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ME. GEOEGE H. DAEWIN ON THE INFLUENCE OE 
First. The precession and nutation of a body slowly changing its shape from internal 
causes, with especial reference to secular alterations in the obliquity of the ecliptic. 
Second. The changes in the position of th e earth’s axis of symmetry, caused by any 
deformations of small amount. 
Third. The modifications introduced by various suppositions as to the nature of the 
internal changes accompanying the deformations. 
In making numerical application of the results of the previous discussions to the case 
of the earth, it has of course been necessary to betake one’s self to geological evidence ; 
but the vagueness of that evidence has precluded any great precision in the results. 
In conclusion I must mention that, since this paper has been in manuscript, Sir 
William Thomson, in his Address to the Mathematical Section of the British Association 
at Glasgow, has expressed his opinion on this same subject. He there shortly states 
results in the main identical with mine, but without indicating how they were arrived at. 
The great interest which this subject has recently been exciting both in England and 
America, coupled with the fact that several of my results are not referred to by Sir 
William Thomson, induces me to persist in offering my work to the Royal Society. 
I. PEECESSION OE A SPHEEOID SLOWLY CHANGING ITS SHAPE. 
I begin the investigation by discussing the precession and nutation of an ellipsoid of 
revolution slowly and uniformly changing its shape. The changes are only supposed 
to continue for such a time, that the total changes in the principal moments of inertia 
are small compared to the difference between the greatest and least moments of inertia 
of the ellipsoid in its initial state. 
For brevity, I speak of the ellipsoid as the earth ; and shall omit some parts of the 
investigation, which are irrelevant to the problem under discussion. 
The changes are supposed to proceed from internal causes, and to be any whatever ; 
and in the application made they will be supposed to go on with a uniform velocity. 
1. The Filiations of Motion. 
M. Liouville has given the equations of motion about a point of a body which is 
slowly changing its shape from internal causes*; these equations, he says, are only 
applicable to the case of the point being fixed or moving uniformly in a straight line. 
They may, however, be extended to the motion of the earth about its centre of inertia, 
because the centrifugal force due to the orbital motion and the unequal orbital motion 
will not add any thing to the moments of the impressed forces. These equations are, 
in fact, an extension of Euler’s equations for the motion of a rigid body, which are 
ordinarily applied to the precessional problem. To make them intelligible I reproduce 
the following from Mr. Routh’s ‘ Rigid Dynamics ’ f , where the proof is given more 
succinctly than in the original : — - 
* Liovville’s Journ. Math. 2 me serie, t. iii. 1858, p. 1. 
f Page 150, edit, of 1860, but omitted in later editions. L, M, N are the couples of the impressed forces 
about the axes. 
