418 Scientific Proceedings, Royal Dublin Society. 
the difference in temperature between the cooling body and its 
inclosure becomes large. 
The most recent advance made in this subject is the important 
discovery, made by Mr. Rossetti, that Newton’s law of cooling 
becomes accurate for great ranges of temperature, provided we 
make the coefficient K a function of the absolute temperature of 
the cooling body, instead of being a constant ; and this function 
turns out to be nearly proportional to the square of the absolute 
temperature. 
Newton's law thus becomes— 
<2 =(0- ©) (a PA). (5) 
where T is the absolute temperature, and f is a very small con- 
stant as compared with a. 
In order to apply Rossetti’s law of cooling to the case of the 
earth’s surface, I suppose a to be the temperature of the layers of 
upper atmosphere which controls the radiation of heat from the 
earth’s surface ; a being regarded as positive when below zero. 
We now have (neglecting 6)— 
6 — e—6 +a 
T =—460+6 
p =0 
and, finally— 
-- a(@ +a) (460 + 6). (6) 
This gives by integration, after some reductions, and writing A 
for 460— 
=a log —_ = pac) tee. . ie 
The following Table gives the annual sun-heat and mean 
annual temperatures of the Northern Hemisphere :— 
Sun-heat. Mean Temperature. Latitade. 
41°9 feet of ice, “i re Sry : oy eS 
463 - cg A cal te - a ae 
Sy (2 Sa a, 60 
66°8 == . B84, 50 
773 = . | S65. > 40 
89 = =) 1Gre oe 30 
92-4 - (MD os 20 
96°5 = ao Sees 1¢ 
978 ~ Ou tei Ss bee 0 
