Graveley, Huntingdon
20 Aug[ust] 1907
Dear Dr Wallace
I am sorry to say that the calculations you have sent me are beyond me. I am very bad at arithmetic and numbers convey very little to my mind. I think best in symbols. I have worked out the enclosed and focused<forecast>the temperature to which I believe the Sahara might be expected to fall during a night as long as the moon’s night. If I understand your figures rightly, I arrive at a somewhat similar result to your’s<yours>. Mine being 213oF degrees absolute and your’s<yours>being 200o degrees. Is this so? I think the most interesting part of my work is the value [2] I get from the constant m which is a measure of the diathermanousy at & radiating power of the surface of the Saraha combined. Unless we knew or could calculate this quantity for the moon I do not think we could arrive at any satisfactory result.
May I ask — is the 32o farenheit which you say Langley1has determined as the maximum for the moon, the outcome of actual observation of the moon’s rays[?illeg] by the volometer or is it a calculated value?. If it is an observed value I am not sure that I could not get a step further in my calculations.
I do not understand on what principle you have drawn your curve of the moon’s temperature. I do not say that it is incorrect, only I do not know how it has been obtained.
[3]I will not lay the matter aside and shall hope to hear from you about Langley’s value for the moon’s temperature.
I remain | yours sincerely | Osmond Fisher [signature]
Status: Draft transcription [Letter (WCP2882.2772)]
For more information about the transcriptions and metadata, see https://wallaceletters.myspecies.info/content/epsilon
On the night temperature in the Sahara
Let θ be the temperature at the time t from sunset.
Then by Stefan's Law the radiation from the surface varies as θ4. Hence in the interval dt the radiation will be dt x mθ4where m will be a constant depending upon the nature of the radiating surface and upon the atmosphere so the m will increase with the diathermancy[?] and be greater where there is high[?] water vapour in the air.
Assuming that the radiation that takes place in the interval of time dt is measured by the fall of temperature of the surface in that interval
Stefan's Law gives
-dθ = dt-mθ4
-dθ/θ4=dt-m
1/θ3 = 3mt + c
Suppose the temperature of the surface to be θ0 at sunset when t will = 0
Then 1/θ3 = c
and 1/θ3 — 1/θ03 = 3mt
[2]It is said that in the Sahara during the night the temperature falls from 130oF * or 590o Abs.) to 32oF (or 492o abs.).
Hence taking our unit of time [t] as 12 hours our equation gives
1/4923 — 1/5903= 3m
log 492 = 2.6919651
log 4923= 8.0758953
log 1/4923= _9.9241047 = log 8.3966 x10-9
log 590 = 2.7708520
log 5903 = 8.3125560
log 1/5903 = _9.6874440 = log 4.8690 x 10-9
m = 1.1425 x 10-9
This is the value of the constant m for the circumstances of the Sahara, the unit of time being 12 hours.
[3]Quaere: to what temperature would the surface of the Sahara fall were the night as long as the night of the moon?
In that case since our unit of time has been taken as 12 hours we must put t = 28
Then our equation gives
1/θ3 — 1/5903= 3.5276 x 10-9 x 28
1/θ3 = (98.7728 — 4.8690) x 10-9
= 103.6418 x 10-9
log 103.642 = 2.0155274
2.3281574 = log 212.89
Therefore θ = 212.89o Absolute, or -247o Fahr.
Hence the temperature to which the Sahara would fall during a night of the 14 days of 24 hours duration would be or -247o Fahr.
Status: Draft transcription [Enclosure (WCP2882.5339)]
For more information about the transcriptions and metadata, see https://wallaceletters.myspecies.info/content/epsilon
Please cite as “WCP2882,” in Beccaloni, G. W. (ed.), Ɛpsilon: The Alfred Russel Wallace Collection accessed on 4 May 2024, https://epsilon.ac.uk/view/wallace/letters/WCP2882