* INTERNAL STRUCTURE Of THE EARTH 



IV., par. xii.) that for a rotating spheroid idiolhj fluid, or even for what are rela- 

 tively to the earth's radius, inconsiderable ocean deptlis, submerging a solid 

 nucleus, the tidal protuberance xijUI be developed; and that it ic'dl be identical 

 with that of the equilibrium theory and hence with "small elliptic deviation" of 

 paragraph referred to. The to-be-expunged paragraphs, of the " Rigidity of the 

 Earth," were, therefore, simply a paraplirase of other forms of expression uni- 

 versally adopted in recognized authorities and which had become axiomatic ; and 

 deductions therefrom which were irrefragable. 



Although the " practical rigidity conferred by rotation"' is explicitly announced 

 in Addendum (p. 38) to my paper cited at the head of this, and although the whole 

 scope of that Addendum is to prove that within an infinitely rigid envelope " the 

 rate of precession would not be afiected by fluidity (whether homo, or hetero-gene- 

 ous), or imperfect rigidity ;" and although there are determinations in it (p. 43 and 

 note) as to the modus of formation of the diurnal tide which should have shown me 

 that there could from it resulc no "couple due to the centrifugal force," it was not 

 until quite recently that I was brought, through a question suggested by Prof 

 Newcomb (at Buftalo meeting of A. A. A. S., Aug. 1876), to a new study of my 

 own results and the present development of their legitimate bearings. 



Tidal development is, as well as precession, the efl"cct of a foreign attraction; 

 and before proceeding further I must refer to the theoretical tidal developments of 

 the equilibrium theory. The well-known classification into " secular" {i. e., semi- 

 annual or semi-monthly), " diurnal," and " semi-diurnal" tides, embraces three 

 specific tidal deformations which, together, make up the "small elliptic deviation" 

 (as elsewhere spoken of), which constitutes the "tide." Regarding the spheroid 

 as a perfect spliere (an assumption, for convenience, always made in computing the 

 tidal development), the " semi-annual" tide is an equatorial protuberance accom- 

 panied with depression at the poles. The " semi-diurnal" consists of two diametri- 

 cally opposed meridianal protuberances, occupying two opposite quarters of the 

 globe, with similar depressions occupying the two intermediate quarters. Developed 

 symmetrically, as regards the equator, neither they, nor the parts of the solar or 

 lunar attractions which produce them, have any disturbing effect on the axis of 



' Sir Wm. Thomson's phrase is " 5«asi-rigiclity induced in a liquid by vortex-motion" — a varia- 

 tion of words only ; and it is in place to remark that there is no .special virtue in vortex motion over 

 motion in general to induce quasi-" rigidity" in a fluid. There can be no continuous motion of the 

 particles which make up a fluid figure, compatible with preservation of that figure, composed of tlie 

 same particles, but rotation or (in otlier words) vortex-motion. Hence a ^wasi-rigidity, which niotioii 

 confers upon a fluid figure, becomes the special attribute of "vortex-motion." Moreover, though this 

 phrase vortex-motion, of recent origin in this connection, is not used, "quasi-rigidity" is brought out 

 as a result by the investigations (Sections 7-15) of the lale Wm. Hopkins, of the pressures exerted 

 and reactions experienced by a revolving fluid within a revolving shell (" Researches in Physical 

 Geology," Phil. Trans , 1839), where he shows that the fluid receives an angular motion "precisely as 

 if it were solid," and, in Sec. 30, where he develops the relative (to the shell) motions of the quasi- 

 rigid fluid; calling this, rightly, "a case of rotary motion which has not before been investigated." 



Although I disprove Mr. Hopkins' conclusion that heterogeneousneps would affect precession, 

 his argument as well as mine not only concedes but proves that the rigid-shell-inclosed fluid would 

 "perform gyration" The remark is made with reference to supposed crucial experiments, with 

 water-gyroscopes (unavoidably endow^ed with rigid envelopes), as to points at issue. 



