fused, and the higher manual arts are well paid, a compositor should work at his own book; but we do hold it to be rather a curious phænomenon, that one of the earliest of such books should be an attempt to associate metaphysics with mathematics, or to introduce the former into the latter, to a greater extent than is usually done. The following is a brief description of the character and contents of the work.

It divides mainly into two parts: the first, on the complete explanation of the symbols of algebra; the second, on the relation of successive differential coefficients, considered as standing to each other in the relation of product and power, or effect and cause. The first part may be looked on as an attempt to evolve the contents of Dr. Peacock's algebra (first edition) in a more à priori form, and to make them the necessary consequences of a metaphysical view of the fundamental operations. Those who know and profit by the clearness of the principle of fluxions (unfortunately, as we think, discarded with its language), will look with satisfaction at Mr. Paterson's attempt to reinstate the differential coefficients in their old position of indicating something more than result of algebraic operation. Every reader who can truly profess to understand the subject, must, if he have thought about the progress of his own mind, remember how much he was indebted to the mechanical connexion of the function and its first and second differential coefficients with distance, velocity, and force. Mr. Paterson has endeavoured to put this connexion on a more abstract footing, and to make the laws of algebraic development a consequence of his treatment of it. We doubt if his success is complete; that is, we doubt whether a mathematical proof of Taylor's theorem fairly results: unless, indeed, the author had more in his mind than he has fully made manifest; a reserve which should always be made in matters metaphysical. Be this as it may, we can but express a hope that, both in Europe and America, investigators will attempt to sound the channels which connect the mathematics with the fundamental laws of thought.

Mr. Paterson is evidently well-read in the writings of mental philosophers. He is far too metaphysical for the general run of mathematicians, and vice versa. Nevertheless, as there are always a few to whom such speculations are welcome, and, even where they do not convince, suggestive, and as upon these few mainly depends the advance of mathematics as a discipline, we hope that he will find encouragement to proceed, and that we have not seen the last of him. Four Introductory Lectures delivered at the Government School of Mines and of Science applied to the Arts; Museum of Practical Geology.

The struggle carried on for some years between the Gymnasialisten and Realisten of Germany has at length found distinct expression in England. Science has found her advocates in the Jermyn Street Institution, who earnestly uphold her claims, and forcibly protest against our present exclusively classical system of education. In 1835, a proposal was made by Sir Henry De la

Beche to take advantage of the opportunity afforded by the Geological Survey for the collection and classification of specimens, the result being that space was granted by Government for the reception of such specimens. As years rolled on the collections increased, additional space was needed, and "finally the necessity of proper accommodation became so pressing, especially after 1845, when the Geological Survey and the Museum of Practical Geology were placed under the same department," that the building in Jermyn Street was erected.

In his Inaugural Discourse, Sir Henry conducts us through the building and describes its stores-its specimens of architectural stones, ceramic products, collections of minerals and fossils, its chemical laboratory, metallurgic and mining departments. Those who have visited Durham Cathedral and other similar edifices in this country, and seen the havoc made of the stone by atmospheric action, will appreciate the importance of a collection for architectural purposes. Had such a collection been open to those who raised the Four Courts in Dublin, the irretrievable ruin of that splendid edifice by atmospheric influence might have been avoided. Our advance in ceramic manufactures is illustrated by the progress made in the transfer of prints to porcelain : a century ago one colour only could be transferred; we can now paint a picture. Referring to the ignorance generally prevailing in mining districts as to the value of minerals, the following striking fact is cited. "Ores regarded only as important for the copper they contained, were raised upon the property of the Duke of Argyll in Scotland. After a time the works were abandoned, as the copper found in the ores was not sufficiently abundant to pay for the cost of obtaining them, and much was thrown aside as not worth dressing. The Duke, impressed with a certain character in the ores, brought specimens to this Institution for analysis; and it was found that they contained 11 per cent. of nickel, a valuable metal, and, as you are aware, extensively employed at this time in different alloys, such as those known as German silver." "Even within these few days," adds the lecturer, "a case has occurred in Devonshire where a field-wall was constructed of grey copper ore, and the breaking of a gate-post led to a knowledge of the fact." Referring to the reclaiming of mud-banks which surround estuaries, the lecturer observes, The body of water entering and passing out is important; and yet what do we often find done, and done, too, by Act of Parliament? The body of water entering, and consequently passing out, is diminished for the purpose of reclaiming, as it is termed, certain mud-banks, often extensive; thousands of tons of water are thus sometimes cut off from performing the work by which they aided in keeping the channel to the sea clear; the bottom of the channel rises, and the port is damaged."

Calling the mineral produce of Great Britain 1, that of Russia is about, of Prussia. of France, of Sweden, of Norway. A country possessing such vast resources in this respect as Great Britain, might be expected to devote particular attention to this point; but this is not the case. "" Although the raw mineral produce of

Great Britain and Ireland is valued at £24,000,000 per annum, or about four-ninths of that of all Europe, there existed until now no means in this country for affording needful instruction to those who thus raise so large an amount of mineral matter; all was left to chance, and the result is well known. Many who can afford it go to other lands to study in the mining schools provided by their governments; some fight through their difficulties at home, becoming valuable and useful men; while the mass of our miners remain uninstructed, except so far as they can pick up practical information from each other in the mines." "Are our miners," demands the lecturer, "less deserving of attention than those of other lands, or are they supposed to be so dull and disinclined to knowledge as not to be capable of profiting as well as the miners of other nations by instruction? Let those who thus believe visit our mining districts, especially such as are metalliferous, where the miner has so often to gain his daily bread by the exercise of his judgement, and they will speedily be undeceived. They will find men as able and willing to profit by instruction as elsewhere in our land. They will see many with powerful minds, who have risen from amid all their difficulties, adding continually and greatly to our stock of practical knowledge, but who would evidently have accomplished far more, if in their early day they had possessed the advantage of starting with the knowledge of the time applicable to their pursuits."

The wants here indicated it is the design of the School of Mines in some measure to supply. It is proposed to instruct by means of the collections, the laboratories, the Mining Record Office, the lectures, and the Geological Survey. It is also purposed to explain by evening lectures to the working men of London,-those really engaged in business, and whose good characters can be vouched for by their employers, such parts of the collections as may be thought to be usefully interesting to them. There are also indications of movements in this direction in the mineral districts; and it is trusted that those who locally distinguish themselves by the application of their abilities may find in the Government School of Mines, free of cost, the means of still further advancing their own knowledge.

We next take up the Introductory Lecture of Professor Playfair, On the National Importance of studying Abstract Science. This lecture opens the Chemical Course for the present session. Ably and convincingly the writer demonstrates the dependence of practical results upon abstract investigations; proves that discoveries, apparently the most remote and unpromising, have resulted in the most important practical issues; takes us to the gardens of the Luxembourg, and shows us Malus looking at the open window through a crystal of calcareous spar-apparently a most unpractical act, yet one, by the following up of which we are now enabled to pierce the ocean and investigate its rocks and shoals, and which in the hands of Biot has led to the most refined method of ascertaining the quantity of sugar in saccharine solutions; introduces us to Galvani operating upon a dead frog on the iron palisades of Bologna, and shows how the discovery there made has resulted in the electric telegraph, and

the manifold applications of the electrotype; exhibits the safety-lamp growing out of the thought of Davy, and chloroform distilling from the brain of Dumas; dwells upon that domestic wonder-a lucifermatch, and shows its progressive development up to its present stage. Schoenbein discovers that cotton, without changing its appearance, becomes more destructive than gunpowder; another chemist finds that it is soluble in æther, and in this state becomes, in the hands of the surgeon, an artificial skin to cover the wounds which it made in its old form. Looms are not now required to make coarse calico fine, for immersion in soda makes it take the form of fine cambric. In the sixteenth century Paris lighted up her streets by fires of pitch and rosin, but to the chemist was reserved the triumph of superseding the clumsy invention by our brilliant coal-gas. These were results unsought for; they are the necessary 'off-shoots,' as the lecturer aptly terms them, of abstract investigation. The necessity of cultivating abstract science is enforced by the fact, that local position no longer gives to nations that superiority which it formerly did. The tendency of things is to make the competition of nations a competition of intellect, and the unfitness and insufficiency of English training for this great race are strongly deprecated. One of the lecturer's remarks in connexion with this portion of his subject has given offence to the Times newspaper: "The philosophy of our times does not expend itself in furious discussions on mere scholastic trivialities or unmeaning questions of theology." It is not the irrepressible yearnings of the human heart of which the Times speaks that are here aimed at, but it is the over-refining of the human intellect-those 'mumps and measles of the soul' which find material for quarrelling and discussion in objects intrinsically worthless. How many months have passed away since the entire theology of England was in spasms over a crotchet of this character?

A few weeks ago, we happened to converse with a thoroughly practical gentleman on scientific subjects. He spoke of a machine recently applied to the electric telegraph, and in which the electricity was generated by magnetism. The result delighted him, and he praised the genius of its Birmingham discoverer. Before us hung a picture of Faraday-one of those capital prints got up by George Ransome of Ipswich; we looked upon the pale features and massy brow, stamped with a certain energy of conflict, as if nature sometimes required to be forced as well as wooed; but no association existed in the mind of our companion between the picture and the machine. The genius which gave this wonderful expansion to the simple experiment of Arago, and to which all practical applications of magneto-electricity must be traced, as streamlets to their spring, was never once thought of!

We now pass on to the Introductory Lecture of Professor Forbes, on the Relations of Natural History to Geology and the Arts. We felt a strong desire to shake the author by the hand as we read his lecture. There is a force and fire within this man which cannot fail to gather disciples round him. In these pages we have clearness of conception, vigour of utterance, and an intellect which can pierce

details, and hold communion with "the great universal thought which pervades the one great creative action." This man is master of his materials, and handles them with the audacity of one who knows his own power; the rocks are plastic in his hand, and the fossils live again. Two grand qualifications are necessary in an educator-the ability to provoke and the ability to instruct; the former, though often forgotten, is the more important of the two. There is merit in the smoothing away of a difficulty, but far greater merit in arousing an amount of force able to cope with and to overcome it. These two qualifications are, if we mistake not, possessed by the man before us. There is life in his sentences which propagates itself to those who read them. Who could resist the following?"In conducting the business of this class, I look forward to the holding of field excursions, regarding them to be quite as essential as lectures for the instruction of the student, who, to benefit by his studies, must become a practical-fossilist, and learn to observe carefully fossils in situ, and appreciate on the spot the evidence afforded by their associations. During the progress of our Winter Courses this can be done effectually in the neighbourhood of London, or by means of the facilities of transport afforded by lines of railroad. I trust that before the end of this session a compact band of undaunted investigators, belted, strapped, and bag-bearing, armed with stout hammers and sharp chisels, under the veteran generalship of our Director-in-chief, and officered by my mineral and geological colleagues and myself, will make the rocks shake and yield up their treasures for many a mile around the great metropolis." Such appeals thrill the heart of the student like electric fire, and awaken an ardour which renders his task heroic.

The lecturer assigns a high vocation to the naturalist. "It is not an uncommon fancy to suppose that naturalists are occupied entirely with the naming and describing of the kinds of animals and plants; that provided they can enumerate, in clear though technical language, the characteristics or features of a being submitted to their examinations, usually in the state of a preserved specimen, and, on discovery of the species being one hitherto unnoticed, give it a name by which it may be remembered by their brother naturalists to the end of time, or thereabouts, they have attained all their aim and fulfilled all their ambition. This notion of their offices and duties is a libel. It takes notice of only a fragment of their labours. To name and describe are but to enrol an object with a true spelling and correct definition, in the great dictionary of science. Words in dictionaries are exhibitions of the raw materials out of which literature is made; and species arranged in zoological and botanical systems are orderly and beautiful displays of the raw materials of natural history science. Words may be wasted and species misused. But the study of species, which is the basis of all natural history science, does not take note merely of their external, or even their internal organization. It deals also with their relation to conditions in time and space. It seeks out the epoch of their first appearance, and traces them through their diffusion under favouring, or limitation and exPhil. Mag, S. 4. Vol. 3. No. 15, Jan. 1852. F