AS AFFECTING PRECESSION AND NUTATION. 15 



pressures exactly counteracting the elevating or depressing force of the attraction, 

 and would maintain the quasi-solidity of the fluid by thus neutraliziiifr internal 

 strains. 



I have shown also that, this state supposed once initially established, there is 

 nothing to maintain its adaptation to the motion in right ascension and declination 

 of the attracting body, and tliat the alleged discovery " is not of anythin» which 

 could have place ir. nature, even if we concede to 'nature' such an ocean as the 

 theory prescribes ; but of a purely mechanical theorem alien to the conditions 

 under which ' tides' are generated.'" 



Tidal theories treat the earth as a perfect sphere, disregarding oblateness. 

 When we couple the hypothetic ocean of uniform small depth with the actual 

 oblateness which must belong to tlie nucleus, we have a shell of uniform thickness 

 nad small equatorial ellipticity; fluid, it is true, but rotating (in order to exhibit 

 Laplace's result) as if it were solid. The laws of " vortex-motion" have been 

 superadded, in what precedes, to the arguments used in paper cited (Proc. A. A. 

 A. S), and forbid the self-adaptation which Laplace's theorem requires of the fluid 

 shell to the sun's position, and sustain my assertion that it is only a mechanical 

 theorem. I have nevertheless suggested in the paper referred to that the inconspicu- 

 ousness of tliis tide in our actual oceans (which ought, on the equilibrium theory, 

 to have a development in height equal to two-thirds that of the semi-diurnal) 

 might, perhaps, be accounted for through an imperfect obtaining of some of the 

 conditions (e. 9., the mcridianally elongated elliptical, horizontal orbits described 

 by the particles in the production of this tide) of Laplace's theorem. 



I will conclude by saying that while the correction of grave errors of conclusion 

 in papers of mine published under the sanction of the Smithsonian Institution, 

 and ostensibly deserving tiie ascription of " Contributions to Knowledge," is a 

 peremptory motive, a secondary object of this memoir is to show that in those 

 papers are to be found essential elements now indicated and brought together (for 

 this paper does little more than to push to their true issue conclusions based on 

 facts there developed), of the " coherently worked out" solution which Sir AVra. 

 Thomson desiderates (Glasgow Address) of the " full problem of precession and 

 nutations, and what is now necessarily included in it, the tides, for a continuous 

 revolving liquid spheroid, whether heterogeneous or homogeneous." 



' Mr. D. D. Heath ("Deep Sea Tides," etc., Phil. Mag., vol. sxxiii., ISfiT) has, in an admirable 

 exposition of the conditions on which depend the attainment of dynamic tidal solutions, shown that 

 the solution of Laplace's for the diurnal tide is " a singular possible case in the midst of impossible 

 ones," "singular in its algebraical no less than in its physical character." Ab.sonce of right ascension 

 and deelinational motions of the attracting body being the imperious condition. The solution is analy- 

 tically "discontinuous" and therefore not admissible as an expression of jihenomcna in which its 

 indispensable condition is wanting; hence "a purely mechanical theorem" (as I have characterized 

 it) " alien to the conditions under which tides arc generated." But though Mr. Heath refers to the 

 " physical character" of the solution, its real physical characteristics, as pointed out by me (from which 

 I arrived at identical conclusions), had not previously been indicated by any of the tidal investigators. 



