268 
Proceedings of Royal Society of Edinburgh. [sess. 
From the two simultaneous equations just mentioned we derive, 
by elimination of t', a differential equation of the form : 
+ n\t - u) = o , 
the integral of which is 
. Ai2 K 2 Z 
t — u 4- + c 2 6 , 
where X Y and X 2 are the roots of the quadratic equation 
X 2 + ,m + 7t 2 = 0 
X l = - 0-382 h; X 2 = -2*618 ft. 
By a careful investigation of the temperatures at several places, 
Weilenmann proved empirically that the arbitrary constant t 2 is 
zero in all cases, so that we have the particular integral 
t = u 4- c e 0 3S ~ 7i " i n units of the hour) . 
From the theoretical point of view, this equation is of great 
importance, giving, as it does, a numerical value of the coefficient 
of radiation h, which was really found by Weilenmann to he a 
constant for all the places considered and all conditions of the 
atmosphere, the average value being 0*375. This numerical value 
seems to represent perfectly the observations at all the stations on 
which I have founded my computations, leaving an error, which 
is certainly below the mean accidental error of the observations. 
Let us now consider the important change of conditions produced 
by the solar radiation during the day. It is well known that the 
sun’s rays passing through the atmosphere suffer a considerable loss 
of their directly radiated light and heat by the absorptive and 
reflective power of the air. But it would be quite insufficient to 
introduce only this direct part of solar heat into our problem 
without noticing those enormous outstanding portions of solar 
radiation which at last reach the earth’s surface after being de- 
flected once, or even oftener, from their direct course by the inter- 
fering particles of the air. W 7 e therefore bring to our aid a careful 
investigation of both the direct and diffused radiation of solar heat 
which is found in an elaborate discussion due to W. Zenker , entitled 
“ Sur la distribution de la chaleur sur le globe.” In this paper the 
