MILL-SPINDLES-CHEAP FAMILY MANGLE. · 103 Only think of the effect of four streams of water falling from the hurst against the partitions, binns, flooring, &c.-for it could not be kept from splashing! Besides, how is the water to be procured in flour mills of three and four pairs of stones, driven by the wind, as in the town of Hull, where there are about forty windmills nearly one hundred feet high each? The stones, though, not at the top of the mill, are situated at a considerable height, and, if all going at once, would want (1 calculate) a separate establishment of water-works to supply them. If "Bellidor" would wish to see some of the best fitted up steam flour mills in the world, let him come to London. It is a bold word (I guess), but not the less true. The best millstone spindles for not heating are now generally made of castiron, and constructed as represented in the following figure: a is the square; b the "cylindrical part, working in a packing; c the conical part where the stone pinion is fixed on; d the bottom, of a sphe. rical shape, working in a gun metal step, which is raised up or let down to its work by the screw on the bridge tree. The total length of the spindle is about 4 feet, its diameter 3 inches. Some fifteen or sixteen years ago, there was a steam mill erected for a Mr. Ritchie, of Deptford, which was of twenty horse power, and had four pairs of French burs, or stones, of 4 feet 6 inches (the common size); and though it often worked day and night, the stone spindles were never found to heat; but then, to be sure, there were a good stone dresser and good millers in the case. I suppose our American friend can first heat his goods, then his stones, and last, though not least, his "toes," as he is pleased to call them. The Americans certainly have hit upon several 104 PLAN FOR PREVENTING VESSELS RUNNING FOUL AT SEA. The prefixed figure is an end view of the mangle, such as I have it now in use at my house. It is 1 foot 4 inches in height, 8 inches in breadth, and 2 feet 2 inches long. A is a screw affixed to a piece of wood, in which the upper roller works, for the purpose of raising it, to put the linen between the two rollers, and then pressing it for working. The pieces of wood 1, 2, in which the rollers work, are fitted into grooves in the upright standards 3 and 4; the dots on these pieces of wood are merely to show the line of the rollers at the other side of them. B B are two strong iron screws, to screw the top 5 on, in which the screw A works. A piece of flat iron is placed on the top of this board (4), to prevent its rising when the screw is set down for use. C the handle, fitted on the lowest roller. DD the rollers, 1 foot 11 inches in length, and 4 inches in diameter. Arctic Cottage, Cowes, Isle of Wight, Feb. 21, 1829, PLAN FOR PREVENTING VESSELS RUNNING FOUL OF EACH OTHER. In consequence of the announcement this week of a Leith smack having been run down by another in the dark, our friend, Mr. Gilman, has forwarded to us the following excellent plan for the prevention of such accidents. It is headed as being an "Extract from Observations made at the time of the loss of the Comet Steam-boat;" and though not literally applicable to vessel. of the description of the Leith smacks, is capable of being very easily adapted to them: "This plan for preventing vessels running foul of each other by night, consists in placing a light at each mast-head fore and aft; the light on the fore-mast to be marked by some peculiarity of form or colour, by which it may be readily distin. guished. Hence, on two vessels approaching each other, the angle occasioned by the divergence of the aft-light, either to the right or to the left of that on the fore mast, would instantly point out the bearing of the vessel coming ahead, when the persons on the look out have only to consider the direction of their own vessel relative to the position in which they stand (a thought of an instant), and the respective bearings of the two vessels would, in a moment, be ascertained with as much certainty as by daylight, and thus in a great measure all danger of contact would be avoided." MR. IBBETSON'S SPECIMENS. MR. IBBETSON'S SPECIMENS. From the difficulty of transferring, by the hand, to wood, figures of the description of those produced by Mr. Ibbetson's geometric chuck, the specimens which we published two weeks ago, furnished, necessarily, but very imperfect exemplifications of the extraordinary nicety and ex. actness with which that chuck performs its operations. This must have been particularly observable with respect to the figures 2 and 3 (p. 56), which were intended to illustrate the power which the apparatus possesses of dividing the peri 105 phery of an ellipsis (whether more or less eccentric) into any number of perfectly equal parts. We have now the pleasure of presenting our readers with impressions of the same figures, taken from blocks engraved by the chuck itself; which will leave no doubt in the minds of any one, of its possessing the power in question (so long a desideratum), in the highest degree of perfection. We give also an engraving of fig. 4, executed by the machine; the line in that which we formerly published having had a curvilinear direction given to it, contrary to the true one. O Mr. Ibbetson adds, that it is on a rotary motion this curve depends, and that he can obtain it by his geometric chuck. In our note to Mr. Ibbetson's last published communication (see page 57), we introduced two specimens forwarded to us by Mr. Child, as proving that he had obtained, by his apparatus, several close approximations, at least, to an equal division of the ellipsis. Mr. Ibbetson observes, in reference to these, in a letter we have received from him :-"I do not dispute Mr. Child's knowing the principle on which a perfectly equal division of the ellipsis is to be effected; but I say he has never yet actually divided an ellipsis into equal parts; he has never thrown the looped figures at equal distances in the curve of an ellipsis; and I have no hesitation in affirming, that he never can do the thing with an apparatus avowedly performing so incorrectly as Mr. Child's does." Mr. Ibbetson's impression on this head seems to derive some confirmation from the following letter, which we have received from another correspondent, on the subject of Mr. Child's per. formances: been favoured with a place for my communication respecting the figures in ornamental turning, in your valuable work, I again request, on the same subject, a corner in its amusing pages. No. 285 contains specimens of fancy turning, by your very ingenious correspondent, Mr. Chapman; and having carefully examined them, I can confidently assert, that the instruments shown to me by Mr. Child, near Halifax, produces all the figures in Mr. Chapman's specimens, and an almost infinite variety of others, perhaps more curious and interesting. I beg leave to ask Mr. Chapman, through the medium of the "Mechanics' Magazine," if he can place ovals (i. e. egg-like figures,-not ellipses) in a circular or elliptical form, at equal distances, and in any position required in respect to the figure in which they are placed? There is also, in Mr. Child's instrument, a motion for producing figures of a very singular form; this motion is, I believe, known to himself alone. The figures produced by it are inimitable,-if it is possible to describe figures which cannot be imitated. It contains, besides, a motion peculiar to itself, and which is, un Sir,-On a former occasion, having doubtedly, according to Mr. C. a3-y3 2 x z3.. x+y=2xy: call this equation (A) x2-y-x y. (A) minus (B) .... 2 y2 = 2 x y2 -x y (B) (C) 2 y 2y-1 (D) By division at (H). y2=—•••y=£√/5. Hence, the value of x, at equation (G), is (5+√/5). The above method I had about five years ago, from my friend Mr. G. Ferrow, of Glasgow. The method, as your readers will perceive, consists in arranging on one side of the equation all the terms in which the quantity fixed upon for extermination appears; and then, by a continual division, the quantity will ultimately vanish. The above example, will sufficiently illustrate the_method. In conclusion, allow me to propose three more questions, to exercise the ingenuity of your algebraical correspondents. First. Given, + xy + y2=52, and x y-x2-8. Second. -2xy-y2 } x2+ 2 x y-y2=101. 31, and Third. x 2 x3+x=132. To find x and y in the first and second, and x, in the third, by simple equations. I am, Sir, Yours, &c. ERROR IN PROFESSOR L SLIE'S "GEOMETRY." Sir,-Professor Leslie, in the 16th Proposition, Book I. of his "Geometrical Analysis" (third edition), gives a solution of the following problem : "From the vertex of a given triangle, to draw a straight line to meet the base; which shall be a mean proportional between the segments of the base." The learned Professor divides the problem into two cases. 1st, When the section is external; and, 2d, when internal; and in both cases the analysis and compositions are strictly true. But he has fallen into a singular blunder, in assigning the limits of the problem in the Scholium he gives, which is as follows:- "Scholium. "In the first case, if the vertical angle be acute, the centre of the circumscribing circle will lie within the triangle; and, consequently, the interior circle not intersecting the base, the construction fails, and the problem becomes impossible. When |