R. Daniels. "The improvement consists," says the patentee, "in the remanufacture of wool into cloths of various kinds, such as broad cloths, kerseymeres, satinets, and others of a similar character, and into cloths in which the warp consists of cotton, silk, or other material, and the filling in whole or in part, of wool; or of cloths in which the cotton, silk and wool are mixed together, and are carded and spun in their combined state; all of which I have successfully essayed. The wool so remanufactured I obtain by taking worn-out woollen goods of various kinds, and also wornout silks, and reducing them to their original state by means of machinery which I have invented for that purpose (and for which I have made application for letters patent, simultaneously with the present application) or reduced by means of any other machinery which will produce said fibres of wool in a state fit for remanufacturing into yarn and cloth. "I sometimes take such restored wool, and card, spin, and weave it, alone, or I mix it with fresh wool in proportion of, at least, one-sixth part of the restored wool to fivesixths of the fresh wool, and I, in either case, thereby obtain yarn or cloth equal in all respects to that which can be obtained from either fresh, or new, wool of the same degree of fineness, a result not heretofore obtained, and by which I am enabled to produce such cloth, and sell it at a price considerably lower than that of cloth consisting entirely of fresh, or new, wool; as it is a fact which I have established by full experience that the reproduced fibres of wool may be obtained from the worn-out woollen goods, pound for pound, at a very trifling cost." NOTES AND NOTICE. A Scientific Commander.-Captain Carpenter is having the pinnace of the Geyser Steam Frigate, to which he has been lately appointed, fitted with his own patent propeller. The Admiralty have given permission to have a small engine of 5 or 6-horsepower from the Disc Company for the purpose. There is little doubt of this portable steam-tug being of great service in towing boats with troops, &c., up the rivers and canals in China, to which station the Geyser is supposed to be destined. Notwithstanding the number of steamers in the service now, there is not one of Her Majesty's steam-vessels employed either in India or China.-Times. -Levels of the Mediterranean and Dead Seas.-At a recent meeting of the Royal Geographical Society, a letter was read from Colonel Chesney, stating that a line of levels had been carried from Jaffa to the Dead Sea by Lieutenant Symonds, of the engl neers. The work is said to have come out admirably, and the result is, that the Dead Sea is 1,607 feet lower than the highest house in Jaffa, which, from the height of Jaffa above the Mediterranean, leaves a difference of 1,400 feet between the level of the two seas. Steam Engines in Belgium.—It is estimated that there are now at work in Belgium 1,300 steam engines, with a total power of 33,100 horses.-Galignani's Messenger. The Little Western.-The proprietors of this steamer (the building of which was announced at page 293 of our last volume), accompanied by several captains of the navy, and gentlemen connected with the commercial and with the scientific and engineering interests of the country, had on the 27th ult., an experimental trip down the river, in order to test the speed and powers of the vessel. The Little Western left her moorings off the Brunswick Hotel at a quarter to 11; the tide then running down, and the wind blowing from the south-west. There was, however, but little wind, and the weather was clear and pleasant. She was accompanied down the river by one of the fastest boats, viz., the Railway, for which she waited off Galleons, and with which she contested head and head to Gravesend. The speed of the Little Western is extraordinary; she reached the Nore Light within 2 hours and 55 minutes from the time of starting, and returned to Blackwall within 2 hours and 25 minutes. The distance is 44 miles. This vessel is built on an improved principle. Her tonnage measurement is a fraction beyond 721 tons. She measures between perpendiculars 200 feet, measurement over all 216 feet. Her keel measurement is 195 feet. Her breadth, clear of her paddle-boxes, is rather above 27 feet; and her breadth over all exceeds 47 feet. Her deck is flush from stem to stern, and she has two masts. Her internal accommodations are very good, as may be surmised from the measurement of her saloon and cabins, &c. The length of her saloon is nearly 44 feet, and the room is elegantly and commodiously fitted up, without being gaudy or fantastic; it is also a good height, and is 24 feet wide. The ladies' cabin is nearly 20 feet long. The engines, which are horizontal and low pressure, are of 80-horse power each. Altogether she is a most elegant craft, and an admirable seaboat; she has weathered a gale off the Land's-end, and proved her capability to contend against a rough sea and a heavy wind. This vessel was built at Bristol, by Messrs. Acramans, Morgan, and Co. She is a vessel excellently adapted for the London and Ramsgate station. Her prodigious speed, superior accommodation, and tractability, render her peculiarly desirable for trips in which convenience and rapidity are imperative.-Times. Intending Patentees may be supplied gratis with Instructions, containing every particular necessary for their safe guidance, by application (post-paid) to Messrs. J. C. Robertson and Co., 166, Fleet-street, by whom is kept the only COMPLETE REGISTRY OF PATENTS EXTANT, (from 1617 to the present time.) Patents, both British and Foreign, solicited. Specifications prepared or revised, and all other Patent business transacted. LONDON: Edited, Printed, and Published by J. C. Robertson, at the Mechanics' Magazine Office, Mechanics' Magazine, MUSEUM, REGISTER, JOURNAL, AND GAZETTE. No. 967.] SATURDAY, FEBRUARY 19, 1842. Edited, Printed and Published by J. C. Robertson, No. 166, Fleet-street. [Price 3d. MR. C. W. WILLIAMS'S HEAT CONDUCTOR BAR.-(ILLUSTRATIVE OF STATICAL AND DYNAMICAL HEAT.) ON THE CAUSES OF INJURY TO STEAM BOILERS. Sir,-In my last communication, I explained some of the reasons which justified our considering that the sources of injury to boilers, (as regards the overheating of the plates,) were referable to the character and heat-absorbing properties of the recipient to which the heat was transferred. I then enumerated the five recipients which present themselves in ordinary boilers, namely, 1. Water; 2. Steam; 3. Air; 4. Incrustation deposit, crystallized; 5. Loose deposit, uncrystallized. Having already examined the conducting powers of the two latter, I have now to consider those of the three first mentioned. Water is, unquestionably, the most rapid and best recipient for ordinary purposes, and air the slowest and worst. So long as the water in boilers remains in contact with, or has free access to the plates, the latter will sustain no injury, inasmuch as the body or stream of heat passing from the fire, and through such plates, by reason of the superior conducting power of the metals, will be taken up by the water as rapidly as it is passed to them. Hence, the plates themselvesthe conductors-remain uninjured, and unaffected, beyond a certain temperature. What that temperature is, I trust I shall be able hereafter to demonstrate, with sufficient accuracy for all practical purposes. That the plates or conductors remain uninjured by the transmission of heat, even of great intensity, may be illustrated by the following experiment. In the prefixed figure, (see front page,) let A represent an iron conductor bar, threequarters of an inch square and three inches long, one end being inserted into the vessel B, containing water, and the other end projecting so as to receive the heat from a powerful laboratory Argand burner, E; the intermediate part at G, between the flame and the boiler, being protected by two shields, F F. The flame was inclosed, as is usual in laboratory burners, with a metallic funnel, resem bling the glass funnels of ordinary lamps, the bar passing through an aperture in it, made to fit. By this means the heat was confined, and its action on the bar was very great. This funnel is omitted in the drawing, for simplicity sake. Immediately over the conductor bar, though BY. C. W. WILLIAMS, ESQ. at first not in contact with it, is placed the thermometer D, further protected by the two shields. In five minutes, the heat conveyed by the bar raised the temperature of the water to 92°, and the bar thermometer to 160°. In twenty minutes, the water reached 212°, and boiled, the bar thermometer being raised to 258°, at which it remained stationary. Here we see the entire heat taken up by the water was passed through the conductor bar, issuing, as it were, from its end at A, and through a section of the boiler side, of but threequarters of an inch square. The thermometer was then lowered until it rested on the bar, when it rose to 270°, and there remained stationary, the water boiling strongly. The Here we have two distinct temperatures, and two measures of heat. first, that which is felt by the bar, I will call statical heat, that is, the heat due to its status as a conductor; the second, that which indicates the current or body of heat conveyed: this I call the dynamic, or power-giving heat. These terms, statical and dynamical, I use from the want of others more appropriate; they are, however, sufficiently indicative of the distinction I am pointing out. I am now desirous of establishing the fact, that the degree of heat by which the conductor may be said to be affected is different from that which is transmitted through it. That there are, in fact, two distinct temperatures or degrees of heat to be attended to; the one, that which the plates or conductors may be said to feel, and which indicates the extent to which their structure or material would be affected; the other, that which is conveyed to the recipient, water, and which it absorbs. Now, to show that these two temperatures are distinct, and that their relation to each other is solely influenced by the absorbing power of the recipient, I give the following proof. The bulb of the thermometer indicating the statical heat stands at 270°, and remains stationary at that point, the water continuing to boil violently. To prove that this statical heat, whatever it may be, is affected by and dependent on the nature of the recipient, let such recipient be changed from water to air. This is done by turning the cock C, thus letting ON THE CAUSES OF INJURY TO STEAM BOILERS. the water out, and allowing the air to have access to the end of the bar at A, from which the heat issues. Air being now the recipient, the current of dynamical heat passing through the conductor bar is not received or absorbed as rapidly as it had previously been, by reason of the inferior absorbing power of the air, as compared with water. The result is, that the current of heat, in its issue at A, being retarded, accumulation takes place in the conductor, the statical heat is increased, and the thermometer instantly tells the fact by rising until it reaches 404, as shown in the following table. Thus we see, that so long as water was the recipient, the statical heat-that by which the metal would be affected, injuriously or otherwise-remained at 270°, but, with air as the recipient, it rose to 404°. This statical heat, then, as it indicates the state or temperature of the conductor plates, decides the main question of injury to the boiler; for if the temperature of those plates is thus kept down by reason of the rapidity with which the water absorbs the conducted heat, it necessarily follows, that it cannot amount to such a degree as to affect those plates by overheating, softening, or bulging. This is the practical application of the subject. Thus we see that the temperature of the plate is dependant, not on the quantity or intensity of the heat passing through it, but on the nature of the recipient, and the rapidity with which such heat is absorbed or taken up. We have thus, I repeat, two distinct temperatures to attend to, namely, the statical-that due to the plate or pin, in the capacity of carrier, conductor, transmitter, or conveyer-and the dynamical heat, that due to the current or quantity 131 conveyed. The former, we see, is dependant on the latter; in other words, the temperature of the conductor plates of a boiler is high or low, injurious or otherwise, in proportion to the rapidity with which the conducted heat is absorbed by the water or other recipient. I will hereafter show the analogy between this stream of heat passing through the conductor, and the pressure of water through a tube; and that the same statical and dynamical distinction may there also be drawn. In proof of the temperature of a conductor plate or pin being below that of injury or overheating, so long as water is the recipient, I have placed several pins in boilers, projecting from two to four inches, and exposed to the most intense heat, even where the adjoining brick-work was at a white melting heat. These pins, nevertheless, remained uninjured, and doing their duty as conductors. I may here mention a familiar experiment, which illustrates the fact of the conductor not being injuriously affected by the transmission of heat through it, so long as the recipient possesses the absorbent property which water has. I inserted a bottom, made of a circular piece of card paper, two inches diameter, and made to fit tight, into a tin vessel, and, by means of a little glaziers' putty, made water-tight round the edge. On being held over an Argand lamp, the water it contained was made to boil, while no injury, even to discoloration, took place in the card-bottom conductor; and on being removed from the lamp, it was found to be apparently cold to the touch: thus proving, that although a high degree of heat, dynamically considered, was flowing through this piece of card, the statical heat of the latter was insufficient to injure it. This leads us to examine the commonly received idea, that the durability of boiler plates will be influenced by the temperature of the furnace, and the degree of activity with which the fire is urged, and which subject I will examine in my next. I am, Sir, yours, &c. C. W. WILLIAMS. Liverpool, February 12, 1842. COMPOUND INTEREST. In this formula it is assumed that, according to common usage, the interest is made payable and added to the principal yearly, the amount for 1 year being only 1a, or the same as the principal would produce at simple interest merely; but it is evident that there is no reason, except a conventional and arbitrary one, why the period of a year should be chosen for this purpose, or why the sum should not bear compound interest during the first year; the interest might, if it were thought proper to do so, be made up half-yearly; the interest then due for every one of these periods of half a year, at the same rate as before, would be and, n years " 2 being equivalent to 2n periods, our formula would become, upon this supposition, = a Now, if these periods have any finite value, however short it may be, the accumulation or adding of the interest to the principal will take place at intervals some finite distance from each other; but it is easy to conceive, that by indefinitely increasing x, this distance may be so diminished as to become inappreciable, and thus the principal and interest may be supposed to accumulate together, continuously, instead of by skips, this continuity being the limit towards which we approach by making indefinitely large, or the period of time allowed for making up the interest indefinitely small. The amount of £1 for 1 year, would then no longer be simply is infinitely great in value. where z This may perhaps be said to be what the law of continuity would seem to suggest as the true theoretical view to be taken of the nature of compound interest, and it may become a question (perhaps, however, rather curious than useful), what difference does this mode of considering it make in the amount? what amount would be produced in n years, by £P put out to compound interest, supposing the principal and interest to accumulate together continuously, instead of at intervals of 1 year, as upon the ordinary system? Or, It will soon be perceived, that the value of the expression ( 1 + in creases when x increases, and it has therefore been supposed by some, that when a becomes infinite, A will become infinite too; or, in other words, that A taking the value of the interest period may be made as large as we please by sufficiently small. This, however, is not the case; we shall find that the expression approximates continually more and more as x is increased, towards a certain limit, which it can never exceed, and therefore this limit will be the value of A of which we are in search. a Expanding (1 + =)" by the bino mial theorem, we find it equal to the following series: |