[Enclosure]

I have read with much interest M^r. George Darwin’s paper “on the bodily tides of viscous and semi-elastic spheroids and on the ocean tides on a yielding nucleus” and I am of opinion that it is suitable for publication in the Transactions. The question raised is undoubtedly a very important one— If what is denoted by A (p 28) have some value intermediate between 3 or 4 hours and 24 or 48h the semi diurnal tides would be nearly the same as if the earth were perfectly elastic and the fortnightly tide and other “long period tides” would be nearly zero (as if the solid mass had scarcely any tidal effective rigidity.) It is just possible that this may be the actual state of the case, and that thus it may be explained how the lunar fortnightly tide is so small as it is. Careful analysis of a large number of tide curves from self-registering tide gauges in different parts of the world made within the last ten years by the Tidal committee of the British Association and more lately have failed to actually prove any sensible tide of this denomination; but they have not proved that it is sensibly smaller than the equilibrium value. In this uncertainty it is well to be prepared with theory to account for whatever result may be brought out by more extended observation and more complete analysis of the results. M^r. Darwin in p 62 refers to the determination from observation, of the times of maximum and minimum of the lunar fortnightly—as capable of giving very important information. The determination of the amount was all that I had pointed out as needed because on the perfectly rigid, or perfectly elastic theory the times must be the equilibrium times; & the amounts would show the value of the tidal effective rigidity. Hence we have renewed and augmented interest in prosecuting the analysis of tidal observations—

The rate at which viscosity, or breaking down elasticity, in one or other of M^r. Darwin’s theories, estimated somewhat as I estimated the effect of the tidal friction of the semi diurnal lunar tide in reducing the angular velocity of the earth’s rotation, will be interesting in connection with the question raised by M^r. Darwin. Will it not give so rapid a diminution of the obliquity as to give an argument conclusive against, or rendering very improbable, the supposition of any so great influence of imperfect elasticity as to be discoverable in deviations of the lunar fortn^y. tide from what it would be were the elasticity perfect?

If Cap. Clarks results quoted in §797 of Thomson & Tait’s N. P. are valid they would seem absolutely conclusive against any breaking down of resistance to change of shape for deviations of the second order of harmonics (elliptic spheroid deviation from fluid equilibrium)¹⁰  The difference of 6378 feet between the greatest and least diameters of the equatorial diameters of the sea level could not possibly I think be explained by greater & less densities in a rigid crust buoyed on liquid, & not resisting such stresses as would give two or three feet of difference of diameter in elliptic deformations such as those of the tide generating influence. I have written on p 57 a pencil remark on a notion which seems to have occurred to many who have thought of the subject, but which I think is fallacious.

Still, though I see much reason for believing the supposition of sensible effects of either viscosity or breaking down elasticity to be improbable, (& indeed M^r. Darwin himself expresses a similar opinion on his last two pages, (including however apparently, a supposition of improbability of elastic yielding, in which I cannot agree) there can be no doubt of the importance of the questions raised and of the validity & fertility of the mode of discussion contained in his paper

William Thomson

P.S. I have also written notes in pencil on pp 42, & 48—