John Frederick William Herschel to Faraday   27 May 1826

Devonshire Street | May 27, 1826.

Dear Sir,

I have read with much interest your paper on the limit of vaporisation¹ and certainly can see no objection to the general argument which appears to me as nearly demonstrative as the nature of physical sciences admits & altogether a material step made toward settling our notions of the constitution of the Atmosphere. Allow me however to pursue the matter a step or two into particulars. Gravity acts perpendicularly to the horizon - Therefore supposing Atoms to be detached by a vaporific nisus from the under surface of Silver at common temperatures - they will be vapour to all intents & purposes till they reach the ground, and to this they will fall not merely as dust of infinite or rather of atomic tenuity - but, exerting all the while their full repulsion on each other in a horizontal direction, in virtue of which they will recede from each other & spread themselves ultimately over the whole surface of the earth - as discrete atoms. The same kind of dusty vapour will emanate from the sides of the silver. But from the upper surface, no vapour can rise, because gravity ex hypothesis is too strong to overcome[.]

Were the Earths Gravity then only considered - all solid bodies would still be in a continual state of diminution by vaporisation & your argument would be untenable. Let us see what other forces we can call in[.]

The silver itself exerts a gravitating force towards itself in all directions which in that almost infinite state of tenuity competent to its vapour at 100 Fahrenheit may be sufficient to restrain the lateral vaporisation - But not that from the under surface[.]

The attraction of Crystallisation does not exist in fluids or is counterbalanced. That of Cohesion however does & it appears to me that it is amply sufficient to establish your point.

We may regard the vaporising nisus as a force urging the particles of a body from its surface and decreasing as the temperature decreases.

The elasticity of a particle of Silver (ie its gaseous repulsion) is directly as some power or function of the temperature & inversely as its distance from the neighbouring particles (& may therefore be represented by T/x)[.]

The cohesive attraction is inversely as some very high function of the same distance x & is probably independent of the temperature - or if it do depend on it is inversely as a power or function of it - It may therefore be represented by 1/T’X[.]

Therefore the total force retaining the atom on the surface at the distance x in opposition to the vaporific Nisus is 1/(T’X)-T/x[.] Consequently when this vanishes, there is nothing to oppose it - This condition establishes a surface of indifference about the silver and within which all is attraction & without - all repulsion.

The distance of this surface from the Silver is that value of x which satisfies the equation & without entering at all into its form, it is clear from its general constitution, (X/x = 1/TT’)

that x must necessarily be greater as the temperature t is less.

Moreover within this surface of indifference the total retentive force is greater as the temperature is less[.]

Now from both these considerations - 1st that the sphere of attraction is increased in extent by a decrease of temperature and 2ndly that by the same cause the retentive force within its limits is increased, it clearly follows, that the vaporific nisus, which decreases as the temperature Sinks - must ultimately be incapable of urging an atom to the distance of the Surface of indifference - and that vaporisation will cease altogether. In this case there will be no dust falling from the under surface, after a certain decrease of temperature[.]

This view of the subject I mentioned to Sir H.D. when first I heard of your idea of a limit to vapour & it seems to me to amount to full demonstration[.]

I remain dear Sir Yours very truly | J.F.W. Herschel