and others. 6. It is the central hoard of treasure, to which resort is always had for gold and silver required either to settle an adverse balance with the foreigner, or to provide for the occasional needs of the internal trade. 7. It is the issuer of a paper circulation of unquestioned credit in every part of the United Kingdom. 8. And with the growth of the commerce and wealth of the country, it becomes every year more and more an international centre towards which gravitates the adjustment of all large financial operations, wherever they may originate.

It is one of the most valuable practical advantages of this country to possess an institution of credit so powerful and so perfect as the Bank of England, and to be able to reconcile its supremacy and preservation with the existence around it of the utmost freedom in the practice of all other kinds of banking, private and joint-stock, for, happily, all the former monopolies possessed by the Bank of England have long since disappeared."

Such a reform would also reunite the functions of Banking and Issue. Under the peculiar circumstances of the Bank of England, they are wholesome and convenient parts of the same business. Nobody in these days believes that the amount of outstanding circulation at any given time, can be determined by the will or desire of the issuer. The public take out and keep out just so many bank notes as their transactions require, and not a single note beyond, and for three obvious reasons, viz. (1.) Interest or expense of some kind is incurred by the retention of the note. (2.) It may be stolen, lost or burnt. (3.) Except for purely retail purposes, it is less convenient than a cheque, because it will not pay by one operation fractional All the practical evidence collected by all the Currency Committees is consentaneous in declaring that no banker ever dreams of forcing out his notes so long as they are strictly convertible into gold on demand. And besides, if this testimony was not enough, we have the evidence of the public returns of the circulation, showing year by year the same cycle of elevations and depressions, and in the same months or weeks. That is to say, the circulation describes a curve of its own, so regular that its course can be accurately foretold-a result utterly at variance with any theory of irregular private action.

sums.

A restoration to the Bank of the function of issue would, moreover, get rid, per saltum, of the irritating and spasmodic jerks

It is sometimes said, that the exclusive right to circulate notes in London and sixty-five miles round it, is a grievous monopoly. The answer is that no London bank would think it worth while to attempt a note circulation even if the law was altered.

7

The Remedies required.

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which now constantly occur at the end of each revenue quarter. At these times the out-standing notes are generally increased for a few weeks by a million or two, and for purely internal purposes, the payment of dividends, salaries, tradesmen's accounts, and the like. Under the present system this temporary and natural demand for bank notes can only be met by a transfer of gold from the banking to the issue department; and it occurs continually that the banking reserve is so ill prepared to bear the transfer that the directors feel themselves compelled to raise the rate of discount. For example, last autumn the Bank rate was raised in nine days (28th Sept. to 7 Oct., 1865) from 4 to 7 per cent., in consequence of a temporary increase of 1 millions in the circulation."

It will be said, we know very well, that if the functions of banking and issue were re-united, and the Directors placed in command of all the assets of the Bank, as their resource for all its liabilities (bank-notes included), two evils might arise. First, the reserve, as in 1835 and 42, might be run too low; and, second, that the Bank Court might be unskilful or negligent.

To take the second point first, the reply is, as we have shown above, that the Act of '44 leaves the really important functions of the Bank-namely, the banking business and the banking reserve just as much or rather more at the discretion of the Directors than ever it was. The Directors are at perfect liberty, so far as the Act goes, to mismanage the Banking department up to the point of stopping payment, and on three occasions it has virtually and in point of fact stopped payment.

As regards the first point, we say with all the emphasis we can command, that the entire question of administering the monetary system of this country resolves itself into the magnitude of the Bullion Reserve of the Bank of England. The present system works badly, painfully, and dangerously, because it has at the bottom of it nothing more substantial than the five, six, or seven millions of reserve in the Banking department. But let the reserve be raised to such a point that on the average of the year, or some more convenient period, it shall be not less than say fourteen millions, and the whole complexion of the case would be changed. A transmission of three or four millions of bullion goes a long way in these rapid days in adjusting even a large foreign balance; and even four millions taken out of fourteen is a very different measure, and leaves behind it a very different residue compared with four millions taken out of eight or nine. Moreover, it might be a by-law of the Bank Court that for every fall of half a million in the treasure below say twelve millions, the official rate should be

raised a half per cent., or in some other proportion to be determined after due inquiry. It is pitiful and mean that a country like this, containing millions of people dependent on trade, cannot afford or manage to keep a Bullion Reserve so reasonably sufficient for the amount and uncertainties of the business carried on, that the arrival or departure of a few parcels of gold or silver produces commercial sunshine or storm. It is with a view of protecting this Reserve that the suggestion is made that the Bank should not go into the discount market when the rate falls below 4 per cent. The effect of such a plan would be that the Bank's securities would run off, and that its reserve would increase; and the reserve so increased would be found ready to meet the demands upon it which all periods of cheap money infallibly produce sooner or later. The Bank would sustain some loss by such a retirement for a time from the discount market, but not by any means so much loss as may at first sight appear. Whatever the loss might be, however, it must be made good to the Bank proprietors, and such an arrangement would not be practically difficult.

We have said nothing concerning the suggested remedy of what is called a suspending supplement to the Act of '44; that is to say, a clause providing for the suspension of the Act at the discretion of the Chancellor of the Exchequer and Prime Minister, acting with or without the concurrence of the Bank Such a clause would manifestly reduce the whole measure to mere book-keeping, and would leave the country burdened with all the evils of the system under every set of circumstances except those of overpowering panic.

The practical steps to be now taken are not difficult of determination.

The chambers of commerce and the large mercantile towns should move the Government and the House of Commons for the appointment of a Royal Commission to consider the existing Acts relating to banking and currency in the United Kingdom. A royal commission fairly chosen would be a more efficient instrument than a committee of either House of Parliament. The commissioners should be instructed to report their recommendations and the evidence received on or before March in next year. The public and parliament would then possess materials on which further discussion could proceed and further legislation could be founded.

N. W.

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ART. VI. (1.) Various Papers on Linear Transformations, Differential Equations, the Theory of Probabilities, and other Branches of the Higher Mathematics. By GEORGE BOOLE.

(2.) The Mathematical Analysis of Logic. By the Same. Cambridge. 1847.

(3.) An Investigation of the Laws of Thought. By the Same. London: Walton & Maberly. 1854.

(4.) A Treatise on Differential Equations. By the Same. Cambridge. 1859. Second Edition, Revised by I. Todhunter. Macmillan & Co. 1865.

(5.) A Treatise on the Calculus of Finite Differences. By the Same. Cambridge: Macmillan & Co. 1860.

(6.) A Treatise on Differential Equations. Supplementary Volume. By the late GEORGE BOOLE, F.R.S., Professor of Mathematics in the Queen's University, Ireland, etc. Edited by I. Todhunter, F.R.S. Cambridge: Macmillan & Co. 1865.

We believe that to the great body of the reading public the name of George Boole first became known, if indeed it has yet become known, through the announcement of his death; the announcement being accompanied in a few of the papers by a brief sketch of his life and works. Boole's researches were not of a nature to be appreciated by the multitude, and he never condescended to those arts by which less gifted men have won for themselves while living a more splendid reputation. When a great politician dies, or any man who has filled a large space in the public mind, and made a noise in the world, the newspapers long ring with the event. But it is otherwise with the great thinker, the mathematician or the philosopher, who has laboured silently and in comparative seclusion, to extend the boundaries of human knowledge. When such a man is removed by death there are public journals, even among those professedly devoted to literature and science, which can dismiss the event with a few faint and cold remarks.* But time rectifies all that. It is found sooner or later that no reputation, however brilliant, is permanent or durable which does not rest on useful discoveries and real contributions to our knowledge. The names that live in the annals of philosophy are not those of men who achieved

The Athenæum for December 17, 1864, after noticing the death of an American writer, says, 'Nearer hoine, science has suffered some loss in the demise of Professor Boole, of Queen's College, Cork, in which 'institution he filled the mathematical chair. The Professor's principal 'works were, "An Investigation into the Laws of Thought," and "Differential Equations," books which sought a very limited audience, ' and we believe, found it. He died on Friday [Thursday], last week.'

immediate fame; they are rather the names of men who, not thinking of fame, betook themselves to the arduous path of original investigation, and succeeded in adding new truths to the existing stock. Their presence was perhaps unobserved by the throng, and comparatively few even heard of their genius, but their works live when they are gone, and their influence and fame are real and abiding. We propose to devote a few pages to an account of the life and writings of the remarkable man, a list of whose principal contributions to science we have placed at the head of this article.

George Boole was born in the city of Lincoln on the 2nd of November, 1815; he died at Ballintemple, near Cork, on the 8th of December, 1864. The facts of his personal history are few and simple, but they serve to illustrate how a man of humble origin, with very slender aids from without, may, by the force of genius and the labour of research, rise to a position of great eminence. We give the facts from documents in our possession, and other sources of information on which we can rely.

The life of Boole may be divided into two distinct periods, the leading events and features of which are soon described. The first, extending over four and thirty years, was, excepting only a short interval, spent wholly in his native county, and for the most part in his native city. This was the period in which he laid the foundation of his future greatness; his mind became furnished with rich and varied stores of information, and he acquired a mastery over processes of thought and methods of mathematical investigation that yielded the most valuable and important results in after years. The second and shorter period commenced with his appointment to the professorship of mathematics in the Queen's College, Cork, the duties of which he entered upon at the opening of that institution in the year 1849, and continued to discharge until his premature and unexpected death. It was during this latter period that he gave to the world those works on which his fame as a philosophical mathematician will principally rest. His father was a tradesman of very limited means, but held in high esteem by those who knew him. Having nothing to support his family but his daily toil, it was not to be expected that he could expend much on the education of his children; yet they were not neglected. Being himself a man of thoughtful and studious habits, possessed of an active and ingenious mind, and attached to the pursuit of science, particularly of mathematics, he sought to imbue his children with a love of learning, and employed his leisure hours in imparting to them the elements of education. The estimation in which his abilities were held by his wife will be learnt from