Ac 20, vol. IV.). The figure represents a strong deal box, resting on pedestals, of an oblong shape, and about four feet long. cording to the height in the clear, shelves are to be fitted, so as to rest on cleats, and be removable at pleasure. The distance between the shelves should be about six inches, and the shelves are to be formed of bars or laths, so that each shelf may consist of a single perforated frame, similar to a gridiron. The cover, which takes off, is to be steam-tight; and when on, is to be fastened by a bar that runs through the two projecting staples. A puppet-valve is to be inserted into the cover, and supported so that it may rise and fall without being thrown out. cock, or spigot and faucet, is to be inserted in the side, and close to the bottom. A The manner of proceeding is as follows:-The linen are to be first rubbed separately with hard soap, then placed on the lowest shelf (the fewer pieces the better), and spread at full length; then put a shelf over these on its rest, with soaped linen on it; then another shelf, and so on; observing to act so as to promote the transmission of the steam as much as possible through the linen. A pipe, having a stop-cock in some part of it, being inserted in the top of the wooden vessel of the boiling machine (p. 20), is likewise to be inserted in the side of the steam washing-box; then it is only necessary to turn the stop-cock by which the steam enters, and the process of steam-washing goes on. After some time, turn the cock of the washingbox, to let off the dirty water; do this at intervals, and when the water is perfectly clear, the linen is strained enough. The linen is then to be taken out and rinsed, when it is fit for drying. Wood that yields colour and turpentine, and metal on the inside of the box, are to be carefully avoided. Should the steam from the waterbox not be strong enough, it may be obtained from a common cooking DESCRIPTION OF THE DANAIDE, A MACHINE ACCELERATED BY FRICTION. SIR,-Although the effects of friction are an insurmountable obstacle to the engineer, yet, nevertheless, there are some machines wherein friction, instead of retarding, actually accelerates the moving force; and I beg leave to place before you the drawing of a machine, where this assertion is strikingly exemplified. As I have never seen any drawing or model of this machine as it came from the hands of its inventor, M. Mannoury Dictot, yet I have endeavoured to sup-. ply this defect to your readers from the description, as given of this machine by Messieurs Perier, Prony, and Carnot, in their Report to the French Institute. These gentlemen also tried to ascertain what might be the amount of the effect produced by the Danaide (for that is the name of the machine), by fixing pulleys in such a manner as to raise a weight from the ground, and, by many repeated trials, they discovered that 7-10ths, and sometimes 75-100ths of the moving power, was the effect produced-an effect, in fact, which is greater than any machine that we are acquainted with. The model by which Dictot exhibited his experiments, consists principally of a trough, the bottom of which has a hole 42 ENCOURAGEMENT OF INVENTIONS AND DISCOVERIES. in its centre; it is cylindrical, nearly as high as it is broad, and made of tin plate. It is fixed to a vertical axis of iron, which passes through the middle of the hole in the bottom, leaving a vacant space all around, through which water escapes as it flows into the trough from above. This axis turns with the trough upon a pivot, and is fixed above to a collar. The object of the inventor was, that the water Sowing into the trough from above, with a certain quantity of vis viva, should communicate the whole of it to the solid parts of the machine, so as to be employed afterwards in producing some useful effect, always excepting the small quantity of force necessary to enable the water to escape by the orifice below. This object he thus obtains :-Within the trough there is affixed to the axis a drum, likewise of tin plate, concentric with the trough, and close above and below; this drum, which turns round with the trough, occupies nearly the whole of its capacity, the space between the two not exceeding an inch and a half: a similar space exists also between the bottom of the trough and the drum; it is, however, less than the former, and is divided into several compartments, by diaphragms proceeding from the circumference to the central hole in the bottom of the trough. These diaphragms do not exist between the sides of the drum and the trough, and the compartments of the bottom communicate with this annular space. The water, which comes from a reservoir above, by one or two pipes, makes its way into this annular space between the drum and the trough; the bottoms of these pipes correspond with the level of the water in the trough, and they are directed horizontally, as tangents to the mean circumference of the trough and of the drum. The force which the water has acquired by its fall along the pipes, causes the machine to move round its axis; and this motion gradually accelerates, till the velocity of the water in the space between the trough and the drum equals that of the water from the reservoir, so that the shock of the water from above upon that in the machine becomes imperceptible. Now this circular motion communicates to the water between the trough and the drum a centrifugal force, in consequence of which it presses against the sides of the trough. The centrifugal force acts equally upon the water contained in the compartments at the bottom of the trough, but obviously less and less as the water approaches the centre. The whole water then is actuated by two forces, which oppose each other, namely, gravity and the centrifugal force. The first tends to make the water run out at the orifice at the bottom of the trough, the second tends to drive the water from that hole. To these two forces are joined a third, namely, friction, which acts an important and singular part, since it promotes the efficacy of the machine; while in other machines it always diminishes that efficacy. Here, ou the contrary, the effect would be nothing, were it not for the friction, which acts in a tangent to the sides of the trough and drum. By the combination of these three forces, there must result a more or less rapid flow from the orifice at the bottom of the trough, and the less force the water has as it escapes, the more it will have em. ployed in moving the machine, and consequently in producing the useful effect for which it is destined. The moving power is the weight of the water running in, multiplied by the height of the reservoir from which it flows above the bottom of the trough, and the useful effect is the same product diminished by half the force which the water retains when it issues from the orifice below. The prefixed, Drawing of this Machine will convey some idea of its construction to your readers. I consider this machine as being worthy the attention of the practical engineer. I am, Sir, Description of the Drawing. Fig. 1. A represents the main for conveying the water; BC, the trough, the bottom and one side being taken away; D, the drum, with its axis; E, the bottom of the trough, as divided into compartments, &c. Fig. 2, section of the bottom of the trough, with the diaphragms; the dotted circle represents the drum. ENCOURAGEMENT OF INVENTIONS AND DISCOVERIES. In the course of our editorial avocations, nothing has been more frequently and painfully forced upon our attention, than the difficulty which men of genius, who are in humble circumstances, or resident in remote parts of the country, experience in turning their inventions and discoveries to practical account, for the benefit of themselves and the public. Our table is covered with letters from individuals thus situated: some stating their inability to bring forward designs, which they conceive to be of undoubted utility; others submitting hints and suggestions, which they wish to be subjected to COMMON ERRORS IN MEASURING ROUND TIMBER. the test of experiments, the expense of which they are unable to defray, or do not feel themselves justified in risking; others, again, complaining, that improvements which they have perfected, and the right to which they have secured to themselves, remain neglected and unproductive, from the insufficiency of the means that have been employed to introduce them into general use; and all soliciting, in one shape or other, assistance, which we have been able in but a few instances to grant or procure for them. The recurrence of these circumstances has led to steps for the formation of a joint stock association, to be entitled, "The British Invention and Discovery Company, for the Assistance, Encouragement, and Protection of Native Genius, and the profitable Investment of Capital, in the prosecution of original Inventions and Discoveries by British Subjects." The proposed capital is 750,000l., to be raised in 15,000 shares of 50l. each. The scheme was first publicly announced on Monday last, and already there are more than the whole number of shares applied for. The time for receiving applications, however, extends to the 7th of May; and it being obviously of great importance to the interests of the Company that it should spread its roots as widely as possible, it is likely that the distribution of shares wili be regulated more by that consideration than by mere priority of application. A more specific prospectus of the objects of the Company, with the names of the Board of Management and other Officers, is to be issued at the close of the time for receiving subscriptions. Such of the friends and correspondents of the Mechanics' Magazine as may be desirous of procuring shares, may address their applications to the care of the Editor. 43 in being the first to show its errors to the readers of your very valuable and justly popular Magazine, and I have no doubt but many of them feel obliged to me for doing so, in a manner capable of being understood by the most illiterate; nor am I at all surprised that there should be found advocates for so palpably erromechanic has been taught, almost from neous a method, when I consider that every his infancy, to believe it as infallible. Your Correspondent "T. M." has said all that he can say in its defence, but he must not forget that "old men are not always the wisest;" for though I have not arrived at that age when the law considers a person capable of being his own master, yet I certainly think that my knowledge of the subject in hand is quite equal to his, though he be an old mau. But, without farther ceremony, I shall proceed to make a few remarks on his last letters; and, in the first place, I consider his supposition of a tree in the form of a triangular prism as perfectly ridiculous. There never was a tree that grew in that shape, or ever approximated toward it; and if we are to possible to find even an approximate rule make such suppositions, it will be imto suit every case that may be supposed, for the circumference of a span may be infinitely great, while the spau itself, or its area, may be infinitely little; it is, therefore, evident, that if we consider trees under any form that they may be supposed to have, and not as they naturally are, that no rule which directs to take the circumference in order to find the content, can be used with any accuThus we may suppose the sections of a racy in every case that may be supposed. tree forty feet long to be right-angled parallelograms, the longer sides of which are 23 inches, and the shorter half an inch, and consequently its solid content is 3 feet 3 inches; while by the common rule its content shape would be found to be 40 feet. But who ever saw a tree growing in this form, or in that of a triangular prism? Every person at all acquainted with timber knows that its shape is geformer letter, I gave the true content of nerally circular. In my reply to T. M.'s a tree 40 feet long, and 48 inches in cir cumference, every section of which, at right angles to the axis, was an ellipsis, having its transverse diameter 17, and its conjugate 13.3 inches, and showed that the difference between its true content and its content, as found by calcu-lating it as a cylinder, was but 1 foot 8 inches, while the difference between its true content, and its content as found by the common rule, was 9 feet 3 inches; and yet T. M. still persists in saying, that that rule is as correct as any other. He also tells us, that "the ellipsis being a regular curvilineal figure, does not greatly vary from a circle, but contains 44 COMMON ERRORS IN MEASURING ROUND TIMBER. more within its circumference than any other figure of the same proportion." By this I suppose we are to understand, that Measurage very well knew, that if he did not consider trees as elliptical, he could not make his case appear so plausible as an ellipsis being a regular," &c. Here your Correspondent has fallen into a sad mistake; and I beg leave to inform him, that the primitives of an ellipsis may infinitely exceed that of a curve, and yet its area may not be so great. The reason why I considered the tree as elliptical, was, because I know that they generally approximate nearer to that figure, or to that of a circle, than to any other figure whatever. I know they are never perfectly of one figure or the other, but the variation is too insignificant to be noticed in timber-measuring. Since I wrote my last letters on this subject, I have examined a great number of trees, and I have not found one in a hundred with so great a degree of eccentricity as the one above named; and as there are ninety-nine out of a hundred that have a less degree of eccen. tricity (indeed, the sectious of a great many approach so near to circles, that the difference is not worth notice), we may safely conclude, that the difference between measuring it by considering its sections as circles, and its true content, in a number of trees which hold of the same size from one end to the other, would not be more than 9 inches in 40 feet; whereas, by the common rule, that difference would be nearly fifteen times as great; and I think it will be allowed by every person of common sense, that when perfect accuracy is unattainable, that rule which approximates nearest to it is the one that ought to be adopted by every person at all concerned in the matters. But without insisting farther on this point, I come now to show, that the rule which T. M. tells us was first introduced by me, actually gives the content of almost every tree too little. This may appear paradoxical to him; but I suppose he will admit, that trees seldom grow of the same size from one end to the other, but are generally in the form of the frustrum of a cone. Now, the soli dity of a frustrum of a cone, expressed D3-13 in algebraic terms, is this:D-d L 3' px 3 where D the greater diameter, d the lesser, p the area of a circle whose dia meter is unity, and L the length. The solidity of a frustrum of a cone, calcu lating it as a cylinder, by taking its diaD+d2 meter in the middle, is L = 2 x px The following examples will make this appear plain to those who may not understand the algebraical process. Ex. 1.-What is the solidity of a tree 40 feet long, and 24.54 inches diameter at the greater end, and 6 inches at the lesser? ANS.-Its true content will be found 57 feet 1 inch, which is 6 feet 2 inches, 40 or (24.54-6)2 x .7854 × more than 12' would be made by taking its diameter in the middle, and calculating it by the rule for a cylinder, and 17 feet 1 inch more than by the common rule! Ex. 2.-What is the solidity of a tree 40 feet long, the sections of which, at right angles to the axis, are ellipses, having their diameters at the greater end 24 and 18.6 inches, and at the lesser 10 and 8 inches? ANS.-52 feet, which is one foot and one inch more than would be made by girting it in the middle, and calculating it by the rule for a cylinder, and 12 feet more than by the common rule. With such proofs as these before their eyes, surely no persons will be found hardy enough to assert that the common method of measuring round timber is as correct as any other. I think this cannot fail of convincing even T. M. himself; but, as he is not willing to receive a rule from a young mau, perhaps the following quotation from "Leybourn's Complete Surveyor," printed more than a hundred years ago, will do more towards convincing him of his errors than all which I have said; it will, at least, show him that I am not the first who has "attempted the cylindrical method." "As there are grand customary errors continually committed in the mensuration of unequal-sided and tapering timber, so there is one also in the measuring of round timber, which transceudeth them all, and that is this :-lu timber trees they usually girt the tree about the middle of the trunk thereof with a line, and take one-fourth part of that girt for the side of a square, and with this they find the content of the tree as if it were a square whose side is equal to a fourth part of that girt; but this is egregiously false, for it always gives the |