UTAH ACADEMY OF SCIENCES 85 
term, the mean annual temperature for the place in ques- 
tion, leave the rest of the equation as it is and the normal 
mean daily temperature for the day desired at the place 
chosen may be calculated. 
The curve representing the twenty-four hour tem- 
perature change (thermograph record), modifies its 
shape gradually each day, flattening out as winter 
appoaches. During the summer, when heat is being re- 
ceived fast one would expect the rise in temperature to be 
greater, for the same time interval, than in winter and 
thus we find that the daily variation in temperature is 
about twice as much in summer as in winter. However, the 
ratio of the hourly temperatures to the mean daily tem- 
perature Fahrenheit is nearly constant whatever day of 
the year is selected, e. g. the ratio of the maximum to the 
mean is very approximately a constant for all days of the 
year. Irregularities will be caused by storms and enough 
ratios must be taken to eliminate these in obtaining this 
constant. These per cents of the mean daily temperature, 
range from seventy for the minimum just before sunrise 
to 130 for late afternoon, (somewhat smaller range for 
humid regions,) and when plotted gave a curve very 
similar to the thermograph record of a clear day. The 
equation of this curve is 
(2) 
P—97.3—25.2 cos (@-67°10’) 4.3.7 cos 2(@—-38°)—1.5 cos 3(9—-23°16’) 
P, representing the per cent of the mean daily temper- 
ature and © the time of day expressed in degrees, e. g. 
6 A. M. would be 90°, noon 180°. etc. This equation 
is also of rather general application, at least approxi- 
mately. 
To determine the normal temperature at any place, 
say e. g. Denver at any day and hour, say May Ist at 
4 A. M.—insert the mean annual temperature of Denver 
for the first term of equation (1) and substitute for © 
the May 1st equivalent which is 1/3 of 360—120° and 
solve for the mean daily temperature for that day. In 
equation (2) insert for @ 4/24 or 1/6 of 360°—60° and 
solve for the per cent corresponding to 4 A. M., multiply 
this per cent by the temperature obtained from solving 
