On Sun-heat and Radiation. 95 
Total heat received in one year 
= 2A x 365:2510:95910 cosd 
+0-04187 tandA sind 
+ 0:00047 tan®\ sind (13) 
+0:000015 tan5d sind 
+ &e, 
It is evident, from this equation, that when the latitude is 
small, the heat received in the year varies as the cosine of the 
latitude. 
It is to be observed that equation (3), which expresses the heat 
received in one day, becomes illusory inside the arctic and antarctic 
circles, when the sun does not set; for then H (the hour of sunset) 
has an imaginary value. We must, therefore, compute the annual 
heat received inside these circles by summing the heat from the 
equinox till the time when the sun does not set or does not rise 
by equation (12); and adding the heat received during the time 
when the sun does not set. 
If D denote the sun’s declination, when he ceases to rise or set, 
equation (12), with D substituted for A, will give the heat received 
during the part of the year when the sun rises and sets, and the 
angle H is real. 
To this must be added the heat received during the time when 
the sun never sets, which may be found as follows : 
Referring to equations (1) and (2), we have, when the sun does 
not set, 
Total heat in one day 
2 ar 
=4 fl cos zdh (14) 
0 
9 9 
=A fo vom r sin ddh+ Sy A cos 6 cosh dh, 
0 0 
=2Az7 sind sind=2A7 sind sinA sini. 
This value must be summed through the time that the sun does 
not set; or, if a be the daily change in sun’s longitude, 
The total heat received during the time that the sun never sets 
=2Am sind sinA {sin/+sin(/+a)+sin(/+2a)}+é&e. (15) 
sin(1+ "5 te sin . 
PEED SP Mie ey sae ae y 
=2A-z sind sin 
- @ 
sa) 
