Answered by Mr. Herbert, Mr. Crampton, Mr. Royds, and

Mr. Hall.

Suppose the cone and cylinder to have the same base and perpendicular. Let r =the radius of the base, h=the perpendicular height, w=the weight of the whole cylinder, and the distance of the centre of gravity of the remaining portion of the solid from the base; then we have by the principle of the equality of moments.

=

.. Distance centre of gravity from the edge of the base

= √ r2 + (§h) 3 = {√/ 64 r2 + 25h2;

Vertical space through which the centre of gravity is moved in overturning the body = √64r2 + 25 h2 ➡ §h.

Hence we have (see Tate's Exercises on Mechanics, p. 24)

J. Herbert, Woolton, ans. 90, 91, 92; J. Royds, Belfield, ans. 90, 91, 92; W. Righton, ans. 90, 91, 92; F. R. Crampton, St. John's Wood, ans. 90, 91, 92; G. Hall, Audley Grammar School, ans90, 91, 92; Prismoid, Tewkesbury, ans. 90, 91, 92; G. Barnacle, Emp, ingham, ans. 90, 91; W. H. Yoel, Shelbourne, ans. 90, 91; T. Sothern, Burtonwood, ans. 90, 91; H. Heppinstall, Manningham, ans90; A. M. Gillingham, ans. 90, 91; Sam Dyer, Wanstead, ans. 90. 91; W. H. Y., ans. 90, 91; G. Morris, Gosport, ans. 90, 91; W. Davison, Sunderland, ans. 90, 91; H. Ford, Norham, ans. 90, 91 ; J. Salter, Durham, ans. 90, 91; Danos, Bishopwearmouth, ans. 92; E. R., Sunderland, ans. 90, 91.

NEW QUESTIONS,

TO BE ANSWERED IN OUR NUMBER FOR APRIL, 1851.

QUES. 93.-Proposed by Mr. Sam Dyer.

If a clock gains 24 minutes per day, at what time will the hands be together between 3 and 4 o'clock, supposing them to start together

at 12.

QUES. 94.-Proposed by Prismoid, Tewkesbury.

A person walks in a straight line the distance of 100 yards; he then turns to the left at an angle of 30°, and walks 100 yards; he then

turns to the right at an angle of 60°, and walks 100 yards, as before; it is required to find his distance from the point of starting.

QUES. 95.-Proposed by Mr. Crampton.

What is the length of a pendulum, which oscillates thrice as often in a minute as it has inches in its length?

CHESTER COLLEGE.

(Extracted from a Letter published in the Chester Courant.)

THE College stands on a rising ground, just out of the town, on the road leading to Parkgate; and the valley, through which the River Dee pursues its course to the sea, rich in verdure and foliage, spreads before you; bounded by the noble range of hills, I might almost say mountains, which separate the Vale of Clwyd from that of the Dee, and form the north-eastern frontier of the Principality. Not to dwell, however, on externals, we entered the building, at the western end, which it seems forms the residence of the Principal, and inquired for him. We were told that twelve o'clock had struck, and that he had just left the class-room, and that he was probably somewhere among the workshops. It seemed odd to hear of workshops in a College; but your friend who knew all the ways of the house, desired us to follow him; and having passed through a small piece of kitchen garden, where two young men in square caps, such as are worn in Cambridge, were digging very neatly some borders into which plants were to be set, we went up a passage through which we entered a yard, in one corner of which was a blacksmith's forge in full activity. The bellows were working merrily; quick and heavy blows were falling on a piece of red hot iron; and bright sparks were flying in every direction from the anvil; while two men were striking, and half a dozen lads were busy, either in working the bellows or in subjecting pieces of metal to the fire. "Mr. Principal,” said your friend, "I have brought you some visitors, who wish to see the College, but do not let us disturb you, if you are busy." One of the workmen stopped, and briefly saying that he was quite at our service, he threw off the leather apron which he had been wearing, put the sledge hammer into the hands of a stout youth who had been standing by, told him in a word how he was to go on, and then presented himself to us as the Rev. A. Rigg, late of Christ College, Cambridge, and Principal of the College at Chester. I could not but ask him what he was about; as I certainly wished to know what it was that had turned a learned ecclesiastic into a blacksmith, and whether it was fancy or amusement that led to this unusual employment. He told me with great good nature, that they were employed in making turning lathes for sale, and that they forged the bar iron into the pieces from which the screws and other parts of the machine were made; and that he had merely taken the hammer in order to show the others the way in which the iron was to be welded. He pointed to a number of tools, such as chisels, &c. which were hanging upon the walls: and said, "We make all these things here; and you will soon see how many we need and the use to which we turn them.' * * We followed him down a short flight of steps, which led into a large subterraneous room, like a well-lighted cellar; and it seemed as if we had got into the workshop of the world. Fifteen or twenty young men, with rather a larger number of boys, were all at work; but all so busy,

*

so merry, and so deeply interested in what they were about, that they took no notice of us, and went on hammering, sawing, turning, and grinding, as if their livelihood depended on what they did. Gradually, as I recovered my senses and was able to look round, I found one group occupied with a lithographic press, striking off circulars from a stone. I found a long table surrounded by others who were executing with extraordinary correctness some Gothic mouldings in oak. A circular saw, which was set in motion by a large wheel, was cutting deal plank into slips with as much rapidity as if it had been paper; and in the farther end there were several turning lathes at work, and articles of use were being thrown off in quick succession. Half a dozen other crafts were, I believe, going on in other corners, and in a laboratory near the door I found three little fellows occupied in colouring glass, and two others were finishing some excellent models of the steam-engine and power loom. The scene was in truth most extraordinary: and I must own the universal animation and goodness which pervaded the party was as wonderful as their activity. All seemed at work, but without collision; the boys seemed to have their own department as well as the men, and not one stepped beyond his line, nor did more than he was wished to do, or able to do. *** We followed him to another workshop, where the boys were making those card-board models for linear drawing, which are now recommended by the best masters. They were working on geometrical rules, and were evidently doing their work both accurately and neatly, and two others were hard at work binding a book. In an adjoining room there were half a dozen more employed in a chemical experiment; in the laboratory two others were melting some brass ornaments out of which they were to construct a paper weight; and in the midst of them, a tall gentlemanlike person, with something more of an academical look than the Rev. Principal, was preparing for a lecture on Agricultural Chemistry by mixing in separate saucers the earths of which he was to give an analysis in the evening. We were introduced to him as the Vice-Principal, and he explained briefly the nature of the lecture for which he was arranging the materials, and in which his young companions seemed to take considerable interest by the attention they paid to what he said.

Passing through these rooms we followed the Principal into another workshop, where a small steam-engine of singularly neat construction was in full operation. It was moving six or eight lathes, and iron and brass were being turned into screws, or holes were being drilled through plates of the same metals, with a rapidity which astonished us; and our astonishment was no doubt increased when I heard from the friend who introduced and accompanied us, that the steam-engine had been constructed by the students in their leisure hours, and that the whole apparatus which I saw was literally home-made, from the engine itself down to the tools with which the men were working.

We went on, and saw the two large class-rooms, and admired the excellent system of ventilation which secured to each a continual influx of warm but pure air; and then on the two upper stories of the house we saw the dormitories of the men who are training as masters for schools; and that for the boys in the commercial school, which is above. In these dormitories each individual has his separate cell, a cell just large enough to hold an iron bedstead, a wash-hand stand, and chest of drawers; all lighted up by gas at the hour of retiring, and all lights extinguished at the same minute. We saw the separate apartment called the hospital, which happily has hardly been ever used, but which contains a good sitting-room, together with four sleeping-rooms, differing only from the others in this, that each room is on a larger scale, and has a small fire-place. We descended to the kitchen, a lofty, light, and spacious room, where an excellent dinner for about 99

hungry men and boys was being cooked by a fire which was less than that which I frequently see in your drawing-room; and we also saw the tables prepared in the hall, for the reception of the whole body. Beyond the hall, we proceeded by a short passage to the College chapel; and here alone can anything like ornament be traced. Throughout, the building is as simple as it possibly can be, though the mass is imposing, and the outline forms a group of no ordinary beauty. The chapel however is elegant. It was elegant in its original design; but the interior is now receiving continued increase of embellishment, through the labour of the young men, who are filling up the panels with mouldings on the best and purest form, and who beyond this are endeavouring to purchase the embellishment of painted windows by the sale of works done in their hours of recreation. When that decoration shall be added, few mansions of our nobility, few Colleges in either University, will possess a building so chaste in design, and so appropriate in its style as the one of which I am writing.

While we were occupied in admiring this very striking scene, the dinner bell had summoned the men and boys from their workshops, and after a very hasty toilette, had collected them in the class-room. We heard the hymn chanted, which is used before meals, and as they slowly filed through the rooms and took their places at the table, the harmony of sound was sustained. The music indeed then ceased, and the clatter of knives and forks testified to the appetite with which the meal was welcomed, after the exertions, bodily as well as mental, included in the morning's employments. My companions were loud in expressing their admiration of what they had seen; but I own that on my mind there was another feeling still more predominant. I had long been thinking and inquiring on the subject of education. I had long been wishing to find a place where a really useful and practical education might be got. I had considered the plans of Pestalozzi, of Fellenberg; and I had been prepared to run some risk and much expense in order to obtain what I wanted, and here to my surprise I seemed to find it, combined with the strictest moral discipline and the soundest religious training, and offered at a price infinitely lower than I had been prepared to expect. The charge was stated as being £30 for a boy below 12 years, and £35 for a boy above, without any of the various et ceteras which swell out the accounts at schools of a different description.

*

The

The boys in the commercial school are mixed with the young men who are being educated as schoolmasters, only at the hours of play and at their meals. The studies are conducted separately and in different rooms. boys in the commercial school learn all that is taught at common schools, such as arithmetic, geography, English grammar, and learn it fully and thoroughly. They may also learn Latin, French, and German, if their parents choose, and they are all grounded in the theory of music and linear drawing. I own, however, that the knowledge they may gain in the workshops is, in my opinion, more valuable than any other; for I know no other place where it can be gained; and I see the purposes of usefulness to which it may be turned. Nor can I forget that this knowledge, which may be so useful, is being gained while other boys are only learning how to play at cricket or wasting their time in idleness and mischief.

Intelligence.