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Darwin Correspondence Project

From William Hopkins   3 March 1845


Mar. 3 1845


My dear Sir

The above diagram contains the solution of the problem which I received from you some time ago.1 The directions of the lines are not given with accuracy in the figure, but the proper measure of each angle is given, so that the diagram might be made as accurate as you please.

All problems of this kind have a certain degree of complexity, but no real difficulty. I would have sent you an answer immediately but since I received your letter till within a few days I have been so entirely occupied during my leisure time in writing on glaciers for the Phil: Magazine2 and in making experiments on the same subject, that I have really not had a moment till just now to work out the numerical results of your problem. But let me assure you that so far from thinking it a trouble to solve any problem of the kind, I consider the proposal of any geological problem, when put in a definite form, as your’s is, as a positive favor. When ever one suggests itself to you, therefore, send it to me.

You might represent the problem pretty well to yourself by fixing a circular piece of stiff paper on an axis passing thro‘ the centre of the paper, and making with it an angle of about 40o. Place the axis horizontal and in a direction supposed to coincide with that of the anticlinal line;3 and then turn the axis and the paper attached to it, till the plane of the paper meets an imaginary horizontal plane thro’ the axis, in a line coinciding with the strike of the beds or laminæ described as dipping originally at 40o. The paper will then be inclined to the horizon at about 40o. and will be parallel to the laminæ just mentioned before their disturbance. Now in forming the anticlinal line we may (instead of supposing a ridge to be elevated) concieve the mass on each side of the line to turn downwards thro’ 45o. This will manifestly produce the same change in the position of the beds as if the anticlinal line were elevated. This movement will be represented for one side of the anticlinal line, by turning your axis and the paper to the right, and for the other side by turning the axis to the left, thro’ 45o. The plane of the paper in each case will represent the position of the beds after the anticlinal elevation, and you will thus be able to observe how that elevation affects their strike and dip.4

I do most sincerely regret both the fact and the cause of the little intercourse you are able to keep up with your friends in general. It wd. have given me much pleasure to hear a better account of your health— I will send you a copy shortly of my letters on glaciers.

Your’s very truly | W Hopkins.


The problem involved the strike and dip of the foliated mica-schist CD observed at Cape Tres Montes, Chile (see Correspondence vol. 1, letter to J. S. Henslow, [10–]13 March 1835, and South America, pp. 158–9). On the diagram are some pencil calculations, by CD, relating to the angles.
The line running along the ridge of the anticline in the direction of the strike.
CD was not entirely convinced by this account and evidently wrote again to Hopkins before the publication of South America, see letters from William Hopkins, 27 April 1846 and 5 May 1846. These three letters from Hopkins are discussed in Schwartz 1980.


Correspondence: The correspondence of Charles Darwin. Edited by Frederick Burkhardt et al. 29 vols to date. Cambridge: Cambridge University Press. 1985–.

Hopkins, William. 1845. On the motion of glaciers. London, Edinburgh and Dublin Philosophical Magazine 26: 1–16, 146–69.

Schwartz, Joel S. 1980. Three unpublished letters to Charles Darwin: the solution to a “geometrico-geological” problem. Annals of Science 37: 631–7.

South America: Geological observations on South America. Being the third part of the geology of the voyage of the Beagle, under the command of Capt. FitzRoy RN, during the years 1832 to 1836. By Charles Darwin. London: Smith, Elder & Co. 1846.


Comments on a compass diagram designed to show the dip, strike, and anticlinal lines of a geological formation.

Letter details

Letter no.
William Hopkins
Charles Robert Darwin
Sent from
Source of text
DAR 39: 53
Physical description
ALS 2pp †

Please cite as

Darwin Correspondence Project, “Letter no. 835,” accessed on 15 April 2024,

Also published in The Correspondence of Charles Darwin, vol. 3