278 Proceedings of Royal Society of Edinburgh. [sess. 
near sunrise, where naturally it does not follow the theory for some 
time, for reasons which may be deduced without difficulty from the 
theoretical considerations already given, we arrive at a formula, 
t — Min. + a . a n cos cf > cos 8 , 
a being a numerical quantity tabulated for each hour of the day 
from sunrise to sunset. Now, these last two epochs also belong to 
the night curve, which we know to be represented by the equation : 
t = u + c . e , 
so that the two unknowns of this last equation can be determined 
by the minimum temperature and the solar constant. Hence we 
arrive at the result that the temperature at every hour of the whole 
day may be represented by the above-mentioned formula : 
t — Min. + aa n cos </> cos 8 . 
It would far exceed the scope of this paper should I attempt to 
introduce the tables of the quantity a, which I hope to publish in 
extenso at a future time. 
Now, having, for instance, three times of observations, the most 
usual being morning, afternoon, and evening, let us denote the 
observed temperatures by i v t 2 , t s ; the respective values of a by 
^2? ^3* Then we have the following relation : 
cu = 
^ — —sec sec 8 . 
la. 2 - a 1 - a 3 
In this way we obtained, by discussion of the observations of a 
great number of stations in Russia and Austria-Hungary, where the 
observing hours were 7 a.m., 1 p.m., 9 p.m., and 7 a.m., 2 p.m., 
9 p.m. respectively, the following values of a m for the mean lati- 
tude 49° : 
April. May. June. July. Aug. September. 
a m = 6°-08 6°T9 6°T1 6°T9 6°T5 6° TO Centigrade. 
On the other hand, by taking again the mean of the six months 
in each year, we arrived at values, which we have given in the 
affixed curves, separately for each of the combinations mentioned 
