20 Clarendon Cres^t

Tuesday ^<1>

My Dear Sir,

I have read over or verified for myself every part of your very elegant set of Theoremendy Fagnanialia

There is just only one point which might perhaps be strengthened. It is Lemma 2 viz. that the deviations must make up more than a given arc. It is certainly true but I question if your reason is quite satisfactory why might not the successive deviations be each (say) the half of the preceding one?

I am Yours truly

P Kelland

H F Talbot Esq
P.S. I have just glanced over your supplement. I dont admit your grounds –but I think you should print your paper in the Transactions that others may judge for them selves – It is at any rate well to keep the subject alive.
Your new demonstration I will not discuss either. I cannot admit any Conversion – either that of a Theorem or my own to your views

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Notes:

1. See Balfour and Kelland letters [ Doc. No: 06374, Doc. No: 08682 and Doc. No: 08712], most likely placing this letter somewhat after 20 May 1863. The paper was published as ‘On Fagnini’s Theorem’, Transactions of the Royal Society of Edinburgh, v.23.