SPHEROIDS, AND ON THE OCEAN TIDES UPON A YIELDING NUCLEUS. 31 
ellipticity to about one quarter of the formerly-received value. Moreover, the new 
value of the polar axis is about 1,000 feet larger than the old one. 
Colonel Clarke himself obviously regards the ellipsoidal form of the equator as 
doubtful. Thus there is at all events no proved result of geodesy opposed to the 
present hypothesis concerning the constitution of the earth. Sir W. Thomson 
remarks in a letter to me that “we may look to further geodetic observations and 
revisals of such calculations as those of Colonel Clarke for verification or disproof of 
your viscous theory.”] 
In the first part of the paper the equilibrium theory is used in discussing the 
question of ocean tides ; in the second part I consider what would be the tides in a 
shallow equatorial canal running round the equator, if the nucleus yielded tidally at 
the same time. The reasons for undertaking this investigation are given at the 
beginning of that part, In § 11 it is shown that the height of tide relatively to 
the nucleus bears the same proportion to the height of tide on a rigid nucleus as in 
the equilibrium theory, and the alteration of phase is also the same ; but where the 
one theory gives high water the other gives low water. 
The chief practical result of this paper may be summed up by saying that it is 
strongly confirmatory of the view that the earth has a very great effective rigidity. 
But its chief value is that it forms a necessary first chapter to the investigation of the 
precession of imperfectly elastic spheroids, which will be considered in a future paper.* 
I shall there, as I believe, be able to show, by an entirely different argument, that the 
bodily tides in the earth are probably exceedingly small at the present time. 
Appendix. 
November 7, 1878. 
On the observed height and phase of the fortnightly oceanic tide. 
In the following note I attempt to carry out the suggestion concerning the fort¬ 
nightly tide made in the preceding paper. 
The reports of the Tidal Committee of the British Association for 1872 and 1876 
contain the reductions of the tidal observations at a number of stations, into a series 
of harmonic tides, corresponding to the theoretical harmonic constituents of the tide¬ 
generating forces of the moon and sun. The tide with which we are here concerned 
is the fortnightly declinational tide. 
The heights of the tides at various times are all expressed in the form It cos ( nt — e ), 
where It is half the range of the tide in English feet, n the “ speed ” of the tide, and 
e the retardation of phase, so that e-i-n is the “ lag” of the tide. 
* Read before the Royal Society on December 19th, 1878. 
