Introductory Lecture on Astronomy,
Delivered in Trinity College, Dublin, November 8th 1832.
By William R. Hamilton, Royal Astronomer Of Ireland

[The Dublin University Review and Quarterly Magazine, Vol. I (January 1833), 72--85.]

The time has returned when, according to the provisions of this our University, we are to join our thoughts together, and direct them in concert to astronomy - the parent of all the sciences, and the most perfect and beautiful of all. And easily and gladly could I now expatiate on the dignity and interest of astronomy, but the very assurance of your complete and perfect sympathy renders needless any attempt at excitement. I must not and cannot suppose that any of those who are assembled here this day, are insensible to the inward impulses, and unconscious of the high aspirations, by which the stars, from their thrones of glory and of mystery, excite and win toward themselves the heart of man; that the golden chain has been let down in vain; and that celestial beauty and celestial power have offered themselves in vain to human view. And if I could suppose that this were so - that any here had been till now untouched by the majesty and loveliness with which astronomy communes - still less could I persuade myself that in the mind of such a person my words could do what the heavens had failed to effect. The heart, because it is human, say rather because it is not wholly divine, lifts itself up in aspiration, and claims to mingle with the lights of heaven; and joyfully receives into itself the skyey influences, and feels that it is no stranger in the courts of the moon and the stars. Though between us and the nearest of those stars there be a great gulph fixed, yet beyond that mighty gulph (oh, far beyond!) fly, on illimitable pinions, the thoughts and affections of man, and tell us that there, too, are beings, akin to us - members of one great family - beings animated, thoughtful, loving - susceptible of joy and hope, of pain and fear - able to adore God, or to rebel against him - able to admire and speculate upon that goodly array of worlds with which they also are surrounded. And often this deep instinct of affection, to the wide family of being, to the children of God thus scattered throughout all worlds, has stirred within human bosoms; often have men, tired of petty cares and petty pleasures, fretting within this narrow world of ours, seeking for other suns and ampler ether, gone forth as it were colonists from earth, and become naturalized and denizens in heaven. Not of one youthful enthusiast alone, are the words of a great living poet[1] true, that

``Thus before his eighteenth year was told,
Accumulated feelings pressed his heart
With still increasing weight; he was o'erpower'd
By nature - by the turbulence subdued
Of his own mind - by mystery and hope,
And the first virgin passion of a soul
Communing with the glorious universe.''

I must not and do not doubt, that many, let me rather say that all, of those whom I now address, have, from time to time, been stirred by such visitations, and been conscious of such aspirings; and that you need not me to inform you, that astronomy, though a science, and an eminent one, is yet more than a science, - that it is a chain woven of feeling as well as thought - an influence pervading not the mind only, but the soul of man. Thus much, therefore, it may suffice to have indulged in the preliminary and general expression of these our common aspirations; and I now may pass to the execution of my particular duty, my appointed and pleasant task, and fulfil, so far as in me lies, the intentions and wishes of the heads of our University; who, in fixing the order of your studies, directed first your attention to the sciences of the pure reason - the logical, the metaphysical, and the mathematical - and call you now to those in which the reason is combined with experience; and who have judged it expedient, among all the physical sciences, to propose astronomy the first, as a favourable introduction to the rest, and a specimen and type of the whole.

It is, then, my office, this day, to present to you astronomy as itself a part, and as an introduction to the other parts, of physical science in general - and thus to greet you at the first steps and vestibule of the majestic edifice which patient intellect has been rearing up through many a past generation; and which, with changes doubtless, but such as rather improve than destroy the unity of the whole, shall remain, as we trust, for the exercise, the contemplation, and the delight, of many a generation yet unborn. It were difficult for any one, and it is impossible for me, to do full justice to so vast a subject; but I shall hope for a renewal of that indulgent attention with which I have more than once before been favoured upon similar occasions, while, in purity and illustration of the subject, I touch briefly, and as it were by allusion only, on the following points:- the distinction between the physical and the purely mathematical sciences - the end which should be considered as proposed in physical science in general - and the means which are to be employed for the attainment of this end - the objections, utilitarian and metaphysical, which are sometimes expressed, and perhaps oftener felt, against the study of physical science - the existence of a scientific faculty analogous to poetical imagination, and the analogies of other kinds between the scientific and the poetical spirit.

I have said that I design to speak briefly of the end proposed, and the means employed, in the physical sciences on which you are entering; and the distinction between them and the pure mathematics, in which you have lately been engaged. It seems necessary, or at least useful, for this purpose, to remind you of the nature and spirit of these your recent studies - the sciences of geometry and algebra. In all the mathematical sciences we consider and compare relations. The relations of geometry are evidently those of space; the relations of algebra resemble rather those of time. For geometry is the science of figure and extent; algebra, of order and succession. The relations considered in geometry are between points, and lines, and surfaces; the relations of algebra, at least those primary ones, from the comparison of which others of higher kinds are obtained, are relations between successive thoughts, viewed as successive and related states of one more general and regularly changing thought. Thus algebra, it appears, is more refined, more general, than geometry; and has its foundation deeper in the very nature of man; since the ideas of order and succession appear to be less foreign, less separable from us, than those of figure and extent. But, partly from its very refinement and generality, algebra is more easily and often misconceived; more easily and often degraded to a mere exercise of memory - a mere application of rules - a mere legerdemain of symbols: and thus, except in the hands of a very skilful and philosophical teacher, it is likely to be a less instructive discipline to the mind of a beginner in science.

Motion, although its causes and effects belong to a physical science, yet furnishes, by its conception and by its properties, a remarkable application of each of these two great divisions of the pure mathematics: of geometry, by its connexion with space; of algebra, by its connexion with time. Indeed, the thought of position, whether in space or time, as varied in the conception of motion, is an eminent instance of that passage of one general and regularly changing thought, through successive and related states, which has been spoken of as suggesting to the mind the primary relations of algebra. We may add, that this instance, motion, is also a type of such passage; and that the phrases which originally belong to and betoken motion, are transferred by an expressive figure to every other unbroken transition. For with time and space we connect all continuous change; and by symbols of time and space we reason on and realise progression. Our marks of temporal and local site, our then and there, are at once signs and instruments of that transformation by which thoughts become things, and spirit puts on body, and the act and passion of mind are clothed with an outward existence, and we behold ourselves from afar.

These purely mathematical sciences of algebra and geometry, are sciences of the pure reason deriving no weight and no assistance from experiment, and isolated, or at least isolable, from all outward and accidental phenomena. The idea of order, with its subordinate ideas of number and of figure, we must not indeed call innate ideas, if that phrase be defined to imply that all men must possess them with equal clearness and fulness; they are, however, ideas which seem to be so far born with us, that the possession of them, in any conceivable degree, appears to be only the development of our original powers, the unfolding of our proper humanity. Foreign, in so far that they touch not the will, nor otherwise than indirectly influence our moral being, they yet compose the scenery of an inner world, which depends not for its existence on the fleeting things of sense, and in which the reason, and even the affections may at times find a home and a refuge. The mathematician, dwelling in that inner world, has hopes, and fears, and vicissitudes of feeling of his own; and even if he be not disturbed by anxious yearnings for an immortality of fame, yet has he often joy, and pain, and ardour: the ardour of successful research, the pain of disappointed conjecture, and the joy that is felt in the dawning of a new idea. And when, as on this earth of ours must sometimes happen, he has sent forth his wishes and hopes from that lonely ark, and they return to him, having found no resting-place: while he drifts along the turbulent current of passion, and is tossed about by the storm and agony of grief, some sunny bursts may visit him, some moments of delightful calm may be his, when his old habits of thought recur, and the ``charm severe'' of lines and numbers is felt at intervals again.

It has been said, that in all the mathematical sciences we consider and compare relations. But the relations of the pure mathematics are relations between our own thoughts themselves; while the relations of mixed or applied mathematical science are relations between our thoughts and phenomena. To discover laws of nature, which to us are links between reason and experience - to explain appearances, not merely by comparing them with other appearances, simpler or more familiar, but by showing an analogy between them on the one hand, and our own laws and forms of thought on the other, ``darting our being through earth, sea, and air''[2] - such seems to me the great design and office of genuine physical science, in that highest and most philosophical view in which also it is most imaginative. But, to fulfil this design - to execute this office - to discover the secret unity and constancy of nature amid its seeming diversity and mutability - to construct, at least in part, a history and a prophesy of the outward world adapted to the understanding of man - to account for past, and to predict future phenomena - new forms and new manifestations of patience and of genius become requisite, for which no occasion had been in the pursuits of the pure mathematics. Induction must be exercised; probability must be weighed. In the sphere of the pure and inward reason, probability finds no place; and if induction ever enter, it is but tolerated as a mode of accelerating and assisting discovery, never rested in as the ground of belief, or testimony of that truth, which yet it may have helped to suggest. But in the physical sciences, we can conclude nothing, can know nothing without induction. Two elements there are in these, the outward and the inward; and if the latter, though higher in dignity, usurp the place which of right pertains to the former, there ensues only a specious show, a bare imagination, and not a genuine product of the imaginative faculty, exerting itself in due manner and measure on materials which nature supplies. Here, then, in the use and need of induction and probability, we have a great and cardinal distinction between the mixed and the pure mathematics.

Does any, then, demand what this induction is, which has been called the groundwork of the physical sciences, the key to the interpretation of nature? To answer this demand, I must resume my former statement of the main design and office of physical science in general. I said, that this design was to explain and account for phenomena, by discovering links between reason and experience. Now the essence of genuine induction appears to me to consist in this, that in seeking for such links we allow to experience its due influence, and to reason not more than its due - that we guard against false impressions from the mechanism and habits of our own understandings - and submit ourselves teachably to facts; not that we may ultimately abide in mere facts, and sensations, and arranged recollections of sensation, but from the deep and sublime conviction, that the author, and sustainer, and perpetual mover of nature has provided in nature a school, in which the human understanding may advance ever more and more, and discipline itself with continual improvement. We must not conclude a law from facts too small in number, or observed with too little care; or if the scientific imagination, impatient of restraint, press onward at once to the goal, and divine from the falling of an apple the law of gravitation, and in the trivial and every day changes which are witnessed around us on this earth perceive the indications of a mighty power, extending through all space, and compelling to their proper orbits the ``planets struggling fierce towards heaven's free wilderness;''[3] yet must such divinations be long received, even by the favoured discoverer himself, if he be of the true inductive school, with candid diffidence and philosophic doubt, until they have been confirmed by new appeals to other, and more remote, and more varied phenomena. If, as in this case of gravitation, the law, concluded or anticipated from the first few facts, admit of a mathematical enunciation, and consequently, can be made a basis of mathematical reasoning, then it is consistent with, and required by, the spirit of induction, that the law should be made such a basis. We may and ought to employ à priori reasoning here, and consider what consequences must happen if the law supposed be a true one. These consequences ought to be mathematically developed, and a detailed prediction made of the yet unobserved phenomena which the law includes, and with which it must stand or fall, the truth of the one and of the other being connected by an indissoluble tie. New and more careful observations must then be made, to render closer and more firm the connexion between thoughts and things. For,[4] in order to derive from phenomena the instruction which they are fitted to afford, we must not content ourselves with the first vague perceptions, and obvious and common appearances. We must discriminate the similar from the same - must vary, must measure, must combine - until, by the application of reason and of the scientific imagination to carefully recorded facts, we ascend to an hypothesis, a theory, a law, which includes the particular appearances, and enables them to be accounted for and foreseen. Then, when the passive of our being has been so far made subject to the active, and sensation absorbed or sublimed into reason, the philosopher reverses the process, and asks how far the conceptions of his mind are realised in the outward world. By the deductive process following up induction, he seeks to make his theory more than a concise expression of the facts on which it first was founded; he seeks to deduce from it some new appearances which ought to be observed if the theory be co-extensive with nature. He then again consults sensation and experience, and often their answer is favourable; but often, too, they speak an unexpected language. Yet, undismayed by the repulse, and emboldened by partial success, he frames, upon the ruins of the former, some new and more general theory, which equally with the former accounts for the old appearances, while it includes within its ampler verge the results of more recent observation. Nor can this struggle ever end between the active and the passive of our being - between the imagination of the theorist and the patience of the observer - until the time, if such a time can ever come, when the mind of man shall grasp the infinity of nature, and comprehend all the scope, and character, and habits of those innumerable energies which to our understanding compose the material universe. Meanwhile, this struggle, with its alternate victories and defeats, its discoveries of laws and exceptions, forms an appointed discipline for the mind, and its history is justly interesting. Nor can we see without admiring sympathy, the triumph of astronomy and Newton; Newton, who in astronomy, by one great stride of thought, placed theory at once so far in advance of observation, that the latter has not even yet overtaken the former, nor has the law of gravitation, in all its wide dominion, yet met with one rebellious fact in successful revolt against its authority. Yet, haply, those are right, who, seeing that Newton himself had sat at the feet of another master, and had deeply drunk from the fountain of a still more comprehending intellect, have thought it just to divide the glory, and award more than half to Bacon. He, more than any other man, of ancient or of modern times, appears to have been penetrated with the desire, and to have conceived and shown the possibility, of uniting the mind to things, say rather of drawing things into the mind. Deeply he felt, and eloquently and stirringly he spake. In far prophetic vision he foresaw, and in language as of inspiration he gave utterance to the vision, of the progress and triumphs of the times then future - nay more, of times which even now we do but look for. And thus, by highest suffrage, and almost unanimous consent, the name of Bacon has been enrolled as eminent high-priest in the spousal temple[5] of man's mind and of the universe. And if, impressed with the greatness of his task and importance of his office, and burning to free mankind from those intellectual fetters in which the injudicious manner of their admiration of the philosophers of Greece had bound them, he appears to have been sometimes blind to the real merit of those great philosophers, and uttered harsh words, and words seeming to imply a spirit which (we will trust) was not the habitual spirit of Bacon; let us pardon this weakness of our great intellectual parent, let us reverently pardon, but let us not imitate it. For, I cannot suppress my fear, that the signal success, which since the time, and in the country, and by the method of Bacon, has attended the inductive research into the phenomena of the material universe, has injuriously drawn off the intellect from the study of itself and its own nature; and that while we know more than Plato did of the outward and visible world, we know less, far less, of the inward and ideal. But not now will I dwell on this high theme, fearing to desecrate and degrade by feeble and unworthy utterance those deep ideal truths which in the old Athenian days the eloquent philosopher poured forth.

I have now touched on some of the points which at the beginning of this lecture I proposed. I have stated my view of the great aim and design of physical science in general - the explanation of appearances, by linking of experience to reason; and aim which is subordinate to another higher end, but to an end too high and too transcendent to come within the sphere of science, till science shall attain its bright consummation in wisdom - the end of restoring and preserving harmony between the various elements of our own being; a harmony which can be perfect only when it includes reconciliation with our God. I have stated the chief means which since the time of Bacon are generally admitted as fit and necessary for the just explanation of appearances - the alternate use of induction and deduction, and the judicious appreciation of probabilities; and have shown how by this use of induction and probability, an essential difference is established between the physical sciences - among which astronomy ranks so high - and the sciences of the pure mathematics; and as example of successful induction, have referred you to the discovery of gravitation. Many other examples will occur in the course of the subsequent lectures, in which I shall have occasion to speak of ancient as well as of modern discoveries, and to show you from the Almagest of Ptolemy, what the state of astronomy was in his time and the time of Hipparchus. You will, I think, accompany and share the interest which I have felt in a review of the science of a time so ancient. The contemplations, like the objects, of astronomy, are not all of modern growth. Not to us first do Arcturus, and Orion, and the Pleiades glide on in the still heaven. The Bear, forbidden here and now to bathe in ocean, circled the Pole in that unceasing round, three thousand years ago, and its portraiture was imagined by Homer as an ornament for the shield of Achilles. And if that old array of ``cycle and epicycle, orb in orb,'' with which the Greek astronomer had filled the planetary spaces, have now departed with its principle of uniform and circular motion, yet the memory of it will long remain, as of a mighty work of mind, and (for the time) a good explanation of phenomena. The principle itself has in a subtler form revived, and seems likely to remain for ever, as a conviction that some discoverable unity exists, some mathematical harmony in the frame of earth and heaven. We live under no despotism of caprice, are tossed about in no tempest and whirlwind of anarchy; what is law and nature in one age, is not repealed and unnatural in the next; the acquisitions of former generations are not all obsolete and valueless in ours, nor is ours to transmit nothing which the generations that are to come shall prize: our life, the life of the human race, is no life of perpetual disappointment and chaotic doubt, nor doomed to end in blank despondence, it is a life of hope and progress, of building on foundations laid, and of laying the foundations for other and yet greater buildings. And thus are distinct generations knit together in one celestial chain, by one undying instinct: while, yielding to kindred impulses, our fathers, ourselves, and our children all seek and find, in the phenomenal and outward world, the projection of our own inward being, of the image of God within us. Astronomy is to man an old and ancestral possession. Through a long line of kings of mind, the sceptre of Astronomy has come down, and its annals are enshrined among the records of the royalty of genius. Its influence has passed, with silent but resistless progress, from simple shepherds watching their flocks by night, to the rulers of ancient empires, and the giants of modern thought. When we this trace its history, and change of habitation, from the first rude pastoral and patriarchal tents of Asia, to some old palace roof of Araby or Egypt, or to the courts of that unforgotten king of China, who, noting in his garden the shadows of summer and of winter, left a record by which we measure after three thousand years the changes that the seasons have undergone; and passing from these imperial abodes of the East to dwellings not less worthy, when we see astronomy shrined in the observatories and studies of Europe, and nation vying with nation, and man with man, which shall produce the worthier temple, and yield the more acceptable homage; when we review the long line of scientific ancestry, from Hipparchus and Ptolemy, to Copernicus and Galileo, from Tycho and Kepler, to Bradley, Herschel and Brinkley; or call before us those astronomical mathematicians, who, little provided with instruments and outward means of observing, while they seemed in the silence of their closets to have abandoned human affairs, and to live abstracted and apart, have shown that genius in the very solitude of its meditations is yet essentially sympathetic, and must rule the minds of men by the instinct of its natural regality, and have filled the interval of the great succession, from Archimede to Newton, from Newton to Lagrange: when the imagination is crowded and possessed by all these old and recent associations, must we not then, if self be not quite forgotten, if your own individuality be not all merged in this extended and exalted sympathy, this wide and high communion, yet long to bow for a while, and veil ourselves, as before superior spirits, and think it were a lot too happy, if we might but follow in the train, and serve under the direction of this immortal band!

In such a mood, can we discuss with patience, can we hear without indignation the utilitarian objection, ``of what use is Astronomy?'' meaning thereby, what money will it make? - what sensual pleasure will it procure.

Against astronomy, indeed, the objection from utility is singularly infelicitous, and almost ludicrously inapplicable: astronomy, which binding in so close connexion the earth with the visible heaven, and mapping the one in the other, has guided through wastes, which else were trackless, the fleet and the caravan, and made a path over the desert and the deep. But suppose it otherwise, or take some other science which has not yet been so successfully applied. What, then; and is the whole of life to be bound down to the exchange and the market-place? Are there no desires, no pleasures, but the sensual - no wants, and no enjoyments, but of the outward and visible kind? Are we placed here only to eat, and drink, and die? Some less magnificent stage, methinks, might have sufficed for that. It was not neeeded, surely, for such a race of sorry animals - so void themselves of power and beauty within, so incapable and so undesigned for the contemplation of power and beauty without - that they should have been placed in this world of power and beauty; and the evermoving universe commanded to roll before our view, ``making days and equal years, an all-sufficing harmony;''[6] that the heavens should declare the glory of God, and the firmament show his handywork. I am almost ashamed to have dwelt so long, here, amid these influences, and before such an audience, on objections of a class and character so quite unworthy of your consideration. More important is it that I should endeavour to answer another class of objections, founded on the misapprehension and misapplication of deep, and inward, and important truth, and of a nature fitted to captivate and carry away the young and ardent spirit.

It is, then, sometimes said, and, perhaps, oftener felt, that astronomy itself is too unrefined - to material a thing;- that the mind ought to dwell within its own sphere of reason and imagination, and not be drawn down into the world of phenomena and experience. Now, with respect to pure Reason, I will grant that this objection would assume a force, which I cannot now concede to it, if it were indeed possible for man, on that etherial element alone, to feed and live. But if this be not so - if we must quit at all the sphere of the pure reason, and descend at all into the world of experience, as surely we must sometimes do - why narrow our intercourse with experience to the smallest possible range? why tread, with delicate step, this common earth of ours, and not rather wander freely through all her heights and depths, and gaze upon the wonders and beauties that are her own, and store our minds and memories with truths of fact, were it not only to have them ready, as materials and implements, for the exercise of that transforming and transmuting power, which is gradually to draw those truths into its own high sphere, and to prepare them for the ultimate beholding of pure and inward intuition? And as to the imagination, it results, I think, from the analysis which I have offered of the design and nature of physical science, that into such science generally, and eminently into astronomy, imagination enters as an essential element: if that power be imagination, which ``darts our being through earth, sea and air;'' and if I rightly transferred this profound line of our great dramatist to the faculty which constructs dynamical and other physical theories, by seeking for analogies in the laws of outward phenomena to our own inward laws and forms of thought. Be not startled at this, as if in truth there were no beauty, and in beauty no truth; as if these two great poles of love and contemplation were separated by a diametral space, impassible to the mind of man, and no connecting influences could radiate from their common centre. Be not surprised that there should exist an analogy, and that not faint nor distant, between the workings of the poetical and of the scientific imagination; and that those are kindred thrones whereon the spirits of Milton and Newton have been placed by the admiration and gratitude of man. With all the real differences between Poetry and Science, there exists, notwithstanding, a strong resemblance between them; in the power which both possess to lift the mind above the stir of earth, and win it from low-thoughted care; in the enthusiasm which both can inspire, and the fond aspirations after fame which both have a tendency to enkindle; in the magic by which each can transform her votaries into a world of her own creating; and perhaps, in the consequent unfitness for the bustle and the turmoil of real life, which both have a disposition to engender. Doubtless there are enthusiasts here this day, whom, without knowing, I affectionately sympathise with: who bear upon them that character of all good and genuine enthusiasm, highly to conceive, intensely to admire, and ardently to aspire after excellence. If any such have chosen poetry for its own sake, and with a hope of adding to the literature of his country; aware of the greatness of the task and responsibility of the office, knowing that the poet should be no pander to sensual pleasure, no trifler upon frivolous themes, but an interpreter between the heart and beauty, and utterer of divine and of eternal oracles; and if no more imperious duty interfere, I do not seek to dissuade him: but if he have only been repelled from science by its seeming to possess no power of similar excitement, I would not that, so far as in me lay, he should be unaware of the kindred enthusiasm. In science, as in poetry, there are enthusiasts, who fixing their gaze upon the monuments which kindred genius has reared, press on to those pyramids in the desert, forgetting the space between. And when I think that among the new hearers whom a new year has brought, it is likely that some, perhaps many, are conscious of such aspirations; that some may go forth from this room to-day, whom after-times shall hail with love and reverence, as worthy children and champions of their college and their county; and that I, in however small a degree, may have influenced and confirmed their purpose: I feel, I own, ``a presence that disturbs me with the joy of elevated thoughts''[7] a sublime and kindling sense of the unseen majesty of mind. Doubtless in that period of generous ardour to which in part the philosophic poet[8] alluded, when, mourning over the too frequent degeneracy that attends the cares and temptations of manhood, the loss of enthusiasm without the gain of wisdom, or with the acquisition only of ``that half-wisdom half-experience gives,'' he framed that magnificent stanza -

``Not in entire forgetfulness
And not in utter nakedness,
But trailing clouds of glory do we come
From God who is our home;
Heaven lies about us in our infancy;
Shades of the prison-house begin to close
Upon the growing boy,
But he beholds the light, and whence it flows,
He sees it in his joy;
The youth, who daily further from the east
Must travel, still is nature's priest,
And by the vision splendid
Is on his way attended;
At length the man beholds it die away,
And fade into the light of common day:''
doubtless, (I was about to say,) in this period of youthful ardour, there are many vague and some determined aspirations after excellence, among those whom I now address; and some assuredly there are, who, burning to consecrate themselves to the service of truth and goodness, and ideal beauty, and wedding themselves in imagination to the spirit of the human race, feed on the hope of future and perpetual fame, and fondly look for that pure ideal recompense, and long to barter ease, and health, and life itself for that influence, surviving life, that power and sympathy, which has been attained by the few, who, after long years of thought, produce some immortal work, a Paradise Lost, or a Principia, and win their sublime reward of praise and wonder;[9] who do not wholly die, but through all time continue to influence the minds and hearts of men; who leave behind them some enduring monument, which, while it shall be claimed as the honour of their age and nation, bears also their own name engraven on it in imperishable characters, like Phideas on the statue of Minerva. Of such emotions I will not risk the weakening, by dwelling now on a conceivable superior state, in which perfection should be sought for its own sake, and as independent even of this fine unmercenary reward: and the spirit, purified even from this ``last infirmity of noble minds,''[10] feel, in the words of one who has attained the earthly and (we will trust) the heavenly fame, the words of the immortal Milton, that
Fame is no plant that grows on mortal soil,
Nor in the glistering foil,
Set off to the world, nor in broad rumour lies;
But lives, and spreads abroad, by those pure eyes,
And perfect witness of alljudging God:
As He pronounces lastly of each deed,
Of so much fame in Heaven expect thy meed.


1. Wordsworth.

2. Shakspeare.


``As the sun rules, even with a tyrant's gaze,
The unquiet republic of the maze
Of planets struggling fierce towards heaven's free wilderness.'' - Shelley.

4. Some of the following remarks on physical science were published in the Dublin Literary Gazette in 1830.

5. And thus, by the divine assistance, we shall have prepared and decked the nuptial chamber of the mind and of the universe. - Bacon.


``And bade the ever-moving universe
Roll round us, making days and equal years,
An all-sufficing harmony.''
        From a Manuscript Poem, by A. de V.

7. Wordsworth.

8. Ibid.


And win he knows not what sublime reward
Of praise and wonder. - Akenside.

10. Milton.


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