of the amplitudes, for constant cp, becomes F^a) / F'(À) as the function of >.. Now, 

 consider F and F' expanded by Foi.ritr's series of the form 



CO CO 



y A„j sin //(). + ^ B,;, cos ih\. 



It is evident that A'„, and B'„, for F' converge more rapidly than the corresponding coelH- 

 cients ft r F, since the daily variation of temj: eraturi\ being greater for the lower layer of 

 atmosphere, will be influenced conspicuously by the minor irregularities of the surface, while 

 the annual variation extending to a higher strata, will depend on the general condition of 

 the wide area surrounding the station in question. Taking he we ver the mean value of the 

 daily amplitude over a wide area, the terms depending on the large values of m will tend to 

 cancel each other, and only the first few terms will remain as the leading terms. Our as- 

 sumption actually amounts to assuming the proptrtionality of A„,, B,,, with A'„., B'„j for the 

 small values of w, which will be in any case not very far from the truth. 



