From George Gabriel Stokes   16 May 1861

Lensfield Cottage Cambridge | 16 May 1861

My dear D^r Tyndall,

I think you must have misunderstood me¹ about precipitation of aqueous vapour, which you say you saw. I never doubted the fact of precipitation. What I said was that I looked on precipitation on the one hand and the apparent obstruction of radiant heat on the other as common consequences of the cold produced by expansion, and that it would not be correct to speak of precipitation as the cause of the observed effect unless it was through that precipitation that the cold took effect on the thermo-multiplier, whereas it appeared to be rather in spite of precipitation that the effect was produced. In fact, in order that your explanation, making precipitation the cause, should be valid, it would be necessary that water should offer decidedly more obstruction, weight for weight, to the passage of heat in the state of liquid than in the state of vapour; in short that a column or layer 1/100 inch thick should offer decidedly more obstruction than the same expanded into vapour, though the length of tube occupied by the vapour at say 60º F and a pressure of ½ inch mercury would be about 1000 inches. Experiment has not shown this to be true or false; and the analogy of coloured bodies would lead us I think to expect that there would probably be no great difference in the absorption according as the water happened to be in the liquid or aeriform state.

On the other hand your experiments indicate a perfect explanation of the observed result by attributing it to the cold produced by expansion taking effect by the dysdiathermancy (if I may coin such a word) and consequent good radiation of the substance HO (water or vapour as it may happen to be).

As to the connexion between radiation and conduction,² I feel that it is not for me to dictate to, hardly even to advise, one who has done such capital work. I can only say that while the generality of the alleged physical connexion seems to me to need further examination, the reasoning by which it is attempted to account for the connexion seems to me altogether inconclusive; perhaps chiefly because it points to a state of things so different from what optical considerations would lead us to regard as probable.

As to the heating of the coke pole,³ I paid no particular attention to the thing at the time, and cannot say that the cause is not what you suggest. But there is no use conjecturing about what a few experiments would settle.

As to the tables “Calculated Results”, the law assumed in the calculation is so evidently a physically impossible one⁴ that any reader I think would take it for what it was worth and no more, nor would he I imagine suppose that the author took it for a law of nature. If the incident rays were homogeneous the intensity would decrease in a geometric ratio, or would be expressed by ${\mathrm{\text{Ar}}}^x$, r being a fraction less than 1, and x the length of path, or (in case of variable density) equivalent path i.e. length with a standard density answering to the actual length with the variable density. If the rays were partly non-absorbable, and the absorbable rays were all absorbed at the same rate, the intensity would be expressed by $A+{\mathrm{\text{Br}}}^x$. But all these are only approximations to the truth; for we have an infinite number of kinds of rays differing in their rate of absorption so that we should have for the intensity

[$A+{\mathrm{\text{Br}}}^x+{\mathrm{\text{Cr}}}^{i^x}+{\mathrm{\text{Dr}}}^{{\mathrm{\text{ii}}}^x}+$] –

We cannot of course determine an infinite number of constants from experiment. Hence wherever we stop there must be something arbitrary in stopping there; and the formula $A+{\mathrm{\text{Br}}}^x$ (equivalent to that proposed by Thomson)⁵ is not rigorously correct any more than your formula $A-\mathrm{\text{Bx}}$, though the former is nearer the truth than the latter, and would be strictly correct under a conceivable mode of distribution of the rates of absorption, which the latter would not.

I think you had best send the paper to press at once, pleasing yourself as to the last chapter.⁶

Yours very truly | G.G. Stokes

D^r Tyndall F.R.S.

RI MS JT/1/S/222

RI MS JT/1/TYP/4/1370–1