14 INTERNAL STRUCTURE OP THE E ART II 



tlie nutations corresponding to the cycloidal path. But if, at the instant indicated, 

 p. 12, the axis of figure, instead of being at rest, be already moving with the proper 

 mean motion, that mean motion will he simpli/ maintained (as demonstrated p. 6, 

 Note 1, "Problems," etc.); and without sewsift/e nutation, though the intensity of 

 the tilting couple slowly wax or wane. Since, however, gyration-area is but trans- 

 formed rotation-area, it follows that the (rigid) earth's rotation-axis must have 

 been tilted (from where it was at the equinox) sufficiently to furnish by transfor- 

 mation the required (mean) gyration-area; that is through half \\\e angle ley. For 

 exactly similar reason, if the mean gyration proceeds from the diversion of the 

 planes of rotation, that tilting, proceeding from a very slowly waxing force, could 

 ensue only to the half amount necessary to formation of the diurnal tide. But 

 though the requisite gyration-area be originally acquired by the tilting of the 

 planes, there is no reason that I can perceive why the resulting distortion should 

 not, pari passu, approximately rectify itself (there being, see end of 7iote, p. 7, a 

 self-rectifying force, proportionate to the distortion, always acting) to the annul- 

 ling, nearly, of the tide. 



And, moreover, for Laplace's case (a continuous ocean of uniform small depth) 

 the absence of the diurnal tide may be something more than a mere suppression 

 of elevations through the counteracting pressure its relative motion develops; it 

 may be this partial absence o'l these motions even ; the fluid shell having at the 

 same time its own precession} In fact, a fluid shell of uniform thickness is cer- 

 tainly as subject to precessional motion, as an entire spheroid of fluid. 



From the foregoing it appears that though I no longer find a "counteracting- 

 couple" arising from the centrifugal forces acting on the substance of the diuriiiil 

 tide, by which the precession of a fluid spheroid is neutralized, yet I do find 

 that, " checked by the counteracting efl'ect of induced gyration" (i. e., precession) 

 the tide itself is in great degree neutralized; that the '■'■practical rigidity" by which 

 (as I showed. Appendix, p. 48, " Problems," etc.) a rotating fluid reacts upon a shell, 

 to maintain the integrity of precession, is equally efficacious though there be no 

 shell. This " practical rigidity" exhibits itself only in connection with the diurnal 

 tide. 



The celebrated result of Laplace, just now alluded to, that for a continuous 

 ocean of uniform depth, the diurnal tide — so closely associated as I have shown 

 it to be with the precessional movement — will have no development in elevation ; 

 but will present itself simply as a determinate relative motion of the water — has 

 been treated by me elsewhere (see Proceedings of the Amer. Association, Buffalo 

 meeting, 1876). I have shown that this relative motion (relative as concerns the 

 solid nucleus) is simply what belongs to a shifted position of the 'diurnally rotating 

 fluid shell, as if it were a solid shell, the angle of separation of axes of fluid shell 

 and solid nucleus being the identical angle elsewhere denoted by y. 



Disregarding, as the illustrious author does, the motion of the sun in right 

 ascension and declination, such a shifted position, initialli/ given, would generate 



' This is hinted at in last paragraph of " Addendum" to note to article cited at head of this paper; 

 but in obscure and erroneous language. 



