G F is an instance of this machine; only here the axle is perpendicular. It will be evident that the power should always, when it can be accomplished, act tangentially to the wheel, for the force of the power is always estimated by its perpendicular distance from the centre. Let the line AB, fig. 8, represent a force acting tangentially to the circle ADE, and let AF be another force acting obliquely. Now, the effect of the force AB will be ABXCA, (for CA is perpendicular to AB), and that of AF will be AFGC, (for GC is perpendicular to AF), but. GC is evidently less than CA; therefore the force AB acting tangentially, is greater in effect than AF acting obliquely. In the same manner it may be proved that the power always. has the greatest effect when it acts tangentially to the centre. When the wheel is worked by a winch, it is generally attended with disadvantage: thus, if a man be the moving power, he is alternately stretching forward and pulling up; and the former being the much more effective position, the motion is very irregular. This is sometimes obviated by using two winches, one being" at each end of the axle; or by two men working at the same winch; for when one man's power is at its maximum, the other is at its mini-. mum, and the sum of these two effects. at any position will be the same. (To be continued.) VELOCITY OF WATER IN PIPES. Sir, I thank your correspondent, Mr. J. Utting, of Lynn, for his early attention to my inquiry; and for his answer to it in your Magazine of yesHe mistook my terday, No. 336. meaning, however, by supposing that the pipe had a slope, since the inquiry clearly stated that the pipe was horizontal; and I cannot think that it would matter much whether the insertion were into the bottom of the re 409 410 DU BUAT'S TABLES OF THE VELOCITY OF WATER, servoir, or not. Mr. Utting has likewise mistaken the drift of the inquiry, by supposing that the quantity of water that would be discharged was sought; or that the discharging orifice was to be half an inch in diameter. Here is the marrow and substance, mind you; and hence Mr. Utting's solution (which though in one sense well enough, yet in a stricter sense is not right, inasmuch as Du Buat's formulæ are incorrect in many respects,) is not the solution required; because the velocity will mainly depend upon the size of the hole at the extremity of the pipe (or in the side thereof), at the respective distances mentioned. I now put the question in this way" All things being as specified in the inquiry (see "Mechanics' Magazine," No. 334), and the pipe plugged at the end farthest from the reservoir, then if in the side of the pipe, within a few inches of the plug, a small hole be drilled not exceeding the thirtieth (or from that to the twentieth) part of an inch in diameter, with what velocity will the water jet out, and to what height would it jet if the hole be vertical upwards, at the several distances assumed?" Every body knows that the velocity will diminish in proportion to the increase of size in the hole; and when the hole became half an inch in diameter, the result would be a degree of velocity not differing very considerably from Mr. Utting's statement, and yet in one sense differing considerably from it. And, as I have said before, a gradual slope all the way is entirely out of the question, and purely of no moment, or at least of very little moment, I am well assured. Allow me to say, that I highly prize your Magazine, and have ordered it to be regularly sent after me as opportunity offers. I am, Sir, &c. AQUEDUCT. Upper Clapton, Jan. 17, 1830. [It will be seen from the following "letter, which we have received from Mr. Utting since the appearance of his answer to 66 Aqueduct's" question, that the use of the word slope for length was an error of the press; and that Mr. Utting is not unaware of the merely approximative character of Du Buat's Tables.-ED. M. M.] DU, BUAT'S TABLES OF THE VELOCITY Sir, In the "Encyclopedia Britannica," vol. xx. p. 653, is given a table, computed with considerable labour from the formula of the Chevalier Du Buat, for finding the velocity of water in pipes, canals, &c. As this table must be valuable to engineers, I shall therefore make no far. ther apology for introducing the following errata to your notice; viz. 4.4 for 0.07898 read 0-07981 9.8 65. 840. 950' - 0.25186 -0.78276 1.40678 0.28186 0.77546 1:40850 1.43464 1.43764 In finding the hyperbolic logarithm of a number not contained in the tables, it is usual to multiply the common logarithm corresponding to the given number by 2·3025851. Dr. Robison, at p. 654, recommends that instead of taking the hyperbolic logarithm of +1.6, we should multiply its common logarithm by 24; or multiply it by 9, and divide the product by 4 which process is vastly easier than taking the hyperbolic logarithm. Now, if the common logarithm of s+1.6 be multiplied by 23, (by the contracted method of multiplication) the operation will be quite as simple and easy as that recommend ed by Dr. Robison; and approximates 20 times nearer to the formula of Du Buat. The common logarithm multiplied by 2.3 may therefore be substituted for the hyperbolic logarithm, in all cases where it is involved in the formula of Du Buat, without sensible error. SOLUTIONS OF MR. LUCOCK'S MECHANICAL EXERCISE. 411A rectangle. It is required to cut it into parts, so that the parts may be joined so as to form a square. Construction. Find AE, a mean proportional between AC and AB, and from the centre A and distance. AE, describe an arc cutting CD in E. Join AE, and draw BF at right angles with AE and BH, parallel to AE, meeting CD produced in H, and HG, parallel to FB, meeting AE produced in G. Then it is apparent that BFGH is a rectangle; also that the triangle ACE and BDH are iden→ tical; also since the angle GEH= AEC FAB, and the angle HGE= BFA, each of them being a right an gle, also GH FB.. the triangles EGH and AFB are identical. It therefore only remains to prove that BFGH is a square. Because the triangles ACE and AFB are equiangu lar AC:AE:: BF: AB, but by construction AC:AE::AE:AB; hence AE=BF, also AE=BH..BF BH. Consequently, BFGH is a square. When the perpendicular BF meets Fig. 2. By Mr. Thomas Hughes, Pupil, Mansion House Academy, Hammersmith. Let ABDC (fig. 1) be the given E F D AE produced in F, upon BF describe the square BFGH. Draw HS perpendicular to AB, then it may be demonstrated as before, that AE-BF-GF...AG = EF, also the angle OEF AEC= GAN, and the angles at G and F are right angles.. the triangles ANG and EFO are identical. Again, the angle AEC GAN HNS-SHB, and the angles at S and C right angles; also HB=GF=AE.. the triangles ACE and HSB, are identical, and HS= AC=BD, and by taking away the angle ABF from each of the equal angles HBF and ABD, there remains the angle HBS=OBD, and the an 412 65 A FEW MORE WORDS FROM gles at S and D right angles, and HS BD..the triangles BOD and HSB are identical; and thus the rectangle ACDB is divided into four parts, AGN, ACE, NGEOB, and BOD, which will coincide with the square HGFB, [The shortest must, of course, be the preferable method of solving this problem; that is, the fewer cuts, and the fewer pieces, the better. Consi dered in this light, the solution of our clever young friend, Mr. Hughes, is by far the best we have received. He shows how by two cuts and the division of the rectangular board 9.6 by 15 into three pieces, the square board required may be obtained." Mr. Lucock employs also, only two cuts in the first of his methods, but the result is four pieces. None of our other correspondents (J. T. H., Mr. Gilbert, jun., Mr. Baverstock, J. O. B., and X. X.) who have favoured us with solutions of this case have proposed to use fewer than four cuts; one requires six, another nine. It is deserving, at the same time, of remark, that Mr. Hughes has shown that his method is one which will stand the test of the most rigid mathematical examination; thus exemplifying a truth which cannot be too often or too strongly impressed on the minds of our operative friends, that the most scientific mode of doing things, is at all times the easiest and best.ED. M. M.] 66 A FEW MORE WORDS FROM A PRACTICAL ENGINEER" TO MR. GILMAN. Sir,-Your remarks at the end of Mr. Gilman's letter of the 4th inst. are so pertinent, and your advice to that gentleman "to grapple at once with the facts of the case," is so judicious, that I had better perhaps have left the matter in your hands; and I believe I should have concluded to have done so, had I not been accused of improper motives for writing my letter to you of the 17th of December, and of "acrimonious invective and personality" therein. I beg to assure you, Sir, that I know not Mr. Gilman at all, and that I never saw him in my life. How then can I have been guilty of acrimonious A PRACTICAL ENGINEER." personality-" which (as Mr. Gilman truly states) is not argument; "only a proof indeed of conscious weakness?" Whether this accusation may not be retorted with more truth on himself, the reader will judge on perusing the few following lines. "Otherwise any malevolent fellow may raise a storm that may cause a great deal of trouble, and perhaps injure a man's character.”—Mech. Mag. vol. xii. p. 351. Now, with all my acrimony and all my invective, I do not think the civil Mr. Gilman can find such uncivil language in all my former letter; although I do not deny that I may have raised a storm about his ears which may give him a great deal of trouble. The fourth and fifth paragraphs, of Mr. Gilman's letter contain some allusions to the facts of the case, but very slight ones. 66 "But the joints!" says Mr. Gilman, aye, the joints! Did he never see such a joint ?" No, Mr. Editor, I never did. "What a pity! Has he ever seen any thing of high-pressure steam? Perhaps not also." Yes, Sir, I have seen a little of high-pressure steam; and "when I want a cast-iron joint particularly sound," I, like Mr. Gilman, never trust to cemented flanges, nor do I trust to joints of not one-half of the width of 3-8ths of an inch, or not 3-16ths of an inch, when the vessel requiring those joints is (like the generator in question) two feet in diameter, whose area is consequently 452 inches, which, with 250lbs. upon the square inch, must sustain a pressure of 112,000lbs. or 50 tons! Mr. Gilman, Mr. Gilman, how can you have the effrontery to tell the public that you can show a hundred joints of those widths as sound as if they were of solid metal, and to affirm that" the bolts, even the bolts too, were really sufficient to confine, and actually did confine steam of between 200 and 300lbs. upon the square inch, and keep sound joints too." Let Mr. Gilman before competent witnesses show that with joints 3-16ths of an inch wide, and with twelve bolts he can confine steam in a vessel two feet in diameter of upwards of 200lbs. pressure upon the square inch, and then I will say we EXPERIMENTS ON RESISTING THE AGENCY OF FIRE. ought to believe, without proof, all his other extraordinary assertions. Now for Mr. Gilman's sixth paragraph; it is highly argumentative certainly, and ought to be taken, as the French say, au pied de la lettre. It may be divided into three parts; 1st. "But I have forgot the pipes; aye, they are uncovered and oxydising, but I must hasten to a conclusion." 2nd. "Did Novelty's' sore place suggest this idea?" 3rd. "I should have suspected him to have been one of those wot drives The Novelty,' &c. &c." I am glad to find that, like a certain boastful knight, "I am not only witty myself, but the cause of wit in other men." I assure Mr. Gilman, I am not one wot drives 'The Novelty,' but he wot guards the Imposition. All this and all the rest of Mr. Gilman's last letter is any thing but "grappling at once with the facts of the case;" and although this sort of badinage is by no means profitable, I see no other mode so proper of treating such an evasive epistle. Hoping Mr. Gilman will adopt the excellent advice you have given him, and proceed to grapple at once with the facts of the case. I am, Sir, Your very obedient servant, A PRACTICAL ENGINEER. Note. In addition to the facts of the case, I wish to know when Mr. Gilman was practising the modifications requiring the pipe F to be fixed at the top of his generator (see his drawing, fig. 1), how he introduced the fuel into it. Was pipe F contrived (like Goldsmith's chest of drawers) a double debt to pay ?" Was it contrived to emit the gases and vapours, and to admit the fuel. 66 INTERESTING EXPERIMENTS BEFORE THE ROYAL SOCIETY ON RESISTING THE AGENCY OF FIRE. At the weekly meeting of the Royal Society on Thursday, the 21st inst., Chevalier Aldini, of Milan (nephew of the celebrated Galvani), exhibited some remarkable experiments on resisting the agency of fire. The fol 413 lowing account of them we extract from the "Literary Gazette :" "The Chevalier handled red-hot pokers as freely as he would walkingsticks; and also supplied asbestos gloves, by which such of the company as chose to make the trial were enabled to do the same. He informed the Society that he had succeeded in constructing an apparatus, or rather clothing, to preserve persons from injury who are exposed to flames; the efficacy of which had been proved at Geneva, where he showed the firemen that a finger, enveloped first in as bestos, then in a double case of wiregauze, might be held in the flame of a spirit-lamp or candle for a long time before inconvenient heat was felt; and then clothing them gradually accustomed them to the fiercest flames. A firemen having his hand in a double asbestos glove, and guarded in the palm by a piece of asbestos cloth, laid hold of a large piece of red-hot iron, carried it slowly to the distance of 150 feet, then set straw on fire by it, and immediately brought it back to the furnace, the hand not being injured at all in the experiment. Another experiment related to the defence of the head, the eyes, and the lungs. The firemen put only on an asbestos and wire-gauze cap, and a cuirass, and held a shield before his breast. A fire of shavings was then lighted in a chafing-dish, and the fireman plunged his head into the middle of the flames, with his face towards the fuel, and in that way went several times round the chafingdish for a period above a minute in duration. The Chevalier stated that he had an application before his Majesty's Ministers for a space of ground and adequate opportunities to exhibit his experiments.' The following interesting account of the material which figures so prominently in these experiments, we extract from the "Virginia Literary Museum:" Amianthus, a variety of asbestos, contains, per cent, about 59 parts of sand (silex), 25 of magnesia, and 10 of lime, besides traces of clay and iron oxide. It is usually found in veins, and consists of fibres very flexible, and somewhat elastic. Friction readily se |