gradually bringing up the desired motions by wheels and pinions of larger diameters. This is a subject which should be well considered before we can determine, in any particular case, what ought to be the pitch of the wheels. In the case above alluded to, where the supposition is a pinion of four feet diameter, or of one foot diameter, it is obvious that the same pitch for both would not be prudent. That for the small pinion ought to be much less than that which might be allowed in the case of the larger pinion. It is also equally obvious that the breadth of the teeth, in the case of the small pinion, ought to be much greater than that in the case of the larger pinion. It is evident, however, that, although great advantage may often be derived from a fine pitch, there is a limit in this respect, as also with regard to the breadth.

Hitherto our enquiry has been confined to what is called spur-geer, or the action of wheels and pinions whose axes are parallel; we come now to speak of bevel-geer, or the action of wheels of which the axes are angular to each other.

The principle consists in two cones rolling on the surface of each other, as the cones A and B revolving on their centres a b, a c, fig. 5; if their bases are equal they will perform their revolutions in one and the same time; or any other two points equally distant from the centre a, as d 1, d 2, d 3, &c., will revolve in the same time as f1,ƒ2, ƒ3, &c. In the like manner, if the cones a,d,e be twice the diameters at the base de as the cones a, f, e, are, then if they turn about their centres, when the cone afd, figs. 6 and 7, has made one revolution, the cone ade will have made but half a revolution; or when a fe has made two revolutions, a de will have made but one, and every part equally distant from the centre a, as f1, ƒ2, ƒ3, &c., will have made two revolutions to e 1, e 2, e 3, &c.; and if the cones were fluted, or had teeth cut in them, diverging from the centre a to the bases d, c, e, f, they would then become bevel geer. The teeth at the point of the cone, fig. 8, being small, and of little use, may be cut off at E and F, figs. 8 and 9, where the upright shaft a b, with the bevel-wheel cd, turns the bevel-wheel ef with its shaft bg, and the teeth work freely into each other. The teeth may be made of any dimensions, according to the strength required; and this method will enable them to overcome a much greater resistance, and work smoother than a face-wheel and wallower of the common form can possibly do; besides, it is of great use to convey a motion in any direction, or to any part of a building, with the least trouble and friction.

The method of conveying motion in any direction, and proportioning or sharpening the wheels thereto, is as follows:-let the line ab represent a shaft coming from a wheel; draw the line cd to intersect the ine ab fig. 10, in the direction that the motion to be conveyed is intended, which will now represent a shaft to the intended motion.

Again, suppose the shaft cd is to revolve three times, whilst the shaft ab revolves once; draw the parallel line i i, at any distance not too great

(suppose one foot by a scale), then draw the parallel line kk at three feet distance, after which draw the dotted line wr, through the intersection of the shaft a b and c d, and likewise through the intersection of the parallel lines ii and kk, in the points r and y, which will be the pitch-line of the two bevel-wheels, or the line where the teeth of the two wheels act on each other, as may be seen fig. 11, where the motion may be conveyed in any direction.

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In almost all modern mills the shafts or spindles for the conveyance of motion, and support of wheels, are made of iron, either wrought or cast. Square shafts are the most common, but sometimes octagon and round ones are used; and if they are very large they are cast hollow, like pipes, and the gudgeons fixed in at the ends by wedges; but the pivots should always, if possible, be formed of the same piece of metal, as the slightest possible deviation from the straight line causes them to strain, and work very irregularly in their bearings. In wooden shafts this is impracticable, and it is one of the greatest objections to the use of them. The best method of fixing gudgeons into wooden shafts is shown in fig. 12. Here A is the gudgeon, made in cast iron, turned true; it has four leaves a, b, c, d, forming a cross, which is let into the end of the wooden shaft R; the front edge of each leaf is considerably thinner than the back, so that a pair of strong iron hoops rr, being driven tight on the end of the shaft, closes the wood round the cross, and holds it fast, and, the back of the leaves being wider than the front, it will not come out. As an additional security screws are sometimes put in these are put through holes in the arms of the cross, which are then made flat the other way, and do not go so far into the wood. The screws go into the timber a considerable distance, where a mortise is cut into the wood, to meet the end of the bolt, and an iron nut is dropped in, to screw the bolt into, when it is turned round by a screw-driver. By this contrivance a gudgeon may be fitted into a wooden shaft very fast; but still it will never come into competition with iron shafts, when the gudgeon is made all in one solid piece with the whole of the shaft. A judicious mechanic will never make more than two bearings upon any one shaft, if it can be avoided, because, if the three by any means, as the warping of the frame work or other cause, get the smallest possible quantity out of the straight line, they can never work well afterwards, but will always strain and wear the bearings with great friction. In very extensive mills, such as woollen and cotton mills, breweries, &c., when the buildings are of great length, it becomes necessary to join several shafts together in length, to reach from one end to the other of a mill. The manner of making the joinings is of some consequence: it is necessary that every shaft should have a bearing at each end, and consequently that the counexion of the ends of every one should be made by uniting the ends of the shafts which project beyond their bearings. This can be done in various ways; one is by having the ends of each of the shafts provided with circular heads A B, fig. 13, which have teeth an one, and corresponding indentations in the other,

to receive them, and thus one is made to turn the other about, at the same time that if any slight settlement of the building or other cause depresses one of the bearings, or raises another, so as to put the two shafts out of the perfect straight line they ought always to preserve, these joints will admit the slight flexure, and still communicate the motion of one shaft to the other. As this accidental settlement in large buildings is almost unavoidable, in some degree, care should be taken to make such joints as will admit of a trifling bending. Sometimes the ends of the shaft are made circular, and turned quite true in the lathe; then a metal tube or collar is fitted truly upon both, to cover the joint, and connect them, a bolt being put through each end, which unites both shafts with the collar, and thus by means of it causes the one to turn the other round. This method is sometimes used to save the great expense of having a bearing at each end of every length of shaft, one bearing to each length being then sufficient, the other end of the shaft being supported by this collar, connecting it with the end of the adjacent length just where it projects beyond its bearing. But this is not a good method, as the shafts are apt to bend and work with so much friction in the bearings, if they get the least out of the straight line, because these kind of joints will not admit any flexure of the shaft; or, if they do, they will only bend on one side, whereas it is necessary for the joints to bend successively on all sides, when the bearings are not precisely in a straight line. Fig. 14 represents a coupling-box, used by Messrs. Murray and Co. of Leeds, for connecting the lengths of a long line of shaft which are to carry a heavy strain: it is so made that it will communicate the motion in the manner of a universal joint, if they should be out of the line. Let A, B, be the two shafts to be united; C, D, their necks or collars which lie in the bearings: the_ends projecting beyond these have boxes E, F, fixed on them, either by a square with wedges, or by a round part with a fillet; one of these boxes E has a piece projecting from the inside of it on each side, and extending into the other box, as is shown at a a, No. 2, which is an inside view the other box F has two similar pieces projecting from it at bb into the other box E; within the boxes an iron cross c c d d is situated; it has screws fixed into the ends of the cross, and by these the motion is communicated: thus the pieces a, a, when the shaft A and box E are turned round in the direction of the arrows No. 2, act against the screws c, c, of the cross, and turn it about: at the same time the other two screws d, d, at the other arms of the cross, press against the pieces b,b, which belong to the box and shaft B, thus turning them round: the cross is placed quite detached in the boxes, and thus acts as a universal joint, to communicate the motion of one to the other: the screws cc, dd, at the ends of the cross, are only put in that the acting points may be made of steel, and made smooth to have but little friction in these parts. Another method of uniting shafts by Mr. Murray is shown at fig. 15: it has the advantage of requiring only one bearing for every length of shaft, whereas the above method requires one

for each end of every length. A, B, represent the two shafts; each has a pivot formed at the end these pivots are fitted into a coupling piece CDE, which is bored out truly to fit them inside, and the outside turned true, with a neck DD, which is received and fitted into a bearing: the two shafts A, B, are connected with the coupling piece D, at C and E, by means of a cross key 7m, put through each shaft, and the ends of them received in notches made within side of the coupling piece at C and E, where it receives the ends of the shafts. It is to be observed that the shafts do not fit tight in these parts E and C, but only in the pivots a, b, within, by which means they have liberty of a little motion, and this without straining the bearing in which D runs, because it is only the short coupling piece which is received therein; and consequently any trifling deviation from the straight line will not strain it, because of the play allowed in the fittings.

In treating of the mill in its complete state we may commence with its simplest form. The hand-mill will first engage our attention. It is shown in fig. 1, plate III. where A and B represent the two stones between which the corn is ground, and of which the upper one A turns round, but the lower one B remains fixed and immoveable. The upper stone is five inches thick, and twenty-one inches broad; the lower one somewhat broader. C is a cog-wheel, having sixteen or eighteen cogs, which go into the trundle F, having nine spokes fixed to the axis G, the latter being firmly inserted into the upper stone A, by means of a piece of iron. H is the hopper into which the corn is put: I the shoe to carry it by little and little through a hole at K, in betwixt the stones, where being ground into meal it comes out through the eye at L. Both stones are enclosed in a circular wooden case, of such a size as will admit the upper one to run freely within it. The under surface of the upper stone is cut into grooves, as represented at Q, which enable it to throw the meal out at the eye L more perfectly than could be done if it were quite plain. Neither of them are entirely flat, the upper one being somewhat concave, and the under one convex. They nearly touch at the edges, but are at some distance in the middle, in order to let the corn go in between them. The under stone is supported by strong beams, not represented in the figure; the spindle G stands on the beam M N, which lies upon the bearer O. One end of this bearer rests upon a fixed beam, and the other has a string fixed to it, and going round the pin P, by the turning of which the timbers O and MN may be raised or lowered, and thus the stones put nearer, or removed farther from each other, in order to grind fine or coarse. When the corn is to be ground it mus be put into the hopper by little at a time. A man turns the handle D, and thus the cog-wheel and trundle are carried round also together with the stone A. The axis G is angular at K; and, as it goes round, shakes the shoe I, and makes the corn fall gradually through the hole K. The upper stone going round grinds it, throwing out the meal, as already said, at the eye L. Another handle, if thought proper, may be put at

the other end of the handle E. The spindle must go through both stones, in order to reach the beam MN, and the hole through which it passes is fastened with leather or wood, so that no meal can pass through.

The construction of a horse-mill does not differ very materially from that of the hand-mill just described; instead, however, of the handle D, the spindle is furnished with a long horizontal lever and cogged wheel, which turns the trundle and stones, as already mentioned.-The stones are much heavier than in the hand-mill.

The mills most commonly in use for grinding corn are water-mills, the construction of which is not essentially different from that of the hand or horse-mills. The lower mill-stone, as already mentioned, is fixed, but the upper one moveable upon a spindle. . The opposite surfaces of the two stones are not flat, but the one convex and the other concave, though in a very small degree. The upper stone, which is six feet in diameter, is hollowed only about an inch in the middle, and the other rises three-quarters of an inch. They approach much nearer each other at the circumference, and the corn begins to be ground about two-thirds of the radius distance from the circumference, and there it makes the greatest resistance, the space between the two stones being in that place only about twothirds or three-fourths of the thickness of a grain of corn; but as these stones, as well as those of the hand-mill or horse-mill, can be separated a little from each other, the meal may be made fine or coarse in them, as well as in the two former mills.

To cut and grind the corn, botn the upper and under stones have furrows cut in them, as is observed in the hard-mill These are cut perpendicularly on one side, and obliquely upon the other, by which means each furrow has a sharp edge, and by the turning of the stones the furrows meet like a pair of scissars, and by cutting the corn make it grind the more easily. They are cut the same way in both stones when they lie upon their backs, by which means they run crossways to each other when the upper one is inverted and turned round; and this greatly promotes the grinding of the corn, great part of which would be driven onward in the lower furrows, without being ground at all, if both lay the same way. When the furrow becomes blunt and shallow, by wearing, the running stone must be taken off, and the furrows cut deeper in both by means of a chisel and hammer. Thus, however, by having the furrows cut down a great number of times, the thicknesses of both stones are greatly diminished; and it is observed, that in proportion to the diminution of the thickness of the upper stone, the quantity of flour also diminishes.

By means of the circular motion of the upper stone the corn is brought out of the hopper by jerks, and recedes from the centre towards the circumference by the centrifugal force; and, being entirely reduced to flour at the edges when the stones nearly touch one another, it is thrown at last out at the hole called the eye, as already mentioned. In Scotland it is frequent to have the stones without any furrows, and only irregu

larly indented with small holes, by means of an iron instrument. Stones of this kind last a much shorter time than those with furrows, the latter being fit for use for thirty or forty years, while the former seldom or never last more than seven. The under mill-stone is considerably thicker than the upper; and therefore, when both have been considerably worn by use, the lower one is frequently taken up, and the upper one put in its place, the former being converted into a running stone.

Water-mills are of three kinds, viz. breastmills, undershot-mills, and overshot-mills. In the former the water falls down upon the wheel at right angles to the float-boards or buckets placed all round to receive it; if float-boards are used it acts only by its impulse; but, if buckets, it acts also by the weight of water in the buckets in the under quarter of the wheel, which is considerable. In the undershot-wheel float-boards only are used, and the wheel is turned merely by the force of the current running under it, and striking upon the boards. In the overshot-wheel the water is poured over the top, and thus acts principally by its weight; as the fall upon the upper part of the wheel cannot be very considerable, lest it should dash the water out of the buckets. Hence it is evident that an undershot-mill must require a much larger supply of water than any other; the breast-mill the next, unless the fall is very great; and an overshot-mill the least. Dr. Desaguiliers found that a well-made overshot-mill would perform as much work as an undershot one, with onetenth part of the quantity of water required by

the other.

Plate III. fig. 2, shows the construction of a common water-mill, where AA is the large water-wheel, commonly about seventeen or eighteen feet diameter from a, the extremity of any float-board, to b the extremity of the opposite one. This wheel is turned round by the falling of the water upon the boards from a certain height, and the greater the height, provided the water runs in an uninterrupted stream, the smaller quantity will be sufficient to turn the mill. This wheel is without the mill-house, but the wheel has an axle B B of considerable length, which passes throngh a circular hole in the wall, and has upon it a wheel D, of eight or nine feet diameter, having sixty-one cogs, which turn a trundle E of ten staves or spokes; by which means the trundle, and consequently the millstone, will make six revolutions and one-tenth for every revolution of the wheel. The odd cog, commonly called the hunting cog, is added, that as every one comes to the trundle it may take the staff behind that one which it took at the last revolution; and thus all the parts of the cogs and rounds which work upon one another will wear equally, and to equal distances from one another, in a little time; by which means a true uniform motion will be produced through the whole work. The trundle is fixed upon an iron axis called the spindle, the lower end of which turns in a brass pot fixed at F in the horizontal beam ST, called the bridge-tree; and the upper part of the spindle turns in a wooden bush, fixed into the lower mill-stone, which lies