1919-20.] 
The Daily Temperature Curve. 
89 
XI. — The Daily Temperature Curve. By L. Becker, M.A., Ph.D., 
Professor of Astronomy in the University of Glasgow. 
(MS. received February 17, 1920. Read March 15, 1920.) 
(1) Outline of Investigation. — During the last half-century the temperature 
of the air has been recorded by thermographs at a number of places, and 
the registered graphs have been measured and mean daily temperature 
curves have been calculated from them for each month of the year. The 
amount of labour entailed in these operations is enormous, and it may well 
be asked whether the figures cannot be put to some further use. It appears 
to me that a comparison of the daily curves obtained at various places 
would furnish important information in regard to climate. To effect this 
the curves may be represented by Fourier’s Series, and the values of the 
constants at the various places may be compared. Another method of 
comparison, however, seems to me more promising. It has been suggested 
that the daily temperature curve might be represented by the differential 
equation 
(I) f + ar + &(t-c 0 ) = F(z), 
which is based on physical considerations. (Its derivation is given in 
section 2.) The constants, a, b, and c 0 , the function, F (z), of the zenith 
distance, z, of the sun, and the two constants of integration are the 
quantities whose values at different places may be compared. The object 
of this paper is to show how the numerical values of these quantities may 
be calculated from the registered figures, and to prove that the observations 
are sufficiently well represented by the integral of equation (I). 
I have used the twelve curves, one for each month, which were calculated 
from the temperatures recorded at Glasgow Observatory in the forty-five 
years 1868 to 1912, on behalf of the Meteorological Council, London. 
In my method I determine the constants a and b and the function F(z) 
from the numerical values of r, r, r as obtained from the curves. The 
constant c 0 and the constants of integration, c 1 and c 2 , are calculated 
from the integral, (II), of equation (I). The integrals T x and T 2 extend 
from the time of rising of the sun, t r , and are calculated by mechanical 
quadrature. 
<n) 
T — Q + Tj - f 2 , 
