17 
the minor axis, when the periodic time and the major axis 
are constant and do not change. This was stated by Sir J. 
Herschel in a paper read to the Geological Society in 1830. 
It admits of easy demonstration, and Mr. Croll quotes the 
paper in his Appendix, and admits the scientific truth. Ho 
thinks, however, the difference is so slight that it may be 
safely neglected, and treated as of no account. But this is not 
so plain. It would be very strange, if a period in which the 
earth receives the most heat from the sun were that in which, 
on the whole, it suffers the most from extreme cold. With 
an excentricity of ‘0575, or 10^ millions excess of aphe- 
lion over perihelion distance, the excess above the present 
would be three-twentieths per cent., or 1^ part in a thousand. 
Let us take 5,000 years on each side of Mr. Crolks date, or 
the interval from 205 to 215 thousand years ago. If a 
northern winter aphelion lay midway between, this would 
include half one whole circuit, in which the aphelion lies 
within the northern winter season. The excess of heat received 
from the sun in those 10,000 vears above its mean amount will 
be, in Mr. Crolhs mode of reckoning, about 27 billions of 
billions of foot pounds. This agrees ill with the hypothesis 
that the period is one marked by extreme and excessive cold. 
29. A third and more decisive objection follows. The season 
which the theory singles out to account for extreme glaciation, 
is that in which the northern hemisphere receives the greatest 
excess of solar heat above the mean value. 
The proof is simple. The total heat received by the earth 
from the sun in its annual orbit is equal for equal angles. 
The swiftness and the nearness, the remoteness and the length 
of time, compensate each other, vai’ying by the same law of 
the inverse square of the distance. But this is not true for 
the separate hemispheres. If the orbit were circular, each 
would receive more in the summer, and less in the winter 
half of the year. But from the excentricity, when the peri- 
helion and aphelion are at the two solstices, the summer heat 
is increased and the winter heat diminished, or conversely, in 
the same ratio. But since the summer heat is greater than 
that of the winter, the total for the hemisphere whose summer 
is in the perihelion must exceed the other. 
30. To make this plainer, let us take approximate values. Let 
theearth’s distance from the sun be 90 millions, the excentricity, 
as in the supposed glacial epoch, one-ninth, or the greatest 
and least distances, 95 and 85 millions. The quantity of heat 
at perihelion and aphelion will vary in a duplicate ratio ; or if 9 
be taken for the mean quantity, 8 and 10. The ratios at 
midsummer and midwinter are as 1 + sin. tto 1 — sin. i , nearly 
VOL. XIII. c 
