LIL.—ON ROSSETTI’S LAW OF COOLING, APPLIED TO THE 
CONSIDERATION OF THE RELATIVE EFFECTS OF 
SUN-HEAT, EARTH-HEAT, STAR-HEAT, AND ATMOS. 
PHERIC CONDITIONS UPON CLIMATES DURING 
GEOLOGICAL TIME, sy Rev. SAMUEL HAUGHTON, 
M.D., D.C.L., F.B.S. 
[Read January 19th, 1880.] 
NEwrTon’s famous law of cooling assumed that the radiation was 
proportional to the difference between the temperature of the 
body cooling and the temperature of the inclosure. 
If 6, © denote these two temperatures, and ¢ denote the time, 
Newton’s law is— 
dé 
aa —@). 1 
3, = * (0-8) (1) 
This gives, by integration, — 
(=e log, (0@—0) +0. (2) 
where K and C are unknown constants. 
This law holds true as long as the difference of temperatures, 
6—8®, is not large, but fails entirely when it is great. 
Under these circumstances a new law of cooling was proposed 
by Dulong and Petit, which, although artificial in its concep- 
tion, and deviating from the simple idea of the Newtonian law 
nevertheless was found to represent observations better than the 
Newtonian law, when the difference of temperatures became 
greater. 
According to this law— 
dé 
where #=1-0077 for all bodies, and A depends on the nature of 
the cooling body. 
This relation gives, after some deductions, by integration, the 
following :— 
po-8 
where K and C are unknown constants. 
Dulong and Petit’s law of cooling fails, as Newton’s did, when 
Scien. Proc.,R.DS. Vou. m., Pr. vi. oF 
= K log = Lo (f) 
