160 ANSWERS TÓ INQUIRIEŚ—CORRESPONDENCE. and lodges in the most crooked parts, or cold endways than sideways. This and stops, in a great measure, the may be proved in the following manvent of the smoke. Sweep-boys, ner:-Let a hole be punched through also, when they are cleansing the the centre of a square plate of iron, chimneys, are almost always sure to touch the edges with a little tallow leave part of the rubbish. or soft wax; then put a hot bar of If “ J. T.” will take a bricklayer's iron through the hole, and that edge advice, he will contract his chimneys on which the tallow first melts will regularly at the throat, and make be the endways of the iron; the them rather smaller there than in any elastic nature of the iron, and the other part. He will also take care stocks giving way, are the causes of not to make them less than nine by the irregularity in the screw. fourteen inches, to have them ga I am, Sir," thered over regularly in all the crooked parts, and to render the Your most obedient servant, whole perfectly smooth. If these · M. MONnom... particulars are attended to, there will be no fear but the smoke will go the right way. I am, Sir, NOTICES CORRESPONDENTS.: TO Hammer "believes that the invention : No. 109.-CUTTING SCREWS. of the gun mentioned by 0. (page 132, Sir,-A Correspondenr, in p.399, vol. iv.) belongs neither to Blanche nor vol. 111., wishes to know the cause of Screws being largest at the ends, Pauly, having seen it applied to a flintwhen cut by the stocks and dies, and lock above twenty years ago." ; how they are to be cut true. This The Inquiries of H. and F. were unmay be effected with good stocks and dies in the following manner : designedly overlooked. Take a piece of round bar iron, or a Communications have been received eylinder that has previously been from M. M.-N. H.-T. C.-Charles M. turned in the lathe; let the pin be --B.-G. U. A.-W. K.-C.–A.G, Gtwo or three inches longer than you intend to cut the screw ; lay it in a Montis, jun.-W. E. K.-Tempus-An good charcoal fire : suffer it to get Old Subscriber-R. M‘Pherson. :? cold of its own accord; clean off the scales by draw-filing, and screw it firmly in the vice; open the stocks. ERRATA, „Page 133, col. I, line 1, for and put them on the pii, about an · louded read leaded gun.- Page 140, col. I, 40 inch from the end ; screw them suf end: screw them suf. line 14 from the bottom, for 24751. read ficiently tight to mark out the 54751. threads on the pin ; turn them down to within an inch of the other end; tighten the stocks, and bring them up again, and so on, until a full Communications (post paid) to be addressed to the Editor, at the Publishers', KNIGHT and thread is used. I find, from a num LACEY, 55, Paternoster-row, London. ber of experiments, that wrought iron more strongly contracts heat Bensley), Bolt-court, Fleet-street. baranid 162 IMPROVED PRINTING PRESS IMPROVED PRINTING PRESS. justing screw :C, a rod, connecting the end of the cross lever, d, to the lever e, Sir, I have sent you a descrip. which we may consider part of the lever tion, &c. of the improved « Russell That Press ;" as I am now manufacturing : the plattin, or upper surface, may always manufacturing remain parallel with the table, or under them, perhaps you may be pleased surface, two cylindrical rods, screwed to insert it in your Mechanics' Ma into bosses on the upper side of the gazine; if so, it is at your seryice. plattin, and at right angles to its surface, are accurately fitted to the inside of two I am, Sit," : cylindrical gun metal guides, which are Yours sincerely, firmly secured to the back of the press by collar-headed bolts. «. i ! Henry RUSSELL. It would be useless to describe the London, June, 1825. other parts, as they are common to most iron presses, except that, instead of employing the drum and girths fon cartying in aud out the table, &c. I have employed On inspecting the drawing, it may be a wheel and rack; which, without conreadily perceived that the power of ihis sidering the injuries sustained by workpress is derived from the twofold appli. men from the breaking of girthsy and the cation of that principle which was 'in- loss of time in replacing them, when troduced to the printing press by Lord time is of great importance, I hope will Stanhope, and which nearly all succeed be found preferable." ing press-inakers have found it advisable The pressman having passed the table, to adopt. with form, tympan, paper, &c. under It is now about four years since my at the plattin, with his right hand draws tention was turned practically) to this the bar-handle towards him, until the subject, and the result was the produc- lever, e, comes in contact with the back tion of that press, called the “Russell of the press; at the same time the conPress,” which name it received from necting rod, c, draws after it the cross Messrs. Taylor and Martineau, engi- lever, Ld, which swings freely upon a neers, in whose service I was at that perpendicular bólt, 'the head of which is time employed. seen at o. The length of the connecting I had, I believe, then seen only the rod, c, is such as to bring the pressure Columbian, the Stanhope, and the ori columns (each six inches in length) ginal screw press; but very soon after, I within 1-8th of an inch of perpendicular, had the pleasure of seeing Ferguson's at which time the impression is given, Lectures, edited by Dr. Brewster, in and the centre of the counecting rod the additional volume of which is a 'de comes within one inch of the centre of scription of a printing press on the same the bolt, r, which is the centre round which the bar-handle describes a section principle, though constructed in a very different manner, by Mr. Wells, of Hart of a circle. The middle of the barford: but the construction of the press handle, or where the pressman may be to which I now wish to call your atten supposed to be to take hold of it, is 20 tion, although the principle is the same, inches from the centre, r. The power differs very much from them both. at the termination of the pull may, there fore, be estimated in the following manAn adjusting screw is introduced, the ner:-The length of the lever bar. (20 head of which is marked A, and has on inches) being divided by the distance of it a ratchet, into which a spring, B, the connecting rod from the centres in catches, to secure it from turning when (one inch), gives a quotient, by which is the press is in operation : the bottom end of this screw, which is of an hemi to be multiplied the power applied to the spherical figure, enters the upper pressure bar-liandle, say 281bs. *28 = 560; column, C, which is hollowed out hemispherically, in a manner suitable for its 5601bs. power is therefore applied to the reception; the bottom of this column is end of the lever, Ld, in length 5 inches, hemispherical, and in like manner en which carries the bolt, a, by whide the ters the bolt, a, which passes through pressure columns are brought to the po sition required. the cross lever, L, and is in like manner This bolt, a, is 2 fitted to the under column, which is also inches from the centre, o; we hare • 19200.liemispherical, and enters the circular therefore ; x 560=55lbs. applied to plate, which is secured to the top of the plattin by the two eye-bolts, bb." These the columns. eye-bolts are entered from the back by a T he power of either column may be forked lever, which passes through an found by dividing its altitude by its deeye, and has at its end a weight, which viation from a perpendicular line, let bears up the plattin, &c. and keeps the fall from the centre of the adjusting upper column in contact with the ads screw, which we have before stated to ON THE USE OF THE SLÍDING RULE-BROWN'S GAS ENGINE. 163 be 1-8th of an inch. This must be di. RULE, vided by the number of columns, which 481' Şet) on B to the number on A, will be equal (or very nearly) To= 24, then against the number on B is the ...idh, FL"!!! 11200 260,000 which multiplied by square on Al; = it! = Dosiahne 24436,4 tons 10., 18..0..20 4. We ! REAMPLE, hare made no allowance for frietion, What is the square of 76?_Set 1 which, in this construction, must be very little : and it imay be remembered on B to 76 on A, then against 76 that we applied a power of only 28 lbs. on B is 5776 on A, the square reThis may, however, be increased by quired. " lowering the adjusting screw, and a much EXAMPLE II. greater effect produced. . Taking advantage of the suggestions Required the square of 144?-Set on the ev velope of the Supplement to the Ion B to 144 on A, then against 144 third volume of the Mechanics' Magazine, on B is 20736 on A, the square I have to státe, that the above presses required. are to be had only at the manufactory, Nobu 10, 41 Macclesfield-street, Canal PROBLEM IV. bridge, City-road. To extract or find the square root "Super Royal, plattin 20 by 26), 55l. of any number.. die jij Dr. Cash... ... 501. ! Warranted two years. Other sizes in RULE. proportion. , Set 1 or 100 on C to the 10 on D, tir. is then against any number on C stands its root on D. mend it to 1. ods! NOTE. THE USE OF THE SLIDING RULE. If we account the numbers on C 315--, (Continued from page 158.) i as tens, those on D will represent units; if on C hundreds, those on D El voti PROBLEM II. tens, and so on. „To divide numbers by each other... EXAMPLE 1; What is the square root of 144?BELOT 99701 . * RULE.";. Set I on C to 10 on D, then against TO1.1998 j-20: - 1 Set the divisor on B to the divi. 141 on C is 12 on D. dend on A, then against I on B is EXAMPLE 11. the quotient on A. What is the square root of 20736 ? -Set 100 on Cto 10 on D, then -""}( dows EXAMPLE I. against 20736 on C is 144 on D. Divide 312 by 24.-Set 24 on B We may here notice that we must, to-312 on A, then against lon B is in this case, reckon the 10 on D as thie quotient, 13 on A. 100, and the 20 as 200, &c.; because 07 Ot heid . "Mi * we have reckoned on Cas thousands, 006 - Dr EXAMPLE II. as in the First Example we reckoned 30: Divide 3136 by 64.-Set 64, the' on Cas hundreds, so on D we reckon divisor on B, to the dividend 3136 as tens, and if we had reckoned the on A, then against l' on B is 49, the number on C as tens, we must call quotient on A. the numbers not as 10, 20, &c. but Godine 19 as 1, 2, &c. G. A. S. To square any number. I . (To be continued.) 19 PROBLEM, III. M 2 ( 164 ) PROPOSITION 1.- PROBLEM. INVESTIGATION AND SUMMATION OF A NEW SERIES, EXPRESSING THE LENGTH OF A CIRCULAR ARC. (Continued from page 153 of our last Number.) In the mean time we shall show how the aproximate sum may be determined by means of an infinite series, in terms of the tanyent of the given arc, in the following manner : nt 2 22 23 n? 12 + 2 nt nts (mmet 2-me-ve+,*-*-, &c.) nt 1 6 62 63 64 & By Division, 12 12 + 6-nt-73 48 + x) 45 77 77 + ny -, &c. nt 12 122 123 124 >ad infinitum: 12.42 +12=17-n343 + 75 45 27 27+ n° 49, &c. int 120 202 203 204 & m2 42 120=ntn3+3+ 75 75 - 7t7+ 9 89~, &c. when the law of the coefficients, or numerators, of the serieses in the vertical column is very obvious; the first column being the sum of a series of units, the second the sum of the triangular numbers, the third the sum of their squares, the fourth the sum of their cubes, the fifth the sum of their biquadrates, &c. &c. Whence, by taking the successive differences of each series, we find that the Ist, 3rd, 5th, 7th, 9th, &c. orders of differences become respectively equal to nothing, and, consequently, we can assign the sum of n terms of each series by means of the well-known differential series : non-l 22.n.n-1.2-2 2, n.n-lin-2.n-3 $na + 1.2 . 1.2.3 .de 1.2.3.4 Let, then, a, b, c, d, &c. denote the sums of the 1st, 2nd, 3rd, 4th,.&c. 0 . 0–1. n-2 + A .., serieses respectively, and we shall ha 3 n3 13 se n.n-1.9-2.9-3.1-5 + B , non-1.n-2.n-3.n-4.n-5.n-6+C 5 25 5 7 ni 17 3. n--4.1-5. n-6.1-7.n—8 +!, &c.; whence e=+ 9n9t9 the capital letters, A, B, C, D, &c. represent the sum of all the terms, minus the last, which arise from substituting :he successive differences in the aforesaid differential series. Now, from the nature of this series, it is evident that the highest power of n in each of the functions, A, B, C, D, &c. will be one dimension less than the bighest power of n in the corresponding denominator. It follows, therefore, that when n is indefinitely great, the successive quotients arising from dividing the said functions by the respective denominations heivg equal to a series of finite, divided by a series of infinite quantities, will be equal to nothing. In this case, also, n = n - 1 = n - 2, &c.; because an infinite quantity is not decreased by subtracting a finite one from it. Hence |