5o6 



Journal of Agricultural Research voi. xviii. no. io 



hours and the concavity during the falling temperatures is mostly due to 

 curvature of the vertical lines of the coordinate paper made necessary 

 by the mechanism of the thermograph. The same temperature plotted 

 on rectangular coordinate paper would make the curve approximately 

 the shape of those of figure i . 



At first the writers thought that after having determined the mean 

 daily temperature for the particular day they would determine the tem- 

 perature for that particular hour by adding or subtracting a constant. 

 The great change in the shape of the curve makes this method impracti- 

 cable. However, it was found that if the temperature at a particular 

 hour, such as the 3 a. m. value, is subtracted from the mean for the day 

 and this answer divided by the mean for the day, the same answer will 

 be obtained within less than 10 per cent no matter what day of the 

 month or what month of the year is used. The variations are largely 

 due to storms. 



From a study of the temperature records of all the counties of Utah 

 and for all months of the year the writers have determined the relation — 

 expressed in percentage — of each hourly temperature to the mean 

 daily temperature. These percentages of the mean for each of the 24 

 hours of the day are given in Table II. They come out practically con- 

 stant for a particular hour of the 24, irrespective of the season, because 

 as winter approaches and the mean daily temperature becomes lower 

 the daily variation becomes less, the curve' flattens (see fig. 3), and thus 

 both values become less. 



Table II. — Relation of hourly tetnperaturcs to mean daily temperatures 



A. M. 



These percentages for the different hours are plotted in figure 5. The 

 equation for this curve has been obtained by the method explained 

 earlier and is as follows : 



^= 97-33 ~ 9-8 cos ^4-0.88 cos 2^ — 0.52 cos 3^ — 23.26 sin 6 



4-3-52 sin 2 ^-1.42 sin 3 (9 + --- -- (5), 



or in terms of just one of the trinonometric functions : 



^=97-33 + 25-22 cos (^ — 67°— 10') +3-71 cos 2(^ — 37° — 59')- 

 1.51 cos 3(^-23°- 16') + (6). 



