23rd. Nov. 1858.
My dear Sir.
I do not think that it would be very good taste in me to offer an opinion1 upon those parts of Mr Moore’s2 paper3 where he as a mathematician differs from other mathematicians. He undertakes to shew the incompleteness of the equation hitherto regarded as containing the expression of the motion of sound in narrow tubes, and proposes one containing an additional plus or minus quantity as a substitute. From his theory he deduces that a wave of rarefaction is more rapidly propagated than a wave of condensation; that hence it is natural that the sensation of sound should be produced, not by condensation, but by the nine rapid signals given by rarefactions; and finally he adverts to the circumstance that these considerations explain an acknowledged difficulty in the ordinary theory of sound—the difficulty namely, that the calculated velocity falls short of the velocity derived from experiment.
The most decisive argument in favour of the idea that sound is produced by rarefactions is drawn by Mr Moore from the construction of the human ear. His observations here are of a highly ingenious and interesting character, but it appears to me that it would be extremely perilous to admit this argument from design4 as capable of deciding a physical problem. The author also refers, though he does not insist on the point, to the double report heard in certain states of the atmosphere, where a gun is fired, as an illustration that sounds are transmitted in duplicate; but it appears to me that in the experiments referred to the double sound was due to echoes from the clouds, and does not favour Mr Moore’s notion.
With regard to the acknowledged difficulty referred to by the author, it is only fair to him to state that other mathematicians also have experienced a similar difficulty in accounting for the discrepancy between the observed & calculated velocities of sound.5 But this never has been an acknowledged difficulty with any one who really comprehended the explanation of Laplace;6 and I think it hardly excusable to call this a difficulty after all that has been recently written upon the subject & more especially after the lucid physical exposition of the theory which we owe to one of the secretaries of the Royal Society. (Phil Mag, 1851. page 309.)7 A paper therefore which, in part at least, rests its merit on the removal of a difficulty which has no real existence is at least of doubtful value to me. But while on physical grounds I am unable to recommend the paper of Mr. Moore for publication in the Phil. Transactions I should be glad to see it reported on by a mathematician. For devotion to other modes of enquiry has so far weakened the portion of mathematical power which I once possessed as to render me doubtful in some degree of my own competence, without great expenditure of time, to offer an opinion upon purely mathematical questions.
I am dear Sir | Yours very sincerely | John Tyndall
Prof. Stokes | &c &c &c | Sec. R.S.
RS RR/3/203 Tyndall 23 November 1858
to offer an opinion: Tyndall acted as a referee for the Phil. Trans., reviewing submissions and sending reports to Stokes, the journal’s editor.
Mr Moore’s: not identified. Perhaps John Carrick Moore.
paper: not identified.
argument from design: one year later, Tyndall’s friend Charles Darwin would publish On the Origin of Species (Murray, 1859), his theory of evolution by natural selection countering the widely held ‘argument from design’ presented in clergyman William Paley’s Natural Theology (1802), which maintained that the complexity of nature showed evidence of design by a creator. Tyndall owned an 1845 edition of Paley’s works (which he dated October 1848), and made annotations throughout, including marking passages in Natural Theology. In his journal entry of 2 January 1849, he wrote, ‘I am willing enough to be convinced upon the subject of which Paley writes, but what he says is insufficient to this end. The Great Spirit is not to be come at in this way; if so, his cognition would only be accessible to the scientific and to very little purpose even here’ (Journal, JT/2/13b/413).
difficulty in accounting for the discrepancy between the observed & calculated velocities of sound: Tyndall later published on this topic. See J. Tyndall, ‘Note on Laplace’s correction for the velocity of sound’, Phil. Mag., 26 (1863), pp. 384–7; and Phil. Mag., 27 (1864), p. 41.
Laplace: Pierre Simon Laplace (1749–1827), a pioneering French mathematician, physicist, and astronomer (CDSB).
(Phil Mag, 1851. page 309.): G. G. Stokes, ‘An Examination of the possible effect of the Radiation of Heat on the Propagation of Sound’, Phil. Mag., 1 (1851), pp. 305–17.
Please cite as “Tyndall1571,” in Ɛpsilon: The John Tyndall Collection accessed on