92 Scientific Proceedings, Royal Dublin Society. 
IxX.—ON THE TOTAL ANNUAL HEAT RECEIVED AT EACH 
POINT OF THE EARTH’S SURFACE FROM THE SUN, 
AND ON THE AMOUNT OF THE LOSS OF THAT HEAT 
CAUSED BY RADIATION INTO SPACE (NEGLECTING 
THE EFFECT OF THE ATMOSPHERE), sy THE REV. 
SAMUEL HAUGHTON, M.D., DUBL., D.C.L., OXON. 
[Read March 18th, 1878.] 
THE heat received by a given surface at any instant is 
A cos 2 dh, 
where 
A =a known constant, 
z =sun’s zenith distance, 
h =sun’s hour angle, 
and 
unrise 
Total heat received in one day = af” cos z dh, (1) 
Sunset 
Now, we have 
cos =sin \ sin 6 + cos A cos 6 cosh, 
where . 
d = latitude of place, 
6 =sun’s declination, 
H = hour of sunset. 
Equation (1) thus becomes— 
+ 
Total heat received in one day = cos 2 ah 
+z +a fom 
=f A sin \ sin édh + f A cos d cos 6 cos h dh, 
-H -H 
=2A {sin \ sin 6 - H+cos) cos 6 sin H}. (2) 
But, since 
cos H = — tan X tan 6, 
the expression (2) may be thus written: 
Total heat received in one day = 2 A sind sind {H-—tan H}. (3) 
This expression might be expanded by means of Leibnitz’ theorem, 
as follows: 
Total heat received in one day 
an®H tan5H , tan? : 
=2 AsinAsind ee) 
