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ANSWER TO AN INQUIRY OF "AN INTENDING EMIGRANT.”

that we please, and of letting down the remaining portion in such quantities and directions as shall best serve to cleanse the river, and keep it in a navigable state.

All that is now offered, however, must be regarded in the light of mere suggestions; to be improved upon, as I earnestly hope, by some of your more experienced correspondents. Diversity of soil, varieties in the nature of the deposits, modifications in the direction and velocity of the stream, may each and all call for corresponding diversities in the nature, durability, elevation, slope, &c. of the jettee or apron, and of the materials employed. I regard myself, therefore, as simply opening the door to a series of papers on this and kindred matters, by which, I trust, your valuable miscellany will instruct

359

the public on a most momentous subject, and remain,

Jan. 4, 1830.

Sir,
Yours, respectfully,

O. C. F.

AN IN

ANSWER TO THE INQUIRY OF
TENDING EMIGRANT," IN NO. 334.
Sir, I send you an answer to the
inquiry of your correspondent," Aque-
duct," in your last number,

And am, Sir, yours, &c.

Lynn, Jan. 8, 1830.

J. UTTING.

First, we have given the length of the pipe 20 miles; the inclination or slope of the pipe 30 feet; and its diameter, half an inch. To find the velocity of the water at the point of delivery?

Now, according to the formula of Du Buat, we have d=0.5 and d−0·1=0·2535534

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√/s-h. log. √(s+1·6) 55·246253

Now 03 (d-1)=0·076066

Whence 1408980–0·076066—1332914, or nearly 14 inches the velocity of the water at the point of delivery in one second.

Whence 1.332914 × 0·52 ×·78539,&c. ×60".

1728

=0·0090874 of a cubic foot, or

15-70303 cubic inches, the discharge per minute; or 13.08586 cubic feet per day.

Secondly, the slope of the pipe being 10 miles?

The final velocity comes out 1.960834 inches per second, and the discharge 19-25045 cubic feet per day.

Thirdly, the slope of the pipe being 15 miles?

The final velocity will be 1-564715 inches per second, and the discharge 15-36156 cubic feet per day.

Lastly, the slope of the pipe being 200 miles?

The final velocity will be 0.350735 of an inch per second, and the discharge 3-44333 cubic feet per day.

The velocity of the water will become nothing, when the length of the pipe greatly exceeds its inclination or slope, as it is evident that if 0.3 307 (/d-0-1)

{\/d–0·1) becomes equal to√s-h log. √/($+1:6) sensible motion, but become stationary.

If every particle of the fluid 'passed in contact with the side of the pipe, since in equal times "they all ex

that the water will have no

perience the same degree of friction;" then the velocity would diminish in the direct ratio of the length of the

360

TEMPERANCE SOCIETIES.

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But it is only the lateral filaments that are exposed to friction-this retards their motion; and the particles of the fluid, or the adjacent filaments which do not touch the pipe by their adhesion to those which do touch it, experience also a retardation, although in a less degree.

The retardation of each particle of the fluid being inversely proportional to its distance from the side of the pipe.

Hence in pipes of small diameters, whose positions are nearly horizontal, the retardation of the fluid occasioned by friction is more than equivalent to the acceleration of gravity; and the fluid is consequently deprived of motion. And although the formulæ give in the last case a velocity of one-third of an inch per second, I much doubt whether or not the water would run at all; as it must experience a considerable retardation from the effects of capillary attraction in pipes of such small diameters.

P.S. The above queries may be more readily solved by the tables given in the " Encyclopedia Britannica," vol. xx. pages 652 and 653; in which work I beg to correct the following errata: viz.

Vol. xx. page 654, col. 1, line 41, for log. 2-49472, read 2.48472. By correcting the subsequent part of the computation, the velocity comes out 19-925, instead of 20-08 inches per second; and the discharge 223-54, in.stead of 228-8 Scotch pints.

J. U.

N.B. The inquiry, I think, is not properly defined, as it is not expressed whether the end of the pipe at the reservoir is placed level with the surface of the water contained therein, or whether it is to be placed 30 feet below the surface of the water in the reservoir; in which case the pipe would be perfectly horizontal in its whole length; which, I think, is not intended, although so expressed in the inquiry.

TEMPERANCE SOCIETY.

The celebrated Dr. Doyle has addressed a letter to the Rev. G. W. Carr, Secretary to a Temperance Society formed at New Ross: from the following passage to which, it will be seen that while he cordially approves of the object which such societies have in view, he agrees with us in thinking that it is only by providing the people with a cheap and wholesome malt beverage, that they will ever be weaned, in any considerable numbers, from that excessive use of ardent spirits, which is at present so fertile a source of crime and misery.

"But the great, the insurmountable obstacle to the progress of Temperance Societies, and to all the efforts which you and I, and such as we can make, to stop the torrent of drunkenness, is found in the revenue laws. Could we but induce the Chancellor of the Exchequer to become a member of our society, and to square his budget by our rules, I have no doubt whatever but we should succeed in removing this pestilence of drunkenness out of the land. To eradicate the use of ardent spirits out of a country having such a climate as ours, and from among such a people as ours, is quite impossible; but to diminish the use of ardent spirits to the one-fifteenth part of its present amount, is, in my opinion, perfectly practicable. But as it would be as easy to stop the mouths of the Euphrates, as to stop the mouths of those who now drink whiskey in Ireland, they cannot be reclaimed until a better beverage than whiskey is provided for them at even a lower expense. All this could be done by the Chancellor of the Exchequer, if he found it more necessary to promote good morals than to secure a large revenue. I am tolerably well acquainted with the making of malt and the brewing of beer, and I have no hesitation in stating, that if malting and brewing were exempted from tax, and the impost on whiskey raised, drunkenness in a little time would almost disappear from the country."

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Sir, I do not recollect any information that I have acquired from the "Mechanics' Magazine" that engaged my attention more forcibly, than the sketch of Mr. Drury's improved method of producing the sound of a bell, as given by Mr. Wm. Baddeley, jun. in your 331st No. of the "Mechanics' Magazine;" a subject entirely new to my mind. I earnestly hope that so important an improvement will not be suffered to expire in diagrams and theory. The whole scheme is so practically illustrated by Mr. W. B. jun., that if any thing be done successfully, it must, I think, be upon the principles advanced by Mr. Drury, so far, at least, as relates to the immoveable fixture of the bell; and the producing sound, by the motion of the hammer, or tongue of the bell. The perfecting of the invention by scientific means, I must, of necessity, leave to persons qualified; and would only humbly beg leave to suggest as a subject for their opinions-whether the improvement might not be put in practice on bells as they already hang. Why not strike the interior surface of the bell, as hitherto (see fig. 1.)? Or even make

use of its present tongue (see fig. 2.)? The S. suggests a stay to the tongue of the bell, that it may not strike that side. The rest of the scheme coincides with the methods (or some such as those) of Mr. Drury's. The proper construction and applications must depend on local circumstances; and the scientific calculations of such as are capable of bringing so excellent a contrivance into actual operation. I only hope some more efficient pen and pencil may have superseded this slight suggestion, which I only offer, to preserve the scheme from sinking, and to excite the ingenuity of mechanics in the construction of what may be requisite to accomplish this improved method of ringing a peal of bells. As for the improvement that may be still wanting in the formation of bells, let it not prevent this capital thought of Mr. Drury's from being applied to bells, as they are at present. Let the bell-founder and the architect lay their heads together, for the more perfect making, firing, and ringing bells, consonant with the safety of their towers. I am, Sir, yours, &c.

C. H.

362

FORM AND ACTION OF THE TEETH OF WHEELS.

FRENCH AND ENGLISH NAUTICAL

ALMANACS.

We have just received the Connaissance des Tems, or French Nautical Almanac, for 1832. We are glad to learn from it, that the French Board of Longitude do not so pertinaciously resist all hints for improvement, as the late English Board of Longitude did; and, comparing little things with great-the ants with the elephants of the almanac tribe-as the managers of the British Almanac have done.

The French Board announce various improvements, some of which will be introduced in the Connaissance des Tems for 1833, others in that for 1835. Among the first, we are very glad to find specified "the angular distances of Venus, Mars, Jupiter, and Saturn, respectively, from the moon," after the manner in our Nautical Almanac of the distances of certain fixed stars from the moon, at intervals of three hours. It is a curious fact, in the history of attempts to prevent the promotion of science, that Professor Schumacher, of Altona, (one of the first astronomers, and one of the most public-spirited men in Europe,) got these distances of the planets from the moon accurately computed for every three hours in an entire year (about eight or nine years ago), offered them gratuitously to the English Board of Longitude, and said he would engage to supply them annually, free of expense-simply requiring a certain, and not a large number of the printed copies, to circulate amongst Danish and German astronomers, and naval menbut that THIS LIBERAL OFFER WAS POSITIVELY DECLINED! Mr. Schumacher, therefore, published them separately; and the East India Company, and some other public bodies, have procured copies regularly from Altona, year after year.

We rejoice to hail the improvements in the Connaissance des Tems; and trust that, ere long, we shall have to congratulate Messrs. South, Baily, and others, who have struggled nobly to accomplish so desirable an object, on the appearance of similar improvements in our own Nautical Almanac.

ON THE FORM AND ACTION OF THE TEETH OF WHEELS,

Sir,-As the most eminent authors are not free from errors, and compilers or book-makers copy from authors and from each other, thereby propagating but your correspondents ought themsuch errors, it cannot be questioned selves to understand the subjects on which they may think proper to offer remarks. Indeed, nothing is more certain than that those who square their ideas entirely by what they read, without any judgment of their own, are by no means fit persons to assume the office of censurers. "S. Y. (a Young Engineer)," No. 332, p. 304, presuming on what he has seen in print, asserts that my remarks on the acting of the teeth of wheels are not such as might have been expected from one who pretends to treat the subject scientifically; and that "the best mode of forming the teeth of wheels is by involutes of circles:" and in support of his assertion, he refers your readers to Gregory's Mechanics, Robison's Mechanical Philosophy, Ency. Brit. and Rees' Cyclopedia. But although the epithet he gives himself of "young" may plead an excuse for the want of knowledge, it is certain that such want but ill accords with the title of "engineer." He tells us that the teeth of wheels working three inches deep, only slide on each other one-sixtieth of an inch; but he does not show us by what magic this is effected.

Now, as it is much better to be guided by strict matter of fact than merely by what any author whatever may happen to advance, there is no necessity for me to consult the authors he refers to-there being no difficulty in proving that the true form of the teeth of wheels are epicycloids, and consequently not involutes of circles; and that they rub or slide more or less against each other the whole depth they work into each other-the curved part of the teeth of one wheel sliding against the straight part of those of the other, the point of contact changing continually in both.

It would be decmed futile to make any remark on the wearing of the teeth, seeing that it is the obvious con sequence of their sliding against each

DR. LARDNER'S LECTURES ON MECHANICEL

other. Nor need any one be told, that if there were no sliding there could be no wearing: but the fact of their wearing, and the manner in which they wear, ought to have convinced “S. Y." that there is a degree of sliding the whole depth they take hold of each other; and which is so considerable in the low numbers of the pinions of clocks, as to render the beneficial effects of rollers very sensible.

It is true that at the line of centres of two wheels there is no sliding, beeause at this point both wheels move in the same direction; but as in receding either way from this line, the direction of the motion of the two wheels is more and more different, and the driving-wheel continuing to press the other wheel forward through all angles comprised between the point where the teeth enter in and that where they come out, the sliding necessarily becomes greater and greater, and in a greater ratio than that in which the angle with the line of centres increases. Hence as the number of teeth which the wheels contain is less, the greater must be the friction in impressing motion upon the driven wheel, because a greater angle is included in the space in which the one acts on the other.

I may observe to "S. Y." that if any farther demonstration was necessary, I could give him a diagram, with a specification, by which this matter might be rendered still more manifest, and that the proper application of epicycloids gives a true form to the teeth of wheels; but as the Editor appears to be so greatly pressed with matter from different correspondents (all of whom he is doubtless desirous of obliging), and has not yet been able to insert either the remainder of my answer to Mr. Wynn, or my reply to his anonymous correspondent, No. 314, p. 424, on the "Momentum of Falling Bodies," both of which have been handed to him some time ago, I shall forbear to trouble him with more matter until these are inserted.

JAMES HARRISON.

Barton-upon-Humber,
Dec. 30, 1829.

363

NOTES OF DR. LARDNER'S LECTURES
ON MECHANICS, AT THE LONDON

UNIVERSITY.

(Continued from page 343.)

The next subject to he entered upon is the consideration of machinery.

A machine is an instrument by means of which a force, of a determined quantity and direction, can be counterpoised, counteracted, or overcome by another force, whose quantity and direction are known.

Or, it may be described as a means of transmitting a force of a given quantity and direction from one point to another.

Again, it is a means of modifying the quantity and direction of forces.

A machine is employed for two purposes, either merely to sustain or absolutely to move a weight. First, if it is required to sustain a weight, the effect must be that equilibrium is to be produced. In sustaining a weight by a power, certain parts of the weight are thrown on certain fixed points: thus it is the fulcrum of a lever that supports both the weight and the power. It is a common opinion that a small weight can (by machinery) be made to balance a larger weight: but this is not true, for both the weight and the power are thrown upon the fulcrum; consequently the weight is balanced by the fulcrum and the

power.

But if the machine be required to move or raise a weight, it is more difficult to explain. Suppose there was a block of stone weighing 20 cwt. to be raised by a weight of 1 cwt.: if the large block be divided into twenty smaller ones, it is evident that (each piece being equal to the small weight) the whole block could be raised by this small weight, taken separately. Now this is the exact use of a machine; viz. a contrivance for overcoming gradually what cannot be done altogether.

The present ohjeet is to examine the varieties of contrivances by which these effects are produced; but great as their number is, they may be all reduced to three classes, although they are often divided into six or

seven.

The first class of machines comprehends a solid body, capable of turning

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