1919-20.] The Daily Temperature Curve. 91 
Weilenmann, with this difference, that he assumes equal values for the 
constants, (p = q = q' = h, p' = 2 h). 
As to solar radiation, let J be proportional to the quantity of heat 
radiated per unit time from the sun on unit area placed at right angles to 
the rays’ path. The heat received by direct solar radiation on unit area 
of soil is proportional to (J cos z), where 0 designates the zenith distance 
of the sun. 0 at apparent solar time, t s , depends on the geographical 
latitude, <p , the declination, S, and the hour-angle, t h , of the sun, and is 
calculated from 
(1) .... cos 2 = sin sin S + cos cos S cos t. 
Again, solar heat is reflected to the soil by clouds, the amount of heat 
being proportional to J. The corresponding change in temperature per 
unit time is given in the right-hand side of equation (2). 
Unit volume of air receives solar heat both directly from the sun and 
also through reflection by soil and clouds. Both amounts are proportional 
to J. The corresponding change in temperature of the air per unit time is 
again proportional to J, and its amount is entered in the right-hand side of 
equation (3). 
(2) t +pV — qr — m =k' cos 2 J + Z'J. 
(3) . . . . r +pr —qT—m= + /J. 
Eliminate t from these equations and find the formula (I) in section 1, 
where 
a =p +p', b =pp — qq', bc 0 = qni -{-pm, 
and 
(4) . . . ¥{z) = [qk' cos z+(gr+p7)]J-f 
(3) The Values of J and F(z). — Consider, in the atmosphere, a tube of 
unit section curved along the path of the sun’s rays. Let s designate the 
total mass of air in the tube. The intensity, J, increases at each step, ds, 
by d J = — n J ds, where n expresses the fraction absorbed by unit mass. 
Hence J is proportional to 10” ws , and ( — n) may thus also be defined as 
the logarithm of the coefficient of transmission ( i.e . ratio of intensity after 
passing through unit mass and original intensity). Laplace’s well-known 
formula gives the following value of s which is expressed in units of the 
mass of air in a tube directed towards the zenith : — 
(5) . . . . . s=i J^-^^secz, 
a 0 sin z a 0 
where R( = a z tan z) is the value of the atmospheric refraction at zenith 
