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SIR ISAAC NEWTON'S DISTRIBUTION OF COLOURS IN THE IRIN.

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Sir,-The accompanying diagram, with its explanation, has appeared in the 4th edition of my work on Perspective Drawing and Painting, which work is now reprinting in a 5th edition-with some considerable additions and alterations. If your acceptance and use of this diagram will at all suit the Mechanics' Magazine, it is at your service; it was an explanation much wanted, and its usefulness may be extended through the wide circulation of your valuable journal.

But here I must express my regret at the backwardness of young students of painting in geometrical research. The very term mechanical, nauseates, and seems to be a barrier to their random excursions in the fascinating fields of nature. Materials and a subject are all they can be prevailed on to think requisite; conceit of genius and imagination, bere takes wing, and soars above rudimental data.-But what does the most successful flights of such, produce and evince? Perhaps nothing, but the want of mathematical truth.

With this conviction, I have offered

One of the best elementary books on these branches of acquirement, with which we are acquainted; being at once remarkably plain, and fiee from all empirical pretension.-ED. M. M.

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this method of ascertaining the propor tions of the arch, and divisions of the colours (according to Sir I. Newton) of the rainbow, by the accompanying scale. The artist having determined (in his sketch) the intended width of his rainbow -he will mark it on the edge of a card, and then place it on that part of the scale (parallel to A) which tallies with the measure on the card, as at ABCD, or any intermediate space between those given measures, as on the converging part of the scale to E, and should a wider board be required than the measure at A, continue the divisional lines that diverge from E upwards, to obtain any greater width. Having thus placed your tally to its two extreme marks, on the converging scale, mark all the intermediate divisions on it; then replace this marked card on your sketch, and remark them there; thus giving each space of colour its true proportion.

It must be observed, that the width of the rainbow is governed by the arch it forms-being somewhat less than 4 degrees of it. The space between the principal bow and the faint one above it is not quite 9 degrees, and the colours are tne reverse of those in the true rainbow. The rainbow is never seen when the sun is more than full 40 degrees above the

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SOLUTION OF THE MATHEMATICAL QUES

TION, NO. 8, vol. xv., p. 63.

QUESTION.-To divide a given circular arch into two parts, so that the excess of the chord of the one may be equal to a given straight line, less than the chord of the whole arch.

By Kinclaven, the Proposer.

Let ABC be a given circle, and ABC the given segment. It is required to draw two chords AB, BC, so that their difference may be equal to a given straight line F.

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Bisect the circumference AED in E, join EA and CB, then AE=EC, (Elem. 29 and 3). From the centre E, and distance EA or EC, describe the arc ADC, in which apply the straight line AD=F, and let AD meet the given circle in B, join BC, then will AB-BC =F, join BE, DE; the angle DEC at the centre, is double the angle BAC, at the circumference (20 and 3) and the angle BAC BEC (21 and 3).. DEB=BEC, and DE=EC, and EB, is common to the two triangles DEB and BEC..(Elem. 4 and 1) DB=BC.'.AB— BC F.

A slight modification in the construction will answer when the sum of the two chords is given, or the following

If, from any point A in the circumference of a given circle ABC, as a centre, a circle CE'BE, be described, cutting the given circle in the points C and B, and if from the point Cany number of straight lines CDE, CE'D', &c. be drawn, meeting the given circle in D and D', &c., and the other in E and E', &c. Join CB, BD, BD', BE, BE', &c., then will DE DB, and D'E D'B, &c., by turning the points AC, AE, AE', AD, AD', AB, &c.

The demonstration will be the same as in the problem.

KINCLAVEN.

[Solutions of this problem have been also received from W. W. F.-—A Westminster Scholar-B. P.-Scholasticusand Tyro.]

PROOF OF SAXULA'S THEORY OF LOCOMOTION, ON THE PRINCIPLES OF RE

ACTION.

Sir,-Permit me to attempt to prove, on the principles of re-action, the truth of the 5th, or main proposition of my Theory of Locomotion, which states generally, that the only effective line of locomotive force is the line of gravity, and I call upon all my ten opponents who are not satisfied, some with my fulcrums, some with my levers, some with my axles, some with my weights, to consider it attentively, to cease to be statumotionists, and learn to be locomotionists.

1st. In muscular or mechanical force,

PROOF OF SAXULA'S THEORY OF LOCOMOTION.

action and re-action are constant, equal, and opposite. If I push at the ground or a wall with a stick, the ground or wall pushes at me with like force.

2nd. The line of re-action is also the line of action in an opposite direction.

3rd. A perfectly smooth body, loose on a perfectly smooth plane, has, out of the line of gravity (in which line the earth and not the body may be considered as the effective resisting substance) no power of re-action against any force but what it derives from its gravity; if its gravity was the least possible, then the least possible force would move it.

4th. The lighter the body, the less its power of re-action, and supposing it could be hard 'and solid, yet have no weight, it would have no power of reaction (out of the line of gravity) against any force applied to it; a cubic foot of cork wood has less power of re-action than a cubic foot of metal.

5th. By the locomotive-power intended now to be illustrated, is meant a power attempting to move its own body (like a steam-carriage) laterally along the ground or sub-plane, and not up or down, such as flying; but no body (or power within a body, not explosive) can progress itself by re-action against itself; suspend a machine of any kind in a vacuum, and no progression can take place by its own power.

6th. Locomotive-power being always a power borne by the body to be moved or progressed, must also be like that body loose, as respects the ground or subplane on which that body moves, and the power of re-action of the whole or any part of that body in motion, being only derived from gravity, the effective action of the locomotive-power, forming an integral part of that body, can only be opposite to gravity; therefore,

7th. The line of gravity is the only effective line of locomotive-power, because its line of power must, of necessity, be its line of effective action and reaction, which is gravity.

8th. Again (and this is a most weighty consideration, and one to which I particularly call the attention of my opponents, especially R. C. jun., because I think it proof of itself), the effective line of action and re-action of locomotive

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force must be the line of gravity, because that is the only line where locomotive force (such as I have defined) does not counteract itself.

9th. If the effective line of locomotive force were in any horizontal or angular direction forward, it would be counteracted and nullified by the re-action in the same line backward, and vice versa. If a man stand upon a carriage, and attempt (without momentum) to force it in any direction forward-suppose with his hands -his feet, which are the points of reaction, will force it in an opposite direction or backward; so locomotion will not take place.

10th. But any locomotive attempt to push a machine downward in the line of gravity is resisted by the earth or subplane, which may be said to push the machine upward; now this resistance upward is not counteractive of locomotion sideways or end ways, because its resisting line is neither backward nor forward; therefore locomotion is free to take place, although the machine be pushed downward by the power, and upward by the earth; and supposing it possible for the upward pressure, a little to exceed the downward, the locomotive line of progress would be in an oblique direction upward.

11th. Any solid substance lying against an abutment or fixed base (I avoid the word fulcrum here, because it is a word of cavil with my opponents) cannot be moved by a direct force, either statumotive or locomotive, passing through the shortest points of contact of that substance and its base; but if the direct force pass on either side the shortest points of contact, the substance can be moved. If I lay a plank in equilibrio on a rail or stone, and push exactly over the bearing point of contact, the ends of the plank will be stationary; but if I push on either side the bearing point, one end of the plank will be depressed.

12th. A locomotive carriage, standing upon a level plane, has its only points of contact in the parts of the wheels touching the plane, and these points are the points on which the locomotive power as well as the carriage finally rests.

13th. A locomotive force passing through these points of contact, could not cause the machine to progress; but shift the force to either side these points,

and the machine will be propelled forward or backward, or the wheels turned round without progressing, as the case may be.

These observations, I think, prove, on the principle of re-action, the correctness of my 5th proposition, and they only amount to my former assertion, at page 150, vol. 15, that in whatsoever line of direction a mechanical power may appear to act, still its only real or effective maximum force is in that line of direction which is opposed to the immoveable (absolutely or relatively) fulcrum or abutment which forms the base or re-action of that power.

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Calculations illustrative of the Present State of the Bobbin-Net Trade," has just been published by a Mr. Felkin, of Nottingham. The results which it presents are exceedingly curious and instructive. The capital employed in the trade is estimated to amount to £2,310,000; the number of persons-men, women, and children-to whom it gives employment at 211,000. The quantity of raw cotton consumed in the trade annually is 1,600,000lbs.-value, £120,000; cotton is manufactured into yarn, and its value increased to £500,000; the yarn is then worked into 6,750,000 square yards of power-net, 15,750,000 square yards of hand-net, and 150,000 square yards of fancy-net, worth altogether £,1,826,245. Of raw silk there is also used about 250,000lbs. value £,30,000; which, when thrown and worked into 750 square yards of silk-net, becomes worth £65,625. The total quantity of cotton and silk bobbinnet, annually manufactured is 23,400,000 square yards, value £1,891,870.

Of

this about one-half is exported in a plain state; three-eighths are sold unembroidered at home; and the remaining one-eighth is embroidered in this country, which increases the ultimate value to £3,417,700. The total number of machines employed is stated to be 4,500; of machine-owners, 1382. Of these machines, 1000 are worked by power; and of the owners above 1000

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Quorndon and Mountsorrel Woodhouse

Sheffield
Newark

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Costock and Leake Ruddington

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ON THE CAUSE OF THE REPORT IN EXPLOSIONS, &c.

"It is a lamentable fact, that one half or more of the 1100 persons specified in the list as owning one, two, and three machines, have been compelled to mortgage their machines for more than they are worth in the market, and are in many cases totally insolvent. This has chiefly arisen, from the fall in prices of nets, beyond the reduction in prices of cotton and wages. This class of persons having become indebted to the cotton merchant, have been compelled to pay a comparatively excessive price for the thread they have used, and to sell their goods at the lowest prices of the market. Besides, their machines are principally narrow, and make short pieces, while the absurd system of bleaching at so much a piece, goods of all lengths and widths, and dressing it for so much, all widths, has caused the new machines to be ell-wide, and capable of producing long pieces, and, of course, to the serious disadvantage if not utter ruin of the small owner of narrow machines."

The bobbin-net, which is exported in a plain state, is embroidered chiefly in Belgium, Saxony, and, until recent events, in ill-fated Poland. Mr. F. thinks that but for the high rate of wages in this country, much of the work which thus falls into the hands of foreign embroiderers would be executed at home. And yet, one would think that the wages of the English embroiderer could hardly fall lower than they have already done. Mr. F. states, that he had under his eye while writing his "Facts," some "splendid specimens of silk bobbin-net shawls, embroidered with the greatest care and beauty by young women, who had worked upon them during six weeks, for six days in the week, and fourteen hours a day, and had earned but one shilling a day by such unremitted and anxious labour." That cheaper bread and freer markets would better this as well as every other manufacture of the country, we by no means however intend to dispute; and we fully concur in the view which Mr. F. takes of the beneficial tendency of the two great measures of reform, alluded to in the following concluding remarks:

:

"If one million and a half sterling, or nearly, be paid abroad for the embroidery of bobbin net because the rate of wages is lower there than in this country, and if our rate cannot and ought not to be reduced while provisions are at the actual average; if also there be any just ground

o fear the successful competition of fo

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reign low-priced bobbin-net laces-even in the home market-have we not a powerful argument for the abolition of the tax on imported corn? It may also be reasonably inquired why an article, the demand for which has extended itself with a rapidity unexampled in the history of manufactures over the continents of Europe and America, should still be almost unknown eastward of the Cape of Good Hope, where it would be thought at least equally useful and ornamental ?* The fact of the East India Company's monopoly, it is presumed, may be advanced as a sufficient, though to the trade of Nottingham a very unsatisfactory reply. For I would here observe, that as no one can say bobbin-net may not, in the event of this monopoly ceasing to stand in the way of its free export and sale, be generally adopted in India and China, so it is a matter of easy demonstration, that if only every woman at the head of a family in India (saying nothing of China) were to use but one square of bobbin-net a year, the whole of the existing machinery of the trade, full-handed, and worked eighteen hours a day, would scarcely produce a supply sufficient for that market. Worked at that rate, our production would be under thirty millions of yards a year, and there are upwards of twenty-seven millions of mothers of families in our Indian possessions. Were it now to become in demand for China (and it is quite as likely to be so as tea once was for England), the quantity exported thither might possibly be immense, the population of China being three times that of India. The writer of these remarks feels that the evils contemplated as likely to result from increase of machinery, and consequent over-production are too serious not to demand a careful and candid consideration, and is confident all will be convinced on reflection, that rather than attempt to decry the increase of the power of production, it is far more rational, and will ultimately be more successful, to draw the attention of the trade to any practicable means of increasing the demand."

ON THE CAUSE OF THE REPORT IN EXPLO

SIONS, &c.

Sir,-At page 427, vol. xv. of the Mechanics' Magazine, it is observed by Mr. Baddeley, that most works on natu

"We can export a durable and elegant article in cotton bobbin-net at 4d. a square yard proper for certain useful or ornamental purposes, as curtains, &c.; and another article, used for any purposes in female dress, at 6, the square yard."

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