with his head in the bucket, drank with long draughts like a horse.

I

After a fit of giddiness and sickness, he found his voice. "My mate is not three hundred yards back on the track, and I am not sure that he is dead. carried him the last mile, and laid him down when I saw your light; come, and " But the man was gone, and, when Tom came up, he found him trying to pour water between the lips of the unfortunate Erne, who lay beneath the tree where Tom had left him-to all appearance dead.

Dead he was not, though, thanks to Tom Williams. Some may say that death is better than life, on the terms on which Erne enjoyed it for a long time after. But life is life, with all its troubles, and death is practically considered by all parties, creeds, and ages, to be a change for the worse; so I suppose that, "humanly speaking," we ought to congratulate ourselves on the fact that Erne Hillyar wasn't dead, and is not dead yet. He had only succeeded in utterly destroying his constitution. To be continued.

MUCH has been said about the impotence of the Pope's Encyclical Letter. No doubt it is the defiance of forces which have proved themselves mightier than the Papal force when it was mightiest; no doubt it is like the nightmare cry of a worn-out giant, dreaming of the serpents which he strangled in his cradle. But we may repeat these obvious remarks till we lose sight of the immense significance of this document; we may despise what is one of the most striking and critical facts in modern history.

There is apt to be a hard and cruel feeling in the minds of most of us who have been bred in a stern Protestantism, and in whom each year's experience has strengthened and deepened it, towards those who exalt obedience to the Holy See above all the convictions of their reason. It seems to us a form of atheism-a denial that there is an eternal truth before which all creatures must bow. Yet if we examine any special instances of this devotion-such, to take the one nearest our own time, as that of Lacordaire, in surrendering all his strongest political and moral persuasions to the decrees of Gregory XVI-it is impossible not to recognise

a beauty and a grandeur in the submission. However incomprehensible it may seem to us, we are obliged to ask ourselves what it meant, and how it was compatible with a disposition, in many aspects of it so heroic, as that of the French Dominican. The still more recent utterances of a countryman of Lacordaire, but a statesman and a Protestant, unlike him in all his traditions and all the habits of his intellect, threw a light upon this question which we cannot afford to lose. M. Guizot, the Genevan, sees in the Pope the bond who holds together the fragments of Christendom, who prevents the loose elements of which its faith is composed from absolutely starting asunder. Such a theory from such a man looks like the reductio ad absurdum of the doctrinaire philosophy. A fiction-to him nothing more-is necessary to keep God's universe from falling to pieces. But it must be accepted also as a confession from a Protestant of what he has seen to be the feebleness and incoherency of Protestant sects. And it may surely offer the best possible apology for a man educated from infancy to consider the Papacy as the centre of unity to the moral and spiritual universe, if he re

garded all his own most cherished beliefs, though imparted, as he felt and knew, by God Himself, as nothing in comparison with the acknowledgment of this centre, the assertion of this unity. In this case it was no doctrinaire theory; no conception, ab extra, of a convenient scheme for making society consist; no patronage of the divine faith and divine order. It was an act of terrible-what would have been to any of us most immoral-sacrifice. But those who at all put themselves into Lacordaire's position, who can look at the world as it appeared to him, though they may tremble even to meditate the contradiction, may reverence him, and wish that in better circumstances they were as truthful as he was.

How deep, how all-possessing, the desire for unity is in our days; how it lies beneath all hearts in all lands; how it manifests itself in all ways—in the best and strongest as well as in the worst and feeblest characters; what bloody offerings it sometimes demands; what torments it inflicts and endures; how it wrestles with the critical spirit in an embrace which may be of love or of hatred, of life or of death-this will be told some day if an historian of our time ever arises who can look through its superficial signs, its apparent discords, to its inmost meaning. He will show how the most opposite sects, associations for the most destructive purposes, betrayed this same instinct; how the most sceptical and scoffing men exhibited the scars of this conflicttheir baffled hopes of unity. And therefore any who strove against the Papal hierarchy-so long as it represented the most partial fulfilment of this craving, the mere image of what a centre of unity might be any who merely complained of it as stifling the demands of the individual conscience, or as an usurpation upon the rights of particular nations-might carry on a moderately prosperous battle against it in the sixteenth century, even when the odds in its favour seemed overwhelming, but have been liable to unaccountable discomfitures even, to de

feats, in the nineteenth century, when it has seemed to be weakest in its leaders, poorest in its allies.

But what no opponents could do, the Pope has done for himself. That which no Protestants, no unbelievers have succeeded in demonstrating, that the Pope is not the Uniter of Christendom -that he is emphatically its DIVIDER ; this he has undertaken himself to demonstrate. Herein lies the unspeakable worth of the late letter. Two reputations had co-existed in the same person. He was accounted the dogmatist of the Christian Church. He was accounted the head and centre of its fellowship. Hitherto the balance between them had been tolerably preserved. Popes had often disturbed it under one impulse or another. But they had seen that, to maintain their last character, the ambition to assert the first needed to be kept in check. Dr. Newman could boast very recently that the decrees and condemnations which have gone forth through a succession of ages had been reluctantly given, and had borne no proportion to the number of questions which had been agitated in Christendom. It seems a frightful irony that the good old man who now fills the chair of St. Peterthe man whose early official years were associated with the ideas of ecclesiastical reformation and Italian unity-should be the Pope who declares, "Henceforth I accept the position of the dogmatist and the denouncer; the other I confess to be absolutely incompatible with it." But this he has done in the series of propositions and denunciations which raise him, the Ultramontane papers affirm, to the level of Hildebrand. They forget their own great claim on behalf of Hildebrand, that, though he set his foot on the neck of kings, he did not care to crush Berengarius. The utmost Pius IX. can do is to ask the Kings for the privilege of cursing some of the strongest convictions of those who are most willing to submit to his authority. The eldest son of the Church refuses that humble petition. He will not give his obolus to Belisarius. Heretical England is not so cruel. If he knows,

being infallible, that he can only curse, she lets him curse over the length and breadth of the land.

It is not, therefore, only with the science, or civilization, or toleration, of this age that the Pope has proclaimed war. He has proclaimed a more deadly war with its longings for unitythat sense of an actual, eternal unity, holding us together in spite of our differences and our hatreds, which has been the great support of his throne when it has been most tottering. It is with the hope of this time, with the deepest, firmest belief, of this timewith the hope and belief of the Roman Catholic, even in one sense more characteristically than of the Protestant countries-that the Pope is at strife. The fiction of M. Guizot is scattered to the winds-that is a reason for almost unmixed joy. The ground for the obedience of such men as Lacordaire was is cut from under them; that change one cannot think of without a mixture of dread. But the true unity will be revealed to these men as the false disappears it is only a natural cowardice that makes one shrink from the thought of the anguish which they must suffer in the process.

And we should turn from any lessons which the letter has for them-lessons that we cannot bring home to them, that we may only weaken by enforcing — to those very pregnant ones

which it contains for ourselves. One is surely this:We have talked of the Pope's temporal, or rather local, sovereignty as if that were the great calamity under which Italy, and the nations of Christendom, were groaning.

It may be a contradiction, but it is a contradiction which has done, and is doing, more to expose the pretence of ecclesiastics to

govern the world-the blasphemy which confounds their kingdom with God's kingdom-than any other. We cannot wish it to disappear till the doctrine which it teaches has been thoroughly laid to heart by every Church in every land. But in this letter it is not the local sovereign who speaks, it is the spiritual dogmatist; it is the man who identifies his decrees, which he considers to be the decrees of all ages, with the truth. It is this identification-this confusion of that which is thought or decreed by any man or any body of men, with that which is-that makes the letter so fierce an attack upon the faith and unity of Christendom, as well as upon science. If its creeds set forth Him who is, and was, and is to come -as we suppose they do-any attempt to put decrees and dogmas for truth must be a subversion of them. If the Sacraments of the Church assert the unity of man in a living and immortal Head, they must be the great antagonists of him who wishes to cut men off for not accepting his opinions. But that assertion is two-edged. It strikes as sharply against all Protestant, all English dogmatism, as against all Romish. The Pope's Encyclical Letter should be framed and glazed, and hung up in the house of every English clergyman, that he may understand what he is aiming at. If it is to do on a small scale what is here done on the largest scale, in the greatest perfection-let him read his sentence in this document. We can but play with tools that have been sharpened to the utmost, and have proved ineffectual. Success would be our greatest calamity; for is it not a calamity to prevail for a little while in fighting against the unity of Christendom, against humanity, against God?

QUEEN'S COLLEGE, Cork, has lost a most distinguished professor, at a time when his genius was in its highest development. Of his early life we know nothing, except that he was not educated at a university, and that, about thirty years ago, a schoolmaster at Lincoln attracted the attention of the mathematical world by some mathematical speculations of unusual originality. By the year 1849 he had gained a name which proeured him the professorship of mathematics at Cork, where he died on the 9th of December last, at some age, we suppose, between fifty and sixty. Of the private life of a person in his pursuits there is usually little to say: of Dr. Boole's the most important circumstance is that for thirteen years out of fifteen he worked at a very small salary, and, owing to the circumstances of the Queen's College, with a small number of pupils. Two years ago the proper feeling of the Government augmented the first source of income, and the growth of the College improved the second. But death has prevented his availing himself of the sunshine; and he leaves a widow and five children unprovided for.

Dr. Boole obtained some share of the honorary rewards which fall to men of science. He received a gold medal from the Royal Society, of which body he was afterwards a Fellow. He had a doctor's diploma from Oxford, and another from Dublin, and he had a prospect, cut short by his death, of admission to the French Institute. The character of his researches was beginning to be widely known.

There is a story which we believe to be perfectly true, and which shows that fortune has something to do in science as well as in war. The mathematical sciences are now distributed into so

many branches that there is not perhaps a man alive who is a competent judge of combined merit and originality in all. Dr. Boole's first communication to the Royal Society was submitted to a gentleman whose eminence lay in quite another line: he could see nothing in it worthy of note, and recommended its rejection. rejection. Casualty threw it under the eye of another person, who was better able to judge; it was accordingly printed, and it was the paper for which the gold medal was given. There is nothing in human affairs, we fully believe, more confidently to be expected than that a true and honest judgment will be formed and acted on as to all communications which get into the right hands. But there is a point which seems to bring the matter to a dead lock: before it can be known who is competent to examine a paper, the paper itself must be examined by a competent person! As to a well-known author there is no difficulty: his line is notorious, and his colleagues in that line. But a new man is liable to such a mischance as had nearly extinguished Dr. Boole, so far as the Royal Society is concerned. The story became public property at the time, and excited some remark: the warning which it gives is wanted, and should be occasionally revived.

This is not the place for a detailed account of Dr. Boole's scientific merits. The point which is most prominent is his power of development of algebraic language. language. The higher parts of the dif ferential calculus-a name which now includes a great part of the higher mathematics have of late years received accessions of power of quite a new kind; one of them has gained a distinctive name, the calculus of operations. Dr. Boole was one of the first and foremost among the labourers in this field. Of

equal note are his views on the higher part of the theory of probabilities and on formal logic.

:

In logic Dr. Boole has started one of the most remarkable developments of our day in originality and suggestiveness the most remarkable, though far out of the common track. He has turned the whole of pure logic into pure algebra, so far as its language and transformations are concerned. He had done this without any intention of publication, and his mind was recalled to the subject by the discussion between Sir William Hamilton and Professor De Morgan. He accordingly published his first work on logic, which appeared, as it chanced, on the same day as Mr. De Morgan's "Formal Logic." It would take many pages to compare the two systems, which are very different, though there is much. resemblance to those who only know that symbols are symbols. Hebrew and Sanscrit have a certain likeness in the eyes of those who know not a word of either the chief difference being that Sanscrit letters seem strung on a clothesline, while Hebrew letters look as if little chips had been knocked off and were lying about. The corresponding distinction between Dr. Boole and Mr. De Morgan is, that the first seems to deal in and, the second in accents and parentheses. The true distinction is that Mr. De Morgan, having some fundamental points closely in accordance with Dr. Boole, brings these points in aid of his developments of the common system; while Dr. Boole, removing himself altogether from common thought, finds in the language of algebra, as it stands, and in the rules of algebra, as they stand, the expression of all the laws of thought. Anybody can understand that, if "everything be either Xor Y," we may therefore say, "that

which is neither nor Y does not exist." The reader of Dr. Boole's system sees the first in

XYXY = 1,

and the second in

(1X) (1 Y) = 0; and a school-boy passes from one to the other, under very different meanings, by the rules of algebra.

Mr. Mansel objected to Mr. De Morgan that he made thought a branch of algebra instead of algebra a branch of thought. Mr. De Morgan replied by declaring that he did no more than show laws which work under cover in thought, the genus, but which work by daylight in algebra, the species. The objection, if valid, would apply still more strongly to Dr. Boole; and the answer would be still more to the point. When the approximation which is beginning, after long separation, to take place between the two great branches of exact science, logic and mathematics, shall have created a school of combined logicians and mathematicians, Dr. Boole will be not merely admired by logicians and mathematicians both, but appreciated.

But

His private character will be remembered with high regard by all who were acquainted with him. There are men benevolent as he was, as amiable, as charitable, as upright as he was. there are very few who can uphold a strong opinion as firmly as he did, without rubbing an opponent the wrong way of the hair. He managed to show the other party a most dogmatical certainty that he himself was wholly right, without making prominent his sense of the necessary consequence that the other party was wholly wrong. And thus we end the few words we can give to the latest instance of combined genius and goodness, cut off in the midst of a great

career.