84 TRANSACTIONS OF THE 
DETERMINATION OF THE NORMAL TEMPERA- 
TURE BY MEANS OF THE EQUATION OF 
THE SEASONAL TEMPERATURE 
VARIATION AND OF A MODIFIED 
THERMOGRAPH RECORD. 
BY DR. FRANK L. WEST, N. E. EDLEFSEN, AND S. P. EWING. 
The normal air temperature is a periodic function of 
the time, there being two prominent periods, a twenty- 
four hour and an annual period. 
The mean daily temperature for the different days 
of the year for Utah was plotted and the following em- 
pirical equation for the curve obtained by the method of 
the Fourier Series. 
(1) 
T—48.5-22.2 cos(@—19°54’)—2.7 cos 2(@-149°5’)-1.0 cos 3(@-17°3’): 
T, representing the temperature, and © the time, ex- 
pressed in degrees, e. g. April lst would be 90°, July 
Ist 180° etc. The same curves for widely separated 
places in the interior of the United States are nearly 
identical in shape and when superimposed on the curve 
for Utah—in the most extreme case—projected at the 
crest but 2 above and at the winter minimum 2 below 
the curve for Utah. The first term in the above equation 
is the mean annual temperature for the place considered 
(a function of latitude and elevation) and simply moves 
the curve up or down the page while the shape or ampli- 
tude is determined by the differences in temperature 
between summer and winter and varies at different places 
in the interior of the United States from the Utah value 
from 1 to 4 degrees. The equation given above therefore 
is of rather general application. Simply insert for the first 
