From John Frederick William Herschel   Nov 22/61.

Collingwood | Nov 22/61.

My dear Sir

You do not say¹ when your exp[erimen]ts were made—but I conclude naturally that you took the opportunity of a full moon. (Interesit multum) Now I cannot believe that the surface of the full moon can possibly radiate cold—for I do not see how it can possibly be of a temperature much lower than boiling water seeing it has been long exposed (the central part of the disc) to unmitigated sunshine. On the other hand I can easily believe that the new moon may be very intensely cold though not so cold as the celestial spaces beyond, yet more cold than the upper region of our atmosphere.

But now let us consider the geometrical relations of the matter.

Suppose ASB the Earth’s surface

C its centre asb the surface

of the atmosphere. CM the

direction of the moon from C

nearly identical (with the small difference only of parallax) with SM from S At 80 miles the density of the air is only 1-100,000,000^th of its density at the surface. Suppose then we take 80 miles for the height of the atmosphere—then the extreme span of the visible horizon from hS, to So will correspond to a terrestrial arc of 10° = hCS = SCo on either side of S—but as there is no use in trying to observe down to the very horizon, I suppose we may limit the effective span or the terrestrial arc over which the portion of upper atmosphere observed extends, to 5° on each side of S—which would make 10° of difference of incidence of the moon’s rays on the extreme edges m and n of that portion of the atmospheric shell exposed.

Suppose the moon at full and at 50° of altitude as seen

from S then the incidence of its rays on m will be 5° and at n, 35°

and at t the point exposed when the instrument is directed to the moon about 39° 3'.

As the whole heat cannot be supposed to be absorbed at the very outside, the differences of these angles are all assuredly materially in excess of the really effective differences—and when reduced accordingly I should doubt very much whether any difference of radiation could be expected. And there ought to be a gradation in passing from n through the zenith to m,—a gradual diminution of heat—so that the direction of the moon itself StM should be colder than the direction Sn, but warmer than the zenith, and that direction (SZ) again warmer than Sm which I do not think agrees with your result as you seem to indicate the moon as the coldest place in the sky.

After all however, the station is so very unfavourable a one and the distribution of the London smoke and hot air and vapour so very uncertain that I should not be disposed to rely on any conclusions drawn from other than a long series of experiments—if then. —Only the pure and equable air of a station far from cities—or in some such atmosphere as that of Egypt or Malta would quite satisfy me on a point of such delicacy.

Any how I think it may be safely stated that if the instrument indicates a maximum of cold in the direction of the moon herself—the cause must lie elsewhere than in her influence in warming the upper regions of the air.

Believe me my dear Sir | Yours v[er]y t[rul]y | JFW Herschel.

PS. I don’t know that any body has ever investigated the law of barometric pressure in an atmosphere of pure vapour without any air. Very peculiar considerations would apply in such a problem.

RI MS JT/1/H/96

RI MS JT/1/TYP/2/512-513

RS HS 23_348 (this is Tyndall’s own transcription)