WCP2400

[1]¹

Harlton

Cambridge

28 July 1879

My dear Sir

I have been looking into the fundamental proposition of Croll’s² theory and have met with a difficulty which I have hitherto over looked.

I have divided separated the value for the temperature T at any place under the large eccentricity of the supposed glacial epoch into two parts[,] one of which depends upon the temperature of space, S, and the other upon the present temperature T[,] and I find that the [2] temperature at that time with the value.0569 of the eccentricity and the winter in operation comes out

T’ = -0.13461S + 0.86539T

T being the present temperature of the place.

We see then that ^{if S be at all a large number} the larger part of the diminution of the temperature depends upon S the temperature of space.

Were the temperature of space the zero of the thermometer[,] the then temperature would be 0.86539 of the present temperature[,] which would not appreciably differ from the present temperature. We see then how extremely important [3]³ an element in the question the temperature of space is.

Yet what is known about it?

I only know of Sir J. Herschell’s⁴ [sic] determination of it in his Meteorology⁵ & I cannot make out his argument and believe it is allowed to be inconclusive though I cannot recollect where I have seen it called in question.

But I find this. If -239 be the tempe[ratu]^{re of space,} Supposing there to be two places in equal north & south latitude and subject to similar geographical conditions as to climate. Then if we compare what their temperatures ought to be as affected by the present value of the eccentricity (.0168) If T_s’ be the Summer ^[Jan[uar]y] temperature

[4]⁶

of the place in the South latitude and T_s the summer ^July temperature of the place in North latitude then

T_s’ =.0695S + 1.0695T_s.

If in this equation we give S the usually assumed value 239° Fah[renheit]

T_s’ = 16.°61 Fah. + 1.0695T_s

or the place in South latitude ought to have a ^Summer temperature nearly 17 degrees Far. [sic] greater than the place in North lat.[itu]^de.

So also for the Winter solstices at the two places

T_w’ = -15.°5 +.93T_w

or the place in South latitude ought to be 15½ degrees colder than the place in north latitude.

The range of temperature in South

[5]⁷

If V, V’ be the July temperatures of the places in North & South latitude respectively & A A’ their January temperatures

A’ — V = 16°.61 Fah +.0695 V

(1) That is to say the January temperature of the place in South latitude ought to exceed the July temperature of the place in equal north latitude by more than 16°.61 Fah[renheit].

Also

V’ — A = -15°.53 -.07A

(2) or the July temperature of the place in South latitude ought fall short of [to be] lower than that of a place in equal north latitude by more than 15°.53 Fah[renheit].

Moreover so long as the July temperature is greater than the Jan[uar]^y in North lat[itu]^de. the difference between the extreme temperatures of the place in South latitude will exceed the [6] difference between the extreme temperatures of the place in the North lat[itude]. by more than 32°Fah[renheit]. ie the range of temp[eratu]^re in S[outh]. Lat[itude]. will be 32° greater than in N[orth]⁸.

(3) There will be a warmth Equator in North latitude where the July & January temperatures are equal.

(4) And at a place on the equator itself the January temperature ought to be 21°Fah[renheit] nearly greater than the July temperature.

You are much more likely than I am to know how far there is any agreement between these results & natural appearances. Of course the temperature of any place is so much affected by local causes that it could only be by [7]⁹ taking the mean of a large number of observations that (1) or (2) could be tested.

I believe (3) accords with observation but my work does not enable one to say where this warmth equator would be — It would be its position not its existence which would be a test of the value of the temperature of space.

As to (4) however I think it affords a fair test: for these must be places on the equator where local causes such as ^{half yearly} changes of currents and winds could not mask so great a difference of temperature as 21° Fah[renheit]. At any rate the radiation of the sun might be measured to see whether anything like this difference [8] exists. If it does not exist then the temperature of space cannot be so low as -239¹⁰.

I have written to Croll on this subject[.] He has not had time ^yet to go into my reasoning but says on the face of it[,] it seems correct.

He asks who wrote the article in the quarterly¹¹. I tell him I have not authority to say. But if you have no objection I should like him to be informed.

I shall be glad to hear what you think of the above.

I may have more to say about other parts of the article but this being fundamental I have alluded to it first. I have bestowed a good deal of time & thought [1 word illeg.] it being rather slow in my ideas.

I may mention that I bring out the temperature of England 210000 000 yearsago [1 word illeg.] your data not 3° but 1°½.

I remain | truly yours | Osmond Fisher¹² [signature]

A R Wallace Esq[uir]e.