To Thomas Archer Hirst   Tuesday night 1848

Tuesday night¹ 1848

Dear Tom

I handed your question over to a youth² who commenced geometry with me about 3 months ago – I send you his demonstration without addition or diminution – I trust you will understand it – Well, Kuppers³ has gone, and the probability is that we shall see his face no more – I was very much attached to him and though at a distance from Halifax, his leaving it affects me as if I had just bidden him good bye –

– In Emerson you behold one of the noblest souls that ever was stuck in clay – every time I rise from his book⁴ I find a new [vigour] in my heart – he teaches one to be so independent that you almost feel disposed to quarrel with himself just to shew how little you cared about even him – There are many parts of his writings very difficult, especially some portions of the Transcendentalist, and Idealism⁵ – the rule he lays down will I believe make all clear – let us by enacting our best insight by doing that which we feel to be right strengthen our powers and purify our vision, and all will be understandable – there is a world of meaning in those two words he uses so emphatically I ought⁶ – you remember Dawson’s⁷ reference to a principle of duty⁸ – and see its identity with the views of Emerson – In his ‘Christian Teacher’ a passage relative to Jesus Christ occurs which surpasses any thing I ever read on the same subject – It is difficult to deal with such a class as yours. I see no way open to you but to allow each to push forward to the best of his ability – it would be a pity to harness a racer to a slow coach – keep them in sections of threes and fours if possible & thus enable yourself to address this number at the same time. I may add that the difficulty lies at your own feet and you alone must meet it – I shall however be happy at all times to render you any assistance in my power – I would recommend you to accompany D^r. Inglis⁹ throughout his lectures – purchase a few things and repeat his experiments yourself – I see no better way of fastening the thing in your mind – the apparatus will be very cheap, bits of chalk, iron filings, clippings of copper, and such mean things are the chemists principal materials – Could you contrive to send me tracings of those small sections which Tidmarsh reduced? If so I should be much obliged – Send me the Guardian¹⁰ by all means –

Good bye & bel¹¹ me dear Tom | Sincerely yours | J. Tyndall | Is M^r C.¹² still in London?

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Given the chord¹³ of a circle and its versed sine to find the diameter.¹⁴

Let (A B) be the chord (C D) the versed sine, which bisects the chord (A B) and is perpendicular to it, consequently if produced it will pass through the centre of the circle.

Produce it to (G) then, having the chord (A B) given the square of half of it will be the rectangle under (A D. D B) but by the 25^th. of the (3^rd.) the rectangle (A D. D B) = the rectangle (C D. D G). Thus we have the area of the rectangle (C D. D G) and one side C D) to find the other side (D G). By dividing the area by the side (C D) we get the side (D G); which added to (C D) completes the diameter of (C G) hence the rule.

Divide the square of half the chord by the versed sine, to the quotient add the versed sine, and the product will be the diameter.

J. Duckwarth.¹⁵

M^r T Hirst | Northgate Offices | Halifax | Yorkshire

RI MS JT 1/HTYP/5

RI MS JT/1/T/512

Portions of letter are LT Transcript Only