History of the paper `On Caustics'.

[The two following extracts are taken from Chapter VI in Volume I of Life of Sir William Rowan Hamilton by Robert Perceval Graves (Dublin University Press Series, 1882.). They describe the submission of Hamilton's manuscript On Caustics to the Royal Irish Academy, and the report of the referees on that manuscript.]

The mathematical investigations respecting the science of Optics, of which the germ had been conceived in 1822, were carried on, as occasional expressions in his letters have intimated, through the years 1823 and 1824 in the intervals of his Collegiate studies. Towards the close of the latter year they had been set forth in the form of a paper `On Caustics,' of which the preface bears date December 6, 1824. The preface has historical value, and I therefore give it at length:-

`The Problems of Optics, considered mathematically, relate for the most part to the intersections of the rays of light proceeding from known surfaces, according to known laws.

`In the present paper it is proposed to investigate some general properties common to all such Systems of Rays, and independent of the particular surface or particular law. It is intended in another paper to point out the application of these mathematical principles to the actual laws of Nature.

`A fortnight ago I believe that no writer had ever treated of Optics on a similar plan. But within that period, my tutor, the Rev. Mr. Boyton, to whom I had communicated some of my results, has shown me in the College Library a beautiful memoir of Malus on the subject, entitled, ``Traité d'Optique,'' and presented to the Institute in 1807.

`Those who may take the trouble to compare his memoir with mine will perceive a difference in method and extent.

`With respect to those results which are common to both, it is propert to state that I had arrrived that them in my own researches before I was aware of the existence of his.'

The second part of the Paper concludes with the following graceful tribute to the friendly and generous encouragement which the author had received from Dr. Brinkley:---

`But whatever may be the opinions of others as to its value, I have the pleasure to think that my Paper is inscribed to the one who will best be able to perceive and appreciate what is original; whose kindness has encouraged, whose advice has strengthened me; to whose approbation I have ever looked as to a reward sufficient to repay me for industry however laborious, for exertion however arduous.'

In the Minutes of Council of the Royal Irish Academy, under date of December 13, 1824, is the following entry:- `Received a Paper on Caustics, Part I., by William Hamilton, Esq., T.C.D., communicated by the President [the Rev. Archdeacon Brinkley, who was in the chair]. Resolved,- That it be referred to a Committee composed of Dr. Mac Donnell, Mr. Harte and Mr. Lardner, and that they be requested to report as soon as convenient.'

The report of the Committee was not received by the Council till the 13th of June following.

[Life of Sir William Rowan Hamilton by R. P. Graves
Volume I, Chapter VI, pp. 176-177.]

It was under date of the 13th of June, 1825, that the Minutes of Council of the Royal Irish Academy contained the following entry:---

``We the Committee appointed to consider the `Memoir on Caustics' presented by Mr. Hamilton, having attentively examined the same, are of opinion that the results at which the author has arrived are novel and highly interesting, and that considerable analytical skill has been manifested in the investigations which lead to them. But we conceive that the discussions included in the Memoir are of a nature so very abstract, and the formulæ so general, as to require that the reasoning by which some of the conclusions have been obtained should be more fully developed, and that the analytical process by which some of the formulæ have been obtained should be distinctly specified. This we conceive to be necessary in order to render the publication of the Memoir generally useful.

`(Signed) HENRY H. HARTE,
`D. LARDNER (for self and

This Report, though not unfriendly, was probably less appreciative of the merits of his Paper than was anticipated by Hamilton. Certainly such an impression was created by it on the mind of his uncle, as is proved by the letter which I here insert; but there is no reason to regret the decision it announced. Hamilton acted upon the advice contained in it, and employed the intervals of his Collegiate studies during the next two years in recasting and enlarging his Paper, which in its new form, and under the title of `Theory of Systems of Rays,' became the foundation of his mathematical fame.


TRIM, July 5, 1825.

`I had the pleasure of your letter by Thornburgh, from which I find I did not quite understand the Academic formula for admitting a Paper to be printed among their Proceedings - the wording of their Report having led me to understand it as making the publication of your Paper in their Transactions an honour only to be hoped for on the conditions of the fulfilment of a task set to the author by them: ``that of more fully developing his reasoning, and more distinctly specifying the analytical processes by which his formulæ were obtained.'' In short, though I did not think the rites of sepulture in the archives the exact honour I wished for your Essay - thinking of Horace's ``Paulum sepultæ distat inertiæ celata virtus'' - yet I was not prepared to acquiesce with complacency in what appeared to me a civil refusal of such ``easement of burial,'' to use the phrase of Mr. Plunket's famous Burial Bill. It seemed to me as if they reserved to themselves as judges the discretionary power of keeping thus the ghost of your Essay flitting about the banks of the R. I. bog. I am glad find those judges of yours are not as stern as I thought. Nor am I sorry that I fell into the error which elicited your lively effusion on the subject of literary fame. The sentiments you express on that head I quite concur in. In my own view for your fame I did, I think, contribute not a little to the degree of it to which you soon reached in College, by my preventing your grasping at fruits before they had ripened. And nothing, I fear is ripe enough for judges who may not have divested themselves of the susceptibility implied in Horace's ``Urit fulgore suo qui,'' &c. I trust this may not be the case with the tribunal in question. But I should also be glad to learn that you were not again to subject your Essay and its merits to their exceptions and buts.'

[Life of Sir William Rowan Hamilton by R. P. Graves
Volume I, Chapter VI, pp. 186-188.]


D.R. Wilkins
School of Mathematics
Trinity College, Dublin