Feb. i6, 1920 



Determination of Normal Temperatures 



501 



without rain. In addition, fully one-fourth of the land area of the earth 

 is equally dry. The departures from the normal temperature, therefore, 

 are least for these areas; and the method to be developed in this paper 

 is most useful for them in predicting actual temperatures. 



Figure i represents the mean monthly temperatures for several widely 

 separated cities of the United States and shows how the temperature 

 changes as the seasons advance. The curves are somewhat alike. For 

 Seattle and San Francisco they are flatter than for the others, showing 

 that the difference in temperature between summer and winter is slight. 

 These cities are said to have an equable or oceanic climate because 

 of their relative position to the ocean with its high heat capacity and the 

 prevailing westerly winds. It is probable that for cities with the same 

 mean annual temperature and with the same difference in temperature 



Fig. i.-rSynoptic chart of annual temperature marches at selected stations in the United States. 



between summer and winter the curves would be just alike. For cities 

 with the same annual variation the curves would have the same slope. 



Figure 2 shows the change in temperature with the season in Utah 

 and represents the mean monthly temperatures for the State. 



Any single-valued periodic function can be expressed by an infinite 

 trigonometric series, or Fourier series, of the form 



T = a + h sinx + c sh\ 2X + d sin 2,x -\- 



-\- e cos X + /cos 2X ■\- g cos 3a; -^ (i); 



or if it is desirable to express it in terms of the cosine only, it takes the 

 following form : 



T = a + lcos{d -c) + dcos2 {& -e) -f/cos 3 (0 -g) -f_._ (2)^ 

 the contents a, h, c, d, etc., determining the shape of the particular curve. 

 The method is well known to mathematicians and is explained in the larger 

 texts on calculus under the head of Fourier's series. 



