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Darwin Correspondence Project

From G. H. Darwin   7 November 1878

Trin Coll Camb.

Nov 7. 78

My dear Father,

I enclose Sir W. T.’s report on my paper which you might care to see. You will easily be able to skip the technical parts. I found my M.S scrawled about in his untidy hand, but I came to a sheet of paper in ink & I felt as if I knew the hand, but only thought that he wrote very differently with a pen. An hour or two after it suddenly flashed across me that it was Rayleigh’s writing, so I spotted the other referees in that way.1 I’ve had another long letter from Sir W. about lunar gravity & he proposes my going down to Glasgow to see an instrument wh. he is going to have made. He does’nt think that it would be possible to do it in a town & I expect I shall have to build a shed somewhere at Down.2 I fancy I shall have to get money out of the R.S fund3 as I suppose it will be expensive. Sir W. also quite agrees about the obliquity of the Ecliptic, & what I say about it.4

I have been examining into the sea-tidal observations and I really do think they show a primâ facie case for the viscous yielding of the earth. These are observations during 12 different years at various stations & the tides at 8 out of the 12 are too early, which wd. show viscosity & out of the 4 where they are too late two are at a station where they say the observations are not accurate enough to judge safely with regard to the particular tide I care about.5 I received Dr. Carret’s pamphlet both from himself & you, & I don’t think his ideas will work at all—tho’ he must be a cleverish man to get so deep.6 Evans had an old idea of the crust of the Earth moving over the inside & I think I can show it to be impossible—at least from the causes which he refers to.7

I’ve really got nothing on Earth to write about except mathcs. & so that must be my excuse for so much axles.8

Is’nt Frank going to pay a visit here— & Jim?9

I’ve had no dissipations lately & am glad of it for I’ve been a little down hill again.

Please return Sir W. T.—

Your affec son | G H Darwin

[Enclosure]

I have read with much interest Mr. 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. Mr. 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 Mr. 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 Mr. 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 fortny. 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 Mr. 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—

Footnotes

George Darwin was working on a series of connected papers modelling the effects of lunar gravity on the earth, and investigating the implications for its structure and behaviour (G. H. Darwin 1878b, 1878d, and 1878e). The referees’ reports by William Thomson and John William Strutt, third Baron Rayleigh, concerned George’s paper ‘On the bodily tides of viscous and semi-elastic spheroids, and on the ocean tides upon a yielding nucleus’ (G. H. Darwin 1878b). The paper had been read at a meeting of the Royal Society of London on 23 May 1878, and was being prepared for publication in the society’s Philosophical Transactions. The referees’ copy of George’s paper was returned to Thomson on 13 December (MSS 421, Register of Papers 1853–1885, Archive, The Royal Society); it has not been found. The published paper included a remark by Rayleigh (G. H. Darwin 1878b, p. 27 n.). See also letter to G. H. Darwin, 17 [August 1878] and n. 3, and letter to G. H. Darwin, 29 October [1878]. For George’s later account of the development of his ideas, see G. H. Darwin 1907–16, 2: v–viii; see also Kushner 1993.
Thomson’s letter of 2 November 1878 proposing Down as a possible location for an instrument to measure lunar gravity is in Glasgow University Library (Kelvin papers D6). Thomson described the instrument as a weight supported by a vertical spring.
The government grant and donation fund of the Royal Society.
The obliquity of the ecliptic is the angle of the earth’s equator to the plane of its orbit around the sun. In his letter, Thomson wrote that on ‘the question of tidal viscosity on the obliquity of the ecliptic’, which the two men had discussed at a recent meeting, he now saw it perfectly and was glad to find George’s result confirmed (D6, Kelvin papers, Glasgow University Library). The subject is not discussed in the main body of G. H. Darwin 1878b, but is worked out at length in G. H. Darwin 1878d, which had been received by the Royal Society on 22 July 1878 but had not yet been read.
An appendix ‘On the observed height and phase of the fortnightly oceanic tide’ was added on 7 November 1878 to G. H. Darwin 1878b (pp. 31–6).
See letter to G. H. Darwin, 2 November [1878] and n. 2. CD had sent George a copy of Jules Carret’s pamphlet on polar displacement (Carret 1878). Adopting a theory of the composition of the earth suggested by John Evans (see n. 7 below), Carret argued that long-term polar displacement had been caused by unequal movement between the earth’s crust and nucleus.
In an attempt to explain the evidence that the climate in some parts of the world had varied between tropical and arctic, Evans had postulated a model of the earth with a thin rigid crust over a molten layer, possibly with a solid core. He suggested that changes in the thickness of parts of the crust through upheaval, denudation, or the accumulation of large bodies of ice, would, through the action of centrifugal force, lead to a change in ‘the relative positions of the solid crust and the fluid nucleus, and in consequence to a change in the axis of rotation, so far as the former is concerned’ (Evans 1866, p. 48).
‘Axles’ was evidently a family word for ‘shoptalk’ (see also Correspondence vol. 27, letter from Francis Darwin to Emma Darwin, 30 June 1879, and letter to Francis Darwin, [2 August 1879]).
No record has been found of a visit at this time to Cambridge by Francis Darwin or by Horace Darwin, whose nickname was Jim.
In section 797 of their Treatise of natural philosophy (Thomson and Tait 1867, pp. 646–9), Thomson and Peter Guthrie Tait summarised the conclusions reached by Alexander Ross Clarke, a captain in the Royal Engineers, about the shape of the earth.

Bibliography

Carret, Jules. 1878. Sur les causes du déplacement polaire. [Read 23 May 1878.] Mémoires et documents publié par la Société savoisienne d’histoire et d’archéologie 17: 231–42.

Correspondence: The correspondence of Charles Darwin. Edited by Frederick Burkhardt et al. 27 vols to date. Cambridge: Cambridge University Press. 1985–.

Darwin, George Howard. 1907–16. Scientific papers. 5 vols. Cambridge: Cambridge University Press.

Evans, John. 1866. On a possible geological cause of changes in the position of the axis of the earth’s crust. [Read 15 March 1866.] Proceedings of the Royal Society of London 15 (1866–7): 46–54.

Kushner, David. 1993. George Darwin and a British school of geophysics. Osiris 8: 196–223.

Thomson, William and Tait, Peter Guthrie. 1867. Treatise on natural philosophy. Vol. 1 (no other volumes published). Oxford: Clarendon Press.

Summary

Encloses William Thomson’s report on GHD’s paper. Some of it was written in Rayleigh’s hand.

Letter details

Letter no.
DCP-LETT-11738
From
George Howard Darwin
To
Charles Robert Darwin
Sent from
Trinity College, Cambridge
Source of text
DAR 210.2: 71, The Royal Society (RR/8/91)
Physical description
5pp enc 16pp

Please cite as

Darwin Correspondence Project, “Letter no. 11738,” accessed on 9 March 2021, https://www.darwinproject.ac.uk/letter/DCP-LETT-11738.xml

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