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IMPERIAL MEASURE. dering the whole power of the engine : BH (=) :: BH ( = ): HG = a propelling one , it's time sI am, Sir, yours, &c.;

and has to this add the altitude of the

ah Ipswich, June 6th; 1825.

ilahi,

frustum (k), and you will have P.S. The wing system, invented by Ah Mr. Dixon Vallance, as in Number h = A = EG ; consequently. A’ 81, is certainly ingenious ;:, but as strength must be combined with

* .7854 (f) the solid simplicity, and a constant applica ;

ah sary, it appears to me it would be found in some respects deficient.

3(A-aj. * f = the solid contents of the cone BGC.; therefore, A? * Ah

ahsen 3 (A-a) * f a? x

* 3 (A ) * f = ANS WER TO INQUIRY. A - ash.

A a x 3 xf = the solid con

tents of the frustrum ABCD ; and, as NO. 80.-IMPERIAL MEASURE.' no particular value is given to A, a, SIR, -As I consider the answer given

and h, it is evident that this is a geneby B. C. to J. H.'s problem (No. 105)

ral formula for finding the solid conerroneous, I shall be obliged by your

tents of a frustrum of a cone. ,! insetting in your valuable Magazine

This premised, we shall now proceed the following:

to the solution of the problem.... A cone is the third part of a cylin

Let the bottom diameter be denoted der of the same base and altitude by x, then (per quart) 7:10.:: 2 : (Eucl, x. 12); hence we easily derive = the top diameter and perpena rule for finding the solid contents of 7 a frustrum of a cone. tis ,

dicular depth -23 (difference ass 14164 CM

of the cubes of the diameters) =

657.23 211789 but by aagvery be

657 2:2

ence of the diameters) = to slynt to

19, which birovi B LE_

x 2016 (third of the depth) x .7954

= 1,6715 x9=277,274 – 138.637 (cubic blioji

inches in two quarts); whence r =

3 138.637 · Let ABCD be the frustrum whose

V 1.6715 = 4,362, diameters of solid contents are required: call the the bottom of the two quart measures bottom diameter (AD) A, top diameter

ninches and 10 x . 43,62 (BC).a, altitude EF)'ni produce AB, in inches, and DC, till they meet in G, then find the

top diameters.

top diameters, . solid contents of the cones AGD, BGC,

Y.,! their difference will give the solid con- By proceeding in the same manner, tents of the frustrum ABCD. But to the dimensions of the quart, pint, and do this we inust first find the altitude half-pint measures, will be found as of the part BGC, which may be done follows :as follows: Draw BH parallel to the axis EG,

. . QUART. and the triangles, ABH, BGF, will be Bottom diameter .... 3,4621 inches. similar ; therefore AH ( = =

Top diameter and per- Lone

14,9458 pendicular depth . ),

9343 which **** (= 10,4 – 2, differ

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IMPERIAL MEASURE-CORRESPONDENCE.
PINT.

PINT.
Bottom diameter . . . 2,7479

Top ...... .5101 Top diameter and per- 30065

A Bottom :5102 pendicular depth : %,9255

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HALF-PINT. I

IT - HALF-PINT, Bottom diameter ... 2,1811

Top .......4048 Top diameter and per- } 3,1158

Bottom .... .4049 pendicular depth . jos

of Bottom . . .8097 To find the thickness of the metal

The thickness of the sides of the at top, take half the difference between

once herween vessel are calculated perpendicular to the top diameters of the enclosed and

dand ihe axis of the cone, not perpendicular enclosing vessels, and you have the to the blank sides. thickness required. Thus, the top

I am, Sir, diameter of the two-quart measure has been found to be 6,231 inches, and the

Your obedient servant, top diameter of the quart 4,9458 inches; ** ' WILTIAM LAKE.' difference 1,2832, which, divided by 2, Bulbourne, near Tring, gives 6426, the thickness required. March 22, 1825.

To find the thickness at the bottom, take the difference between the top and bottom diameter of the enclosing ves

" [In a former communication of mine sel, and the difference of the depths of the enclosed and enclosing ones, and

(Vol. 111. No. 78, page 350) I find one thus say, as the depth of the enclosing

or two typographical errors. In the vessel is to the first difference, so is the

first column, for " and that the variasecond to the difference of the diame

tions of a degree in latitude," read

" although the variations,&c. Second ter of the bottom of the enclosing vegsel and its diameter at the bottom of

column, for “consequently the descent the enclosed one, which difference,

of a heavy body from within one second," added to the bottom diameter of the

read “ consequently the descent of a former, will give the diameter at the

heavy body, for rest, is one second," bottom of the latter ; from which take

&c. &c.] the bottom diameter of the enclosed vessel, and half the difference will be the thickness required.

The Managers of the Mechanics' Thus the top and bottom diameters of the two-quart measure have been Instilutions are respectfully informed, found to be 6,231 and 4,362 inches; that they may, on application to our consequently their difference is 1,869; the depths of the quart and two-quart Publishers, be supplied, gratis, with measures have been found to be 4,9458

proof copies, framed, of the Portruit and 6,231 inches, difference 1,2852 ; therefore 6,231 : 1,869::1,2852:3,855, of their distinguished friend and advoadded to 4,362, gives 4,7475, from which cate, Mr. BROUGHAM ; and that our take 3,4621, and you will have 1,2854, half of which will give the thickness Publishers will micke a liberal deducof the metal, at the bottom of the quart 'tinn from the price of all Bonts nur. measure, 6427. The difference of the · depths of the enclosed and enclosing chased for the use of the Mechanics' vessels will be the thicknesses of the Institutions and Schools.' bottoms.

The following are the thicknesses of the metal in the quart, pint, and half- Notices to Correspondents in our next. pint measures :-

QUART.
Top ...... 6426 inches.
Bottom .... .6427
Of Bottom : : 1.2282

Communications (post paid) to be addressed to

the Editor, at the Publishers', KNIGHT and

LACEY, 55, Paternoster-row, London, Printed by Mills, Jowett, and Mills (late

Bensley), Bolt-court, Fleet-sireet.

Mechanics' Magazine, MUSEUM, REGISTER, JOURNAL, AND GAZETTE.

No. 96.)

SATURDAY, JUNE 25, 1825.

[Price 3d.

"No man ever reached to excellence, in any one art or profession, without passing through the slow and painful process of study and preparation.”-Horace.

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178 DESCRIPTION OF A WATER-HORSE-ELECTRICAL TELEGRAPHS.

been made to the extent of nine DESCRIPTION OF A WATER-HORSE. miles, the shock has invariably re

Sir, — It is good sometimes to turned, without any perceptibie loss unbend, and study the agreeable. I of time. If the same - results will present you, therefore, with a draw. hold good to the distance of several ing of a Water-Horse, which I have hundred miles, and I see no reason constructed. The body of this aqua. to doubt it, it is, of all known means, tic steed is a frame of wood, covered the best calculated for telegraphic with canvas. The canoes, six feet dispatch. The great nuinber of stalong, are composed of skin stretched tions at present necessary would be on a frame, and made perfectly water- reduced to one at each extremity; tight above and below. The inotion and, what is of more importance, is coinmunicated to the paddle-wheel the communications may be made by by a strap passing over a wheel in night or by day, in hazy or clear the shoulder, turned by either hand weather. with a wince. A rudder is affixed to The method of working may be, I each canoe, and connected by an imagine, effected by the following iron rod to a cross-beam which passes simple means :-The present telebeneath the horse, and, moving on a graphic communication is effected pin at the centre, with a stirrup. by means of six shifting boards, in leather at each side, serves at once a manner with which your readers to support the feet and work the are doubtless conversant. Now, if rudders.

it be practicable to lay down one The manner of steering is shown wire, it will be equally practicable in Fig. 2, where the beam is seen to lay down six; and the cost of the connected to the arms, AB, placed wire would be nearly all the differat right angles to the rudders, CC; ence in the expense. Let the wires so that when the right foot is pushed terminate in a dark room. On one forward, the arm, B, advances, and wall let there be the figures, 1, 2, 3, A recedes, thus making the rudders 4, 5, 6, prepared in tinfoit, accordform a correspondent inclination, or, ing to the method practised by elecsimply, the motion, is just that of tricians, in forming what are called the hammer.lever.

luminous modes und figures. “* Bring Very agreeable equestro-aquatic ex. the six wires in contact with the six cursions might be taken on the back figures separately. With this conof this floating Hippopotainus, and, trivance, all the signals may be perperhaps, by means of your valuable formed, as at present, with six shiftmiscellany, we shall shortly have the ing boards. Ā shake of the arm, as satisfaction to find that we have added Moderator suggest's, may call the one more to the novelties and amuse- watch to his duty; and he could ments of the age.

name the signals, as they appear, to I remain, Sir,

his assistant, as is the present cus

tom in the established telegraphs. Your very obedient servant, His assistant must, of course, be se

Thomas H. BELL. parated from the dark room by a Alnwick.

slight partition, that should be proof against light, but not against the full

hearing of the human voice. :**?. ELECTRICAL TELEGRAPHS..

These few hints, Mr. Editor, may

serve as food for reflection to some Sır, If the following hints on the of your readers who are fond of novel • subject started by your Correspond improvements. Should you think ent, “ Moderator,” should be wore the subject worthy of notice, I will thy of notice, their insertion in your explain, at greater length, at some valuable work will oblige a constant future time. reader.

I am, Sir, To whatever length the conducting wires have been extended, and, - Yours, respectfully, if I mistake not, experiments have

R--H-

do so.

CASE OF THE SHIPWRIGHTS-USE OF THE SLIDING RULE. 179

spect to those who do employ themny CASE OP THE SHIPWRIGHTS.. when they work well, and also cheap,

By inserting the following letter, employing them is decidedly more we hy no" means intend to con- satisfactory than giving way to insóvey any opinion of 'onr own on the lence at home. The extent to which points of difference between the Mas- this remedy has been sought this ter and Journeymen Shipwrights, year is considerable, and the effect but simply to open our pages to a of turning the stream of capital cancandid discussion of the question. not be far remote; the extent to We dare say the journeymen will which this mode of relief will be not leave our " Ship-owner" unan sought, will be equally general, as swered.

is the desire of man to take care of

his own interest. My object in Tag., 70 tri puta sa vor Sir,-Being one of a numerous

writing this letter is to show the class who have lately suffered much

effect produced by an unnatural inconvenience, as well as loss, by the found that the wages of labour are

cause; and as, on comparison, it is combination of Shipwrights for in

already by far too high in this councreased wages; it may not be amiss

try, abundance of employment will to show, through the medium of ont

only eventually be secured, in a peryour publication, the injurious con

manent shape, by a very serious resequences which must result, at no very, distant period, to those mis

duction. Until that takes place, we

must continue to employ foreigners, guided, stubborn, and short-sighted

wlien it'is manifestly our interest to workmen who are the cause of the evil. In a trade where workmen are uso:

Tam, Sir, known to earn from 701. to 901. per..!! annum, paucity of wages is a bad Hd Your obedient servant, plea.. The objects of these men ist .,!! A Shirowser. for an increase,î and obviously also sol ? ' to form such laws or standing rules , amongst themselves as will regulate the rate of labour, not only at their USE OF THE SLIDING RULE. will, but also render it imperative (Continued from page 163.). upon all to employ the workmen belonging to their Union. This spe

PROBLEM V.; i.. . cies of dictation cannot be submitted : To find a mean proportional be10 tamely; the evil has driven my- tween two numbers. self and many others to the necessity cii RULE. of seeking a remedy elsewhere. Se- - Sot either of the nimhe

e. We Set either of the numbers on C to veral vessels in which I am interested

the same on D, then against the required rather extensive repairs, which, from the cause stated, I could

other number on C stands the mean

proportional on Do y not get offected here, and they have

pres . been sent to the North of Europe in č.! EXAMPLE I. this imperfect state at my own risk; Required the mean proportional and I have now the satisfaction of between the numbers 77 and 274?knowing that I shall there accom Set 74 on C to 71 on D, then against plish my repairs in an equally secure 274 on C stands 139 on D. manner; and at a much less expense,

NOTE. in some cases for one-half, and in

. Here we reckon the 10 on D as no instance for so much as two-thirds, of the cost of etfecting such repairs

en hundreds, as in the former problem. here: In this ivay some thousands ... EXAMPLE II. ...:, ". will be expended, and confess it What is the mean proportional bewould be more gratifying to my feel- tween 5 and 207-Set 5 on C to 5 ings to expend this at home than in on D, then against 20 on C stands employing foreigners ; but when 10 on D, the mean proportional they evince a proper feeling of re- sought.

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