Dear Sir,

I regret that from circumstances which I need not detail the invitation with which you honoured me to write something for the collection of papers which are being put together in commemoration of Abel has remained so long without reply.

At my age you will perhaps hardly expect me to produce something new and original. The subject ought to be one of pure mathematics, for it is in honour of Abel, and most of my work refers to applications of mathematics. There is one thing I thought might perhaps do, but it has, I fear, been too long before the public to make it suitable. However, it is published in the Proceedings or Transactions of the Cambridge Philosophical Society, which are not, I believe, so widely known as many other serial works. I thought that just a short résumé of my results might not be wholly uninteresting.

The subject is the discontinuity of arbitrary constants that appear as multipliers of semi-convergent series, the variable according to powers of which the series proceed being a mixed imaginary. My results are contained in three papers read before the Cambridge Philosophical Society in the years 1857, 1868, and 1889, which are published respectively in the Cambridge Philosophical Transactions, Vol. x, p. 105, the Transactions, Vol. XI, p. 412, and the Proceedings, Vol. VI, p. 362.