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mation which it contains will render it acceptable as a reading-book to many who have not the means of procuring a separate work on each of the subjects on which it treats. Generally the facts seem to be accurately stated, though we observe errors in it, for instance, where Mr. Rhind makes the Australians and the inhabitants of Madagascar belong to the Malayan race.

JUDGMENT IN THE CASE OF THE KIDDERMINSTER SCHOOL. Sir G. TURNER has recently delivered an important judgment relative to Kidder. minster Grammar School, declining to interfere with the scheme of the Master laid down for its management in 1844, with the exception of the exclusion of Dissenters from its benefits, which he reversed, and affirmed an important principle in regard to grammar-school regulations, which he thus laid down :

“It was said that no boarders ought to be taken by the masters, and that this rule ought to be applied to all schools, the endowments of which afforded a sufficient income for the master without the aid of boarders. In support of this prin. ciple he was referred to the decisions of the late Vice-Chancellor of England in the cases of the Tiverton and Manchester schools. The Vice-Chancellor had proceeded on the terms of these endowments, and on what he collected to have been the opi. nion of Lord Cottenham in the Manchester case. Whether the Vice-Chancellor had rightly construed the endowments before him, or had rightly gathered the opinion of Lord Cottenham, it was not for him to say; but, after examining the cases, he could find no such rule laid down. It was clear, from many cases before Lord Cottenham, that he was averse to the admission of boarders, but he could not find that he had prohibited it. The cases referred to, however, had proceeded on the construction of particular endowments, under particular circumstances, and the present case was one of a different endowment, under different circumstances, The observations of Lord Eldon, in considering whether the master of a grammar school should be allowed to take boarders, in the case of the Attorney-General v. Hartley, were these :- In the evidence I find no contradiction to the allegation that children boarding with the inhabitants of Bingley have been admitted, and that obliges me to consider whether, if you destroy the right of the master to take boarders, you can leave untouched the ancient practice with respect to other persons taking boarders. I think it probable, from the evidence, that the boarders were first introduced at an early period of the mastership of Mr. Hudson. What is the effect of the fact of the master not having taken boarders before that time is a question to be considered by and by, but if even up to this time the master had received no boarders, there would be considerable difficulty in determining that for that reason he should not hereafter have them.' The evils apprehended were those arising from the inequality of rank and from the degree of favour with which the boarders might be treated. The latter evil, if it occurred, would be an abuse on which it would be the duty of the trustees to interfere. With regard to the former, inequalities of grade, must always exist, and upon this point he might refer to what had been said by Lord Lyndhurst, in the Attorney-General v. Lord Stamford, speaking of free grammar schools, and of the association of children of parents of different ranks of life :• There is another consideration also connected with these establishments-that they are the avenues by which the humbler classes, by industry, activity, and intelligence, can force their way into the highest situations of the State, and by fur. nishing the means of uniting at an early age the upper and lower classes, they tend to bind together by the strongest ties the whole system of society.' Against the necessity or expediency of receiving boarders it was objected the income of the school was sufficient to obtain a competent master; but the question was not whether a competent master could be bad, but by what means the services of a superior master might be obtained. It must also be remembered that there was some evidence of a practice having formerly existed of taking boarders; and that after what had taken place boarders could not be excluded during the incumbency of the present master. He was of opinion that the Court ought not to interfere with the scheme on that point,"

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ON THE STUDY OF ABSTRACT SCIENCE IN CONNECTION WITH

INDUSTRIAL EDUCATION, (Extracted from the report of Dr. Lyon Playfair's Lecture.) The raw material used by industry for the production of useful objects doubtless forms the basis of manufactures, but possesses a fluctuating value in relation to that of the object into which it is converted. In the successful prosecution of manufactures, apart from the influence of mere capital and labour, two elements are involved, each forming a factor which, in a competition of industry, may be made to assume very different values. The first element is the raw material; the second, the skill and knowledge used in adapting it to the purposes for which it is designed. Thus in America cotton is indigenous, and consequently cheap; and fuel, the other raw material employed in its conversion to a textile fabric, is not expensive. In England the same cotton is much dearer, but the fuel may be assumed to be equal in price. The competition between the two countries in respect to calico, resolves itself into the necessity that England, to overcome the disadvantage of the greater cost of the raw material, must infuse a greater amount of skill and knowledge into the processes employed in its adaptation to useful purposes. England bas succeeded in doing this, and, consequently, the mills of Manchester may render unproductive the mills of Lowell. But reverse the conditions of the two countries, and a similar result attests the truth of the same principle. Sheffield produces steel, which in large quantity is exported as a raw material to America. The history of that country has created a knowledge of the conditions required for the manufacture of edge tools. The forests were not cleared, or the prairies converted into arable land, without that observing nation understanding the qualities and the requirements of the axe, the adze, and the spade. The knowledge thus attained was applied to the manufacture of edge tools ; and commerce returns to England its own steel, but under a new form, and endowed with an excellence, a temper, and a cheapness yet unattained by our artisans. Without this application of greater skill it would have been impossible for America to have competed with the country which furnished the raw material. A nation, if it combine ordinary intelligence with its local advantages of cheap raw material, may long preserve almost a monopoly in special manufactures, and will continue to do so, either until the competing nation has risen so high above her in intelligence as to make this more than an equivalent for the local advantage of the other, or until a greater equalization in the price of the raw material renders a small amount of superiority in the intellectual element of sufficient importance to secure successful competition. But should any great transition of the world take place, and should means arise by which local advantages were levelled, and the raw material confined to one country became readily attainable by all, the difference in its cost being inconsi. derable, then the competition in industry must become a competition in intellect; and that nation which most quickly promotes the intellectual development of its artisans, must, by an inevitable law of nature, advance ; while the country which neglects its industrial training must as inevitably recede. It requires no mental acumen to perceive that we are rapidly approaching to, if we have not yet arrived at, this period of wonderful transition when nations must speedily acquire the levels due to their different amounts of intellectual development. It is quite true that a superabundance of capital may for a time preserve a country from a quick depression, even should it lapse in its intellectual training ; but the support thus given can only be temporary and illusory, for if, by the purchase of foreign talent, the necessary knowledge is infused into home manufactures, this can only have the effect of raising the intellectual element in the foreign country, and thus finally accelerate its success as a competing nation. There never was a time when was so necessary as now that skill and science should be united for the promotion of the industrial arts.

At former periods of human history local advantages or accidental combinations were the foundation of a nation's prosperity. The time is not distant when it was thought that the possession of mineral fuel indicated a country as the natural manufactory of those necessaries of life which employ machinery in their production, while the existence of large tracts of land, warmed by a genial sun, stamped another nation as essentially agricultural, and employed its population in the labours of the field. Each country fell into a routine of manufacture, and Italy and France produced their silks and shawls with as little thought of competition as England its machinery and calicoes. Science in advancing has created resources unthought of before, and has removed those local barriers which had retarded the progress of industry. Countries

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are no longer confined in their aspirations by smallness of territory, for this, by the aid of science, enlarges its powers. The country which in its agricultural poverty can support only a scanty and miserable population, expands itself for the reception of increased numbers as the produce of its land augments; and thus knowledge in the improvement of agriculture wins by a bloodless victory vast additional territory to aid in the industrial resources of the nation, for a land with a two-fold increase in agricultural production has, for all practical purposes, unfolded itself to twice its size. Science, in its progress, is improving and simplifying processes of manufac. ture, while it is opening at the same time a communication between the nations of the earth. The amazing facilities of transport afforded by the introduction of steam, enable a ready interchange of their natural riches, and mere adventitious local ad. vantages, apart from skill and science in their adaptation, become of much less moment than they formerly were. The proof of this is in the fact that the staple manufactures are now carried on in all parts of Europe, and that there is a constantly increasing and active competition of most of the great nations in all the markets of the world. If England still continue in advance it will not be that her coal and iron are plentiful, but because she unites science with practice, and because she enables her discoveries in philosophy to keep pace with her aptitude in applying them. But is it true that England does act thus wisely? and is it true that science does hold in this country its just position in public esteem, or that it is fostered sufficiently to make that progress which it is now doing in other lands? To all such questions a negative reply must be given ; for beyond a theoretical recognition of the importance of science in its relations to practice, and the establishment of this museum and college-a very important measure I admit—the State and the public only look to the empirical result, and have not deemed it necessary to foster that knowledge which directly led to it. But England is the only European state which is thus blind to its own interests, and which has not yet thoroughly awakened to the importance of giving an intellectual training to those intrusted with its manufactures. This is proved by the large endowments given by foreign governments for the support of institutions connected with industrial science, and it finds expression in the writings of their thinking men.

Hour after hour might be employed in recording the triumphs of chemistry in its investigations into the play of the organic elements. Looking back no further than the last few years you see how it has thrown open the most hidden processes of animal and vegetable life-how it has taught us to increase and economise the food of man. It is even yet the practice of those who have not followed her discoveries into the wondrous affinities of the few simple organic elements, to depreciate the importance of following their infinite creations. If, however, there were no other result from doing so than the one great achievement of having explained the ingredients in food used to build up the muscular frame and those employed in the support of animal heat, the importance of that discovery would have repaid all the labour of the past century. Almost all the staple manufactures of this country are founded on chemical principles, a knowledge of which is absolutely indispensable for their economical application. In a few educational establishments, and in some of our Universities, the alphabet of chemical science is taught; it requires an institution such as this, devoted to a special object, to teach how to use that alphabet in reading manufactures. The extension of scientific and technical education is a want of the age.

• The great desideratum of the present age,” says Liebig, “is practically manifested in the establishment of schools in which the natural sciences occupy the most prominent places in the course of instruction. From these schools a more vigorous generation will come forth, powerful in understanding, qualified to appreciate and to accomplish all that is truly great, and to bring forth fruits of universal usefulness. Through them the resources, the wealth, and the strength of empires will be incalculably increased.” Institutions such as this are not substitutes for, but supplements to, the Universities. It is the industrial training which we profess, and everything else is made subsidiary to that object. Not that we do or should forget abstract science as such, because I believe the disco. veries in abstract laws are of more real benefit to industry than their immediate applications. The technical man is perhaps of more use to bimself and to his time and generation than he who discovers the abstract laws which the former applies to the purposes of industry; but it is the abstract philosopher who benefits all time and confers universal and eternal benefit on society.

After giving numerous examples of the advantages of scientific knowledge to the

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manufacturer, and of the failures which have continually resulted from the want of it,-Dr. Playfair thus concluded :

For a long time practice, standing still in the pride of empiricism, and in the ungrateful forgetfulness of what science had done in its development, reared upon its portal the old and vulgar adage : “An ounce of practice is worth a ton of theory. This wretched inscription acted like a Gorgon's head, and turned to stone the aspirations of science. Believe it not; for a grain of theory-if that be an expression for science-will, when planted, like the mustard-seed of Scripture, grow and wax into the greatest of trees. The pressure and difficulties of the age, and the rapid advancement of intellect in continental nations, have been the Perseus to cut off this Medusa's head from the industry of England, and to fix it on the shield of Minerva, who turns to stone such as still believe that science should be ignored by practice, but, reversing that shield, wisely conducts those who would go further under her guidance. It is now rare to find men who openly avow, although they actually entertain a belief in, a necessary antagonism between theory and practice. Theory is, in fact, the rule, and practice its example. Theory is but the attempt to furnish an intelligent explanation of that which is empirically ascertained to be true, and is always useful, even when wrong. Theories are the leaves of the tree of science, drawing nutriment to the parent stem while they last, and their fall and decay affording the materials for the new leaves which are to succeed. I have now said enough to show you that it is indispensable in this country to have a scientific education in connexion with manufactures, if we wish to outstrip the intellectual competition which now, happily for the world, prevails in all departments of industry. As surely as darkness follows the setting of the sun, 80 surely will England recede as a manufacturing nation, unless her industrial population become much more conversant with science than they now are.

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ANSWERS TO THE MATHEMATICAL QUESTIONS.

Ques. 114.- Proposed by Mr. O'Clazey, Durham. Ir a person travel round the earth at the equator, how many square mil of its surface may he see, supposing the earth to be a perfect sphere, 8000 miles in diameter, and the height of the person's eye five feet? Answered by H. P., Mr. Sothern, Mr. Salter, Mr. Dyer,

Prismoid, and Mr. Righton, Jun. The surface to be found will be very nearly the convex surface of a cylinder, whose girt is the circumference of the earth and height equal to twice the distance seen by the eye of the observer when elevated 5 feet above the earth.

Circumference of the earth 8000 x 3•1416; and by Tate's “ Geo. and Mensuration,” page 59,

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5 ... Surface seen by the observer 8000 x 3.1416 x 2 8000 x

5280 138351 sq. miles. Ques. 115.- Proposed by Prismoid, Tewkesbury. To determine an expression for the area of an octagon in terms of the side. Answered by Mr. Sheppard, Mr. Levy, Mr. Herbert, and

W. Thompson. Here we have, putting a for the side,

180° Area polygon of n sides

a>. cot

4
.'. Area polygon of 8 sides 2 ao cot 2210

= 2 a® (1 + 12).

n

n

Ques. 116.---Proposed by Mr. Sheppard. A wheel 6 feet diameter is obstructed by a stone 3 inches high. Required the force necessary to surmount this obstacle, supposing the line of traction to pass through the axis at an angle of 30° to the horizon, and the load upon the axis to be 10 cwt. Answered by Mr. Levy, A.M., Prismoid, Mr. Herbert, and

W. Righton. Here the wheel will turn upon the stone as a fulcrum. Suppose two perpendiculars to be drawn from this point, one (a) to the line of traction, and the other (6) to a vertical line let fall from the axle; then we have by the equality of moments :

P xa = 10 cwt. x b.
Now b = (37) – (31 – 4)2 = 14 feet,
and by trigonometry we find a = 3.22307 feet;

hence we have P x 3.22307 = 10 x 14,

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Prismoid, ang. 114, 115, 116; W. H. Levy, Shalbourne, ans. 114, 115, 116; A M., ans. 114, 115, 116; W. Thompson, Chelsea, ans. 114, 116; J. Salter, Durham ans. 114, 115, 116; S. Dyer, Wanstead, ans. 114, 115, 116 ; J. Rowlatt, Evercreech, ans. 114, 115, 116; J. Sheppard, ans. 114, 115, 116; J. Herbert, Woolton, ans. 114, 115, 116; H. P., Newcastle, ans. 114, 115, 116; T. Sothern, Burtonwood, ans. 114, 115, 116; T. Abbott, ans. 114, 116; W. Righton, Jun., ans. 114, 115, 116; M. N. J., ans. 115; E. Carthew, Roehampton, ans. 114.

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NEW QUESTIONS,
TO BE ANSWERED IN OUR NUMBER FOR JANUARY, 1852.

Ques. 117.- Proposed by A. M. At what time between eleven and twelve o'clock will the hour and minute hands of a watch be equidistant from 1?

Ques. 118. Proposed by Miss Levy. A ship sails from Liverpool, lat. 53° 24', to New York, lat. 40° 42', and during the voyage touches the tropic of Cancer. Find the length of the voyage, supposing it to be the shortest possible, and allowing the earth to be a perfect sphere whose circumference is 25,000 miles.

Ques. 119.- Proposed by J.J. R., Portsmouth. The total weight of an engine (including the driving wheels with their cranked axle, which weigh 3 tons,) is 23 tons. If the train be moving at the rate of 60 miles per hour, and the centre of gravity of the driving wheels be displaced 2} inches during a revolution, the diameters being 5 feet; find whether or not the wheels will have a jump on the rail.

To Correspondents.

E. J. Bi's communication in our next.

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