20 
the ratio of the heat received from the sun at the winter 
solstice is also defective. The excess of that winter tem- 
perature over the temperature of space is held to be strictly 
proportional to the amount of solstitial heat received. But 
this combines a mere hypothesis with a defective law of dis- 
persion or loss by radiation. A simpler rule may be deduced, 
in a less hypothetical way, from the experiments of MM. 
Dulong and Petit. According to these, when heat radiates 
from a hotter to a cooler body, and the difference of their 
temperatures is constaut, the radiation increases or diminishes 
in the ratio of P165 to 1 for a rise or fall of 20° C. or 36° F. 
in their two temperatures. Of course, if the lower body has 
a fixed temperature, and the hotter alone varies, the ratio 
should be slightly greater. To establish an equilibrium 
between the heat received from the sun and that radiated 
into space, the midwinter heat must thus be lowered till the 
radiation is lessened in the same proportion as the solar heat 
received. 
Adopting this rule, and retaining Mr. CrolPs values for 
the excentricity *0747 and *0575, and the answering ratios 
of midwinter heat, the lowering of temperature will not be 
45°*3 and 37°* 7 F., but 41°*94 and 34°*34 only, a difference 
of more than three degrees. But with the con’ected values 
•06676 and '05192 they will be 38°‘45 and 31°*84 only; or 
the winter heat at the later period, Mr. CrolPs proper 
ice age, will be 7 0, 2 F. instead of 1°*3, a difference of six 
degrees. 
34. But a further correction is plainly required. The equi- 
librium between the heat received and lost is clearly not at 
the solstice itself. The greatest heat in summer and cold in 
winter is well known to be about a month later, that is, at a 
distance of about 30° from the solstice. Thus the distances, 
on which the solar heat, when the solstice is in the perihelion 
or aphelion, depends, will not be 1— e and 1 + e, but 1— £e\/3 
and 1 + \c\/ 3. 
Introducing this correction, the lowering of the heat with 
the two uncorrected values of the excentricity will be 35 0, 45 
and 29°'81, but with the corrected or reduced values *06676 
and *05192, it will be 33°*18 and 28°*73; so that, instead 
of — 6°*3 and +1°*3 F. for the extreme or midwinter tem- 
peratures, the corrected values would be + 5°*8 and + 10°*3, 
or in the earlier period twelve, aud in the later period nine 
degrees higher, than the value Mr. Croll has given. 
35. The summer heat, in Mr. CrolPs theory, is supposed to 
depend on wholly different principles from tho winter cold. 
He speaks of it as follows. 
