# From G. H. Darwin   24 October 1874

Trin. Coll. | Camb.

Oct 24. 74

My dear Father,

I will try & answer yr. heat question,1 but as I do’nt know exactly how you propose to use it, I fear I must give you a good deal you don’t want

Bodies cool in 3 ways

(1) conduction

(3) convection

Conduction takes place within the body, whilst radiation is only from the surface. Conduction can only take place in a body one part of which is hotter than another. It has been supposed to be explicable as molecular radiation, i.e radiation from one molecule of the body to the next; but however that may be it takes place as a current or flow. This current always flows from the hotter to the colder parts.

Suppose for example we had a rod, & imagine an ideal partition across it & that on one side the temp: of the rod is higher than the other, then a flow of heat will pass thro’ this ideal partition from hotter to colder so long as there is any difference of temp: The rate of flow is proportional to the difference of temperature, i.e the amount of heat passing thro’ our partition in a second is proportional to the diff. of temp. In this case the unit of heat may be taken as the amount of heat requisite to raise 1 lb of water 1o Fahr., & the amount of heat means the number of such units. A numerical example will perhaps best explain this to you,—the Nōs being imaginary.

Suppose when one side of our partition is 10o Fahr. hotter than the other say the temps. are 0o & 10o that one unit of heat passes across in a second

Then when the temps. of the two sides are 0o & 20o, two units of heat will flow per sec.

When 0o & 30o, 3 units per sec.

0o & 40o, 4 ———

& so on one unit of heat more per sec. flowing for every 10o more of difference of temp:

Convection is where a cooling body heats the air touching its surface by conduction; the air becomes lighter from being warmer & flows away, to be replaced by cooler air. Thus air currents are established which carry away the heat by conduction & subsequent motion.

Radiation takes place from the surface only & is greater from a hotter than a cooler body.

Suppose a warm body be placed within an envelope coated with lamp black, which absorbs all the heat striking it, & that the envelope contains no air or gas. Then as the temperature of the body increases in arithmetical progression, the rate of radiation increases in a geometrical progression. A numerical example will again best explain my meaning.

Supposing a body under the above circumstances has a temperature of 0o, & that it loses l unit of heat per sec. and that when it has a temp. of 10o it loses 1$\frac{1}{4}$ or $\frac{5}{4}$ of a unit per sec.

Then when its temp is 20o it loses $\frac{5 2}{4 2}$ or $\frac{25}{16}$ or 1$\frac{9}{16}$ units a sec

When its temp: is 30o it loses $\frac{5 3}{4 3}$  or $\frac{125}{64}$ or nearly 2 units per sec

When its temp: is 40o it loses $\frac{5 4}{4 4}$ or $\frac{500}{256}$ or nearly 2$\frac{1}{2}$ units per sec

at 50o it loses $\frac{5 5}{4 5}$ or $\frac{3000}{1024}$ or nearly 3 units per sec.

& so on for every 10o of increase of temp: we must raise $\frac{5}{4}$ to one higher power.

This does not depend on diff: of temp., as does conduction.

The above is Newtons law of cooling2

Under ordinary circumstances all the surrounding bodies radiate back to the cooling one, which thus regains heat at the same time as it loses it. The rate of cooling is then the difference betw. the rate at which the body is cooling according to the above law, & the rate at which it is gaining.

At the same time convection takes place, & the inner parts keep supplying the surface deficiency caused by radiation, by means of conduction

Secondly

All crystals conduct heat with different rapidities in different directions.3 Some have only two rates of conduction viz: along or perpendicr. to an axis—& these are called uniaxal crystals. Some have 3 rates of conduction, in three directions mutually at right-angles, & these are called biaxal crysals.

All fibrous bodies conduct heat at a different rate along and perpendicular to the fibres. Thus a piece of the trunk of a tree conducts heat at 3 different rates

1st. parallel to the trunk

2nd. from the centre of outwards, & lastly if the piece be not cut from the heart of the tree there is a third rate along a horizontal line touching one of the rings of growth

The line (a) is supposed to stick out perperdincular to the paper.

[DIAG HERE]

I wrote to Spottiswoode & told him what I proposed to lecture on if I did so & offered to give him a table of contents when I’ve got it more in shape. He writes back that Pol. Econ. wd. be a proper subject—4 I’m wobbling towards doing it—aut Cæsar aut nihil—5 When I’ve spoken at debatg. Socs. I’ve been hardly nervous when once started & so I do’nt think I shd. break down—& I do’nt think my style of ill-health wd. make me much more likely.

I’ve not decided yet, & rather think I’ll run down in abt. 3 wks. & have a talk to you when I’ve got the thing more into shape. You may imagine I’ve been working hardish, when I tell you it has reached 60 pp of M.S & the greater part has been written out twice over   I’ve not said nearly all yet so I cd. only give a selection at the R. I.   If I do it, it will be Jan. 22 or 29. & then I shd. try & publish it in extenso in Contemp.,6 for it’s worth it, if I’m any judge of my own work.

Thank Jim for Steam Engine reference. I’ve read the passage, for Maxwell gave it me on Wedn. just before I started for Abinger.7

It was awfully cold & its a tedious journey & as I was’nt very well I rather repented going. As ill-luck wd. have it Thursd. was the only really bad morng. I’ve had for a month, but I got immensely better in the afternoon.

I fell in with Mr & Mrs. Erskine8 at the station & we drove up in the dark together. He’s rather a dry sort of bird. I found a perfect bevy of girls—all pretty 2 Miss Erskines, Miss Shadwell Miss Farrer—a cousin, Ida, & Miss Whichelo—the prettiest of all & I guess the nicest.9 Then there was T. H & last but not least Effie.10 It’s one of the most charming houses I ever saw, the hall is a chef d’œuvre11—& I was lodged in the same room you were in. There was a dinner party of Bosanquets Sir Geo Hewett an Irvingite &c.12 They bore me rather, for one can hardly get eno’ to eat of the simple things & is drawn in desperation to take snacks of the unwholesome. I do’nt know whether it’s my fancy but it seems to me that the wine is abominable; perhaps it is, as T. H. says he has lost his smell & taste almost in toto13 from a fever. Whatever it was I was very seedy next morning. However in the afternoon I went a very nice ride with T. H. over Holmbury to Hopedene,14 where we only fd. At. Fanny15   I went prepared to be charmed but am terribly disappointed. Not a rag of shelter, tho’ a very pretty view. The back elevation of the house is very pretty, but the front I do’nt like; T. H says it’s a row of outhouses. It seems to me to be built by a contortionist who said now I must be original & I’ll make it comfortable if I can. There are innumerable little meaningless bits of roof & windows, wh. only cd. have a meang. in a ho. built by patchwork. The end of dining room is askew wh. adds nothing to its beauty & is inconvenient. The drawing is all window at one end & pitch dark at the other. I can’t believe it’s good art—that elaborate want of straight-forwardness. However I daresay its very comfortable, only I’m glad its not my house. Of course I kept my opinion dark, except to T. H. with whom I thoro’ly agree

In Evening Uncle H. At. F Hope & Eddy Forster16 came to dinner & we had a v. pleasant evening. In the a.m I had a nice little walk over the hill to the station & came up with T. H. & Effie 1$\frac{3}{4}$ hrs for 25 miles! I got here at 1. & found lots to do with my two sets of proof sheets.17

I’ll do index as quick as I can, but its v. long.

The Environs of Abinger are delicious & must suit you to a T.

Jackson18 & Uncle H are both disgusted with Mivart’s answ.19 & so am I the more I think of it; but it doesn’t make much odds now I’ve had my say.

The Cooksons20 were to have come up today, but can’t   Then this has take nearly 1$\frac{1}{2}$ hr’s to write

so goodbye | George Darwin

I’ve sent L. 3s worth of Yankee introdns. to New Z.21

It is Dr. Caufield not Dr. Canfield (on horns of Antilocapra 234)22 —I’m so sorry I didn’t correct index before it went to press as I cd. easily have cut off 10 pp. without losing a reference, but cutting out the ‘on’s & ‘the’s & superfluous words.23

Yrs affly | G. H. D.

## CD annotations

16.1 Secondly] ‘The greater the heat the farther it will be conducted to produce an apparent effect’ pencil

## Footnotes

Isaac Newton’s observations appeared in Philosophical Transactions of the Royal Society of London 22 (1701): 825–9.
George had been invited by William Spottiswoode to give a Friday evening lecture at the Royal Institution of Great Britain, and had been undecided in his choice of topic. CD suggested political economy would be a more suitable theme than development in dress. (See letter to G. H. Darwin, 19 October [1874] and n. 3.)
Aut Caesar aut nihil (Latin): either a Caesar or nothing; figuratively: all or nothing.
George refers to the Contemporary Review. See letter from G. H. Darwin, 5 December 1874 and n. 7.
Jim was a nickname for Horace Darwin. George also refers to Abinger Hall (the home of Thomas Henry Farrer). In 1867, James Clerk Maxwell wrote a classic paper on governors in the steam engine (Proceedings of the Royal Society of London 16: 270–83), but the passage has not been identified. See also letter from Horace Darwin, 17 August 1874.
Claudius James and Emily Georgina Erskine.
Maitland Katherine Erskine, Edith Emma Hay Erskine, Helen Cecilia Farrer, and Alice Clara Wichelo. Ida was Emma Cecilia Farrer, who became Horace Darwin’s wife in 1880. Miss Shadwell has not been identified.
Thomas Henry and Katherine Euphemia Farrer.
Chef d’oeuvre (French): a masterpiece.
George probably refers to Samuel Courthope Bosanquet and George John Routledge Hewett; an ‘Irvingite’ was a member of the Catholic Apostolic Church.
In toto (Latin): entirely.
Hopedene House is to the south of Holmbury St Mary, a village in the Mole Valley district of Surrey, three miles south of Abinger. It was designed by Richard Norman Shaw.
Frances Allen (Emma Darwin’s aunt).
Hensleigh Wedgwood (Emma Darwin’s brother), Hope Elizabeth Wedgwood (Hensleigh’s daughter), and Edward Morgan Llewellyn Forster.
CD had sent the proof-sheets for second edition of Descent; see letter to G. H. Darwin, 22 October [1874].
Henry Jackson.
St George Mivart had attacked George’s essay on marriage (G. H. Darwin 1873a) in an anonymous review ([Mivart] 1874); see letter to John Murray, 18 October 1874 and n. 1, and letter to G. H. Darwin, 19 October [1874] and n. 7.
Montague Hughes Cookson, and his wife, Blanche Althea Elizabeth Cookson.
Leonard Darwin was in New Zealand on the transit of Venus expedition; see letter from G. H. Darwin, 18 October 1874 and n. 19.
CD added a reference to Colbert Austin Canfield in Descent 2d ed., p. 234 n. 40; the spelling is correct. For Canfield’s correspondence about the pronghorn, or North American antelope, Antilocapra americana, see Correspondence vol. 19, letter from C. A. Canfield, 5 August 1871.
CD had sent the proof-sheets of the index of the second edition of Descent with his letter to George of 22 October [1874]. The superfluous words were not cut from the published edition.

## Summary

GHD explains conduction, radiation, and convection.

His paper on political economy for Royal Institution lecture has reached 60 pages. Plans to send it to Contemporary Review.

## Letter details

Letter no.
DCP-LETT-9695
From
George Howard Darwin
To
Charles Robert Darwin
Sent from
Trinity College, Cambridge
Source of text
DAR 58.2: 54; 210.2: 42
Physical description
14pp