286 
ME. GEORGE H. DARWIN ON THE INFLUENCE OE 
This equation has been obtained on the supposition that the change in the earth’s 
form never becomes so great that a£, b£, c t exceed small fractions of C — A ; a condition 
which is satisfied in the case of such geological changes as those of which we have any 
cognizance at present. 
It will appear from a comparison with results given hereafter, that t cannot 
ever exceed two or three degrees ; and since ^ is a very small fraction, it follows that 
the obliquity of the ecliptic must have remained sensibly constant throughout geological 
history *. Also the instantaneous axis of rotation must always have remained sensibly 
coincident with the principal axis of figure, however the latter may have wandered in the 
earth's body. 
It has hitherto been assumed that the change of form and the angular velocities of 
the principal axes in the earth’s body are uniform. But the preceding investigation 
shows clearly that no material change would be brought about by supposing the 
changes to proceed with varying velocities. This being so, dynamical considerations 
may be dismissed henceforth ; and accordingly the next part of this paper will be devoted 
to the kinematical question, as to the change in position of the earth’s axis of figure as 
due to geological changes. 
The various assumptions made above will incidentally be justified in the course of 
the work. 
For some remarks of Sir William Thomson on this part of the paper see Appendix C. 
* During the Glacial Period there must have been heavy ice-caps on one or both poles of the earth. The 
above equation will give the disturbance of the obliquity of the ecliptic produced thereby. 
I will take what I believe is the most extreme view held by any geologist. Mr. Belt is of opinion that an 
enormous ice-sheet, which was thickest in about lat. 70° N. and S., descended from both poles down to lat. 45° ; 
the amount of ice was so great that the sea stood some 2000 feet lower than now throughout the unfrozen 
regions between lat. 45° N. and S. 
Suppose that the whole of this equatorial region was sea, and that the water contained in 2000 feet of depth 
of this sea was gradually piled on the polar regions in the form of ice. Then the effect in diminishing C and 
increasing A cannot be so great as if the whole of this mass were subtracted actually from the equator and 
piled actually on the poles. This latter supposition will then give a superior limit to the amount of alteration 
in the obliquity of the ecliptic. I have calculated this alteration by means of the above formula, taking the 
numerical data used later in this paper, and taking the specific gravity of water to that of surface-rock as 4 to 11. 
I find, then, that the superior limit to the increase of the obliquity of the ecliptic would be •00045"; that is 
to say, the position of the arctic circle cannot have been shifted so much as half an inch. And this is an accu- 
mulated effect, and the matter is distributed in the most favourable manner possible. 
In this case the amount of matter displaced is enormous, and is placed in the most favourable position for 
affecting the obliquity ; hence, a fortiori, geological changes in the earth cannot have sensibly affected the obliquity. 
But although this equation leads to no startling results in the geological history of the earth, I hope to show 
in a future paper that it may have some bearing on the very remote history of the earth and of the other planets 
(see a paper “ On a Suggested Explanation of the Obliquity of Planets to their Orbits,” Phil. Mag. March 1877).— 
[In consequence of a mistake in the work it was erroneously stated in the abstract of this paper in the ‘ Pro- 
ceedings ’ that the change in the position of the arctic circles might amount to 3 inches, instead of to half an 
inch . — Added August 18, 1877.] 
