29th Dec. 1861
My dear Stokes,
You have, I am glad to see, received the first and largest instalment of my paper1—I sent it off at once on receiving your last letter,2 but was unable at the time to write & tell you that 40 or 50 pages still remain in my hands. I shall be ready for the 16th if you desire it, but it will be rather hard work to hold forth at the R S on the 16 and at the R I on the 17th. The Xmas lectures moreover leave me but little time for preparation.
The “convection” part of the paper I have not yet sent to you as I wished to look over it once more. In addition to it I have short sections on the deportment of ozone & of aqueous vapour & a critical analysis of the last papers of Magnus.3 I will send them all to you very soon.
In your note of the 27th4 you touch the point which chiefly interests me, when you speak of the aperture in a thin plate being resorted to to get rid as far as possible of internal friction.
Mr Graham5 you know has made two series of experiments;6—in one he drives his gas through a small aperture in a thin plate, in the other through long capillary tubes. The former process of transfer he calls Effusion, the latter Transpiration—the velocities of discharge being totally different in both. Now it appeared to me that the physical difference between transpiration & effusion was that the former dealt with external resistance mainly and the latter with internal resistance. Suppose the capillary tube to be of such a size as just to admit two atoms of the gas to pass through it abreast: these atoms being urged by the same force have no tendency to slide past each other, and the consequence would be that the resistance offered to their passage would be wholly derived from their rubbing against the walls of the canal. Two men equally swift, equally strong & equally desirous of getting forward, would, if jammed abreast in a narrow passage, pass through it from beginning to end, without any tangential sliding of man past man.
In the presence of a small aperture however the particles immediately in front of the orifice are driven swiftly past their fellows right & left, and internal friction ought to come prominently into play. Effusion is like the crush at a theatre door where man elbows himself past man, whereas when the crowd has got past the portal, and into the passage the elbowing ceases, effusion being changed for transpiration.
Graham finds that the velocity of transpiration of any gas is proportional to the pressure, and inversely proportional to the length of the capillary tube. In effusion on the contrary he finds that augmenting the density has but little influence, a double pressure producing only a slightly augmented discharge. How can this be explained otherwise than by assuming that for the same gas the internal resistance augments approximately as the pressure. It is a case of E/R where E represents the elastic force & R the resistance. As in the voltaic current you may augment E, but if R be augmented in the same proportion the discharge remains the same. Miller7 describes the effect of pressure in these words. “Change in the density of the gas has but little influence on the rate of effusion, the volume effused in a given time being nearly uniform whatever the amount of condensation or rarefaction.” 8 And again with reference to transpiration he says—“The rate of transpiration for the same gas increases directly as the pressure . . . . This is a very remarkable result & stamps the process of transpiration with a character quite unlike that of effusion.”9 (Chem. Phys. Pl. I pp 89-91).
What strikes me principally is this, that in my experiments on convection I find that augmented density plays the same part as in Graham’s experiments on effusion—but in my case the ineffectiveness of the greater density is I think due to internal friction, which augments approximately as the density. The question is do not the results of Graham admit of the same explanation?
Yours very sincerely | John Tyndall.
RI MS JT/T1398
my paper: full version published as Tyndall (1862) and noted as received 9 January and read 30 January.
your last letter: letter 1846.
last papers of Magnus: as recommended by Tyndall, these had appeared in translation in two issues of the Phil. Mag. in July and August, 1861 (G. Magnus, ‘On the propagation of heat in gases’, Phil. Mag., 22 (1861), pp. 1–11; 85–106). The German original had been published in April of that year (G. Magnus, ‘Ueber die verbreitung der warme in den gasen’, Annalen der Physik und Chemie, 112 (1861), pp. 497–548).
in your note of the 27th: letter 1846.
Mr Graham: Thomas Graham (1805–69).
has made two series of experiments: as described in, T. Graham, ‘On the motion of gases’, Phil. Trans., 136 (1846), pp. 573–632.
Miller: William Allen Miller (1817–1870).
“… condensation or rarefaction”: W. Miller, Elements of Chemistry: Theoretical and Practical. Part I Chemical Physics 2nd ed. (London: John Parker and Sons, 1860), p. 89. The final clause, ‘whatever the amount of condensation or rarefaction’, does not appear in first edition.
Miller, Chemical Physics (see n. 8), p. 90.
Please cite as “Tyndall1847,” in Ɛpsilon: The John Tyndall Collection accessed on