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 40^o. 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 40^o. The paper will then be inclined to the horizon at about 40^o. 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’ 45^o. 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’ 45^o. 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 w^d. 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.