14 
of twice the excentricity to the sine of the inclination. Hence 
an increase of the inclination from 23° 28' to 35° 56' with the 
present excentricity would cause the same degree of inequality 
as an increase of the excentricity to ‘0747, its supposed 
amount 850,000 years ago. If glaciation would result, as 
Mr. Croll contends, from the latter combination, it must have 
done so from the other, and for the same reason. On the other 
hand, if a hotter summer undoes and reverses the effect of 
a colder winter with an increased obliquity, it must equally 
do so with an increased excentricity. 
24. The real error of Lieut.- Col. Drayson’ s theory is its 
contradiction to the laws of physical astronomy. The pole of the 
equator, by precession, is receding 50" in longitude annually at 
a right angle to the pole of the ecliptic. But the obliquity is 
also slowly lessening, and the poles are coming nearer together. 
Lieut. -Col. Drayson finds that the two plienonema will be recon- 
ciled, and the observations of precession and polar distance satis- 
fied from Tycho down to the present day, if we assume the pole 
of the equator to revolve round a point at 6° distance from the 
pole of the ecliptic. In this case, the nearest approach would 
be about five centuries hence, the period of revolution 31,840 
years, and B.C. 13,600 the obliquity would have its maximum 
value, or 35° 26'. The excentricity, by Mr. Croll’s table, 
would then be '01875, and the effect to produce inequality of 
heat at midwinter and midsummer, the same as with the 
present obliquity and an excentricity of '1095, or half as great 
again as the maximum in Mr. CrolPs table. 
25. But the mistake is here. The precession or backward 
motion of the pole of the equator, and the diminished 
obliquity or the motion of the pole of the ecliptic nearer to 
that of the equator depend on two wholly distinct causes. 
One is due to the action of the sun on the equatorial protu- 
berance, and must be at right angles to the line which joins 
the two poles at the moment and in no other direction. The 
other is due to the disturbing action of the other planets on 
the earth’s annual orbit. It does not make the pole of the 
equator move with reference to that of the ecliptic, but the 
reverse, that is, the pole of the ecliptic approaches to or recedes 
from that of the equator. Thus the earth’s polo does not 
revolve round a fixed centre 6° away from the pole of the 
ecliptic, but round a pole itself moving in a small self-returning 
curve of definite limits. It moves in fact in a sort of cycloid of 
a rather complex kind, and not in a circle. No doubt a circle 
may be found, as Lieut. -Col. Drayson has proved, to satisfy the 
observations, which range over only four centuries. But this 
is a striking example of the danger of trusting to a purely 
