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upwards of 1500 copies, among the most learned and best educated men in this country; and I did so, in the hope that some one of them would take up the consideration of this important question from my point of view, and afford me the opportunity of a candid and careful discussion of it. In this hope I have not been altogether disappointed.

My correspondent claims, and justly claims, to be an "authority" on this great question, having obtained the highest mathematical honors at the University of Oxford. He undertook to point out that (what he has been pleased to term) my highly ingenious reasoning in the pamphlet, rests on a fallacy. Our readers will judge, after perusing the correspondence, how far he has succeeded in accomplishing the task.

My theory is, that in every circle, the circumference is exactly equal to three and one-eighth times its diameter; and the area exactly equal to three and one-eighth times the area of a square described on its radius; and I have demonstrated these facts by a variety of diagrams, and could have adduced many more, had I thought it necessary.

I submit, that my correspondent has entirely failed to subvert this theory, and for the best of all reasons : "It is one of the great truths of nature, which can admit of no doubt, and which it is not in the power of any man living to subvert.” The latter sentence I quote from the letter of another correspondent, only recently received, who, in all his former communications had, with great

fairness and candour, conscientiously opposed me.

Previously to the twenty-ninth meeting of the British Association, at Aberdeen, in 1859, my enquiries had been confined to an examination of the relations existing between circles and squares, but even this limited condition of the enquiry had thoroughly satisfied me, as to the true relation between the diameter and circumference of a circle; and I resolved to bring the subject under the notice of the Association, of which I have been a member almost from the earliest period of its existence.

A short time before the meeting of the Association, I addressed a letter to the Honorary Secretary, informing him that it was my intention to attend the meeting, and that I purposed reading a Paper “On the true Circumference and Area of a Circle." I received a reply from him, to say my Paper was placed on the books, and requesting me to inform him, on what day I should be prepared to read it. To this I replied, that I should be prepared to read it on the first day of the meeting of the Sections, if necessary, or on any subsequent day if more convenient to the Association.

I was told by several of my acquaintance that the Association would never give me a hearing, and that if I wished to spare myself considerable annoyance I had better stay at home. I felt that the subject was of too much importance to the interests of science, to justify me

in permitting it to be stifled, without any effort on my part to prevent it, and I resolved, at all risks, to attend the meeting of the Association.

I had the pleasure to hear His Royal Highness the Prince Consort, the President of the Association for that year, deliver his opening address, and I shall ever remember the gratification I felt, on hearing His Royal Highness make the following remarks:-" Remembering that this Association is a popular Association, not a secret confraternity of men, jealously guarding the mysteries of their profession, but inviting the uninitiated, the public at large, to join them, having as one of its objects, to break down those imaginary and hurtful barriers, which exist between men of science and so-called men of practice." Surely, thought I at the moment of hearing these words, the friends who advised me to stay at home must have been mistaken. Little did I suppose, that before the end of the meeting, I should discover the practice of the Association to be so widely at variance with the theory of its constitution, as set forth in such flattering terms in the opening address of its Royal President.

The following morning I presented my Paper to the Committee of the Mathematical Section, and was told without any hesitation, I could not be permitted to read it; that the subject was prohibited from being introduced into the deliberations of the Association. For a short time, and with considerable earnestness, I endea

voured to reason with the Committee as to the propriety of such a determination; but the Association had evidently arrived at the same conclusion as the late Baden Powell, viz., That "no amount of attestation from innumerable and honest witnesses, would ever convince any one versed in mathematical science, that a person had squared the circle," and the attestation of so obscure and unknown an individual as the writer, in all probability produced in the minds of the Committee a feeling of the most profound contempt. Be this as it may, I reasoned in vain.

I then changed my tactics, and prepared a short Paper, entitling it, "On the Relations of a Circle inscribed in a Square," and I again presented myself before the Committee, but with no better result. Subsequently, however, through the intervention of an individual member of the Committee, (J. Pope Hennessy, Esq., M.P. for King's County, Ireland, and to whom I take this opportunity of tendering my grateful acknowledgments,) my second Paper was inserted for reading in the programme of the following day, but was placed the last on a list of thirty Papers. All these Papers could not be disposed of that day, and many of them had to stand over till the next sitting of the Section, mine being among the number. What was my astonishment on finding it asserted in the programme of the following morning, that my Paper had been read the preceding day. This appeared to me to

be positive evidence of a determination to burke the subject, by any means, however dishonest, and I at once resolved upon my course. I took my seat in the Section, and waited until Sir William Rowan Hamilton, the Astronomer Royal of Ireland, took the chair for the day, in the absence of Lord Rosse. I then rose, and made my complaint, demanded to read my Paper, and gave the Section to understand, that I was not the man that would permit even the British Association to trifle with me. It was not an every-day scene in the Sections of the British Association, and Sir W. R. Hamilton will not have forgotten the circumstance. He permitted me to read the Paper. (See Appendix B.) Though short, it introduces to notice some of the fundamental truths of this important discovery.

I left a written copy of the Paper with the Secretary to the Section, and subsequently forwarded a printed one for insertion in the Transactions of the Association. If the reader will refer to the Report of the Association for 1859, he will find it recorded in the Transactions of the Mathematical Section, page 10, that J. Smith read a Paper "On the relations of a Circle inscribed in a square." I should like to know how much wiser any reader of the Transactions of the Association would be, for this wonderful piece of information. Could this learned confraternity have devised any better method, of jealously guarding the mysteries of their profession? or, could they have af

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