Archdeacon Pratt^s Reply to M. Delaunay. 421 



VI. — Eeply to M. Delaunay's Objections to the late Mk. 

 . Hopkins' Method of Determining the Thickness of the 

 Earth's Crust, by the Precession and Nutation of the 

 Earth's Axis. By Archdeacon Pratt, M.A., P.E.S., etc. 



To the Editor of the Geological Magazine.^ 

 Sir, — Having lately read the translation of a paper by M. De- 

 launay in your Magazine of November, 1868, Vol. V., p. 507, and 

 your commendatory notice of that gentleman's views regarding the 

 late Mr. Hopkins' method of estimating the thickness of the earth's 

 crust by Precession and Nutation, I beg to send you a paper in which 

 1 have endeavoured to vindicate that method and to point out where 

 M. Delaunay appears to have mistaken it. Mr. Hopkins was no 

 average mathematical physicist, and was not likely to have advanced 

 a theory to be so easily refuted, as M. Delaunay's paper would im- 

 press readers not well versed in mathematical physics. — I am, etc., 

 MuRREB, Himalayas. TnTr-w TT P-ratt 



May 29, 1870. '^^^^ ^' "t^^^^^' 



It is only two days ago that I saw for the first time M. 

 Delaunay's strictures ^ upon the late Mr. Hopkins' method of ascer- 

 taining the least thickness of the Earth's Crust by means of 

 the phenomena of Precession and Nutation, although I had pre- 

 viously seen a notice that such strictures had been laid before the 

 Erench Academy. Having now that gentleman's paper before me, 

 I write to endeavour to convince your readers that the point of Mr. 

 Hopkins' reasoning has been altogether missed, and that his method 

 stands altogether unimpaired by these strictures. 



2. I am ready to allow, and so would Mr. Hopkins have allowed, 

 that if the crust of the earth revolved round a steady axis, always 

 parallel to itself in space, and if at some particular epoch a differ- 

 ence existed ' between the rate of movement of the crust and of the 

 fluid within it, the resulting friction would gradually destroy this 

 difference and bring about a conformity in the motion of both parts. 

 I will even go further, and allow that the effect of the internal 

 friction and viscidity of the fluid may be such that the resulting 

 rotary motion may be the same as that which the whole mass would 

 have had at the epoch if it had suddenly become one solid body and 

 thereby suddenly retarded the rotation. This, before proceeding, I 

 will illustrate by an example for the use of your mathematical 

 readers. 



3. Suppose a spherical shell or crust of mass C to have within it 

 a solid spherical nucleus, of radius h and mass N, fitting it exactly ; 

 and the crust to receive an angular velocity of rotation around an 

 axis fixed in the crust, the nucleus at that moment having no angular 

 velocity; but suppose that a slight force of friction between the 



1 We gladly publish Archdeacon Pratt's reply to M. Delaunay, which appears, by 

 some error on the part of the author, to have been inadvertently sent, in the first 

 instance, to the Philosophical Magazine, in which it appeared in July last. — Edit. 

 Geol. Mag. 



2 Translated in the Geological Magazine, November, 1868, Vol, V., p. 507. 



