certain known mechanical principles and powers, and in their application or adaptation to various purposes, according to the modes hereinafter detailed, and not in the separate parts of which the machine is compounded. Two wheels firmly fixed on the same axis so as to be incapable of moving separately are made to revolve round, within, or upon another wheel which is not at liberty to move with them, and which I call the primary wheel. One of these first mentioned wheels (which may be called double wheels) is connected with the primary wheel, by teeth, cogs, chains, straps, ropes, or the friction of rough surfaces, and they both are made to revolve round their own axis, by performing a revolution round the axis of the primary wheel; the primary wheel is not attached to the axis which passes through it, but is occasionally fixed to the frame of the machine. Another wheel is firmly fixed upon this axis, which I therefore call the axis wheel; and upon this axis is also fixed the barrel or any other mechanism, which is to produce the effect intended by the machine. The axis wheel is put in motion by the other double wheel, by means of a winch applied to the metal frame M M, in which the double wheels move. All the wheels above-mentioned may be either circular, or of such other forms as to be capable of acting upon each other in the ordinary manner of toothed wheels or band riggers; and if a wheel is employed broad enough to work both in the axis and primary wheel, one such wheel will in some cases answer the purpose of both the double wheels; that is, when both the double wheels are equal as to the number of teeth to each other, and the primary and axis wheels have a considerable number of teeth, the power gained by this machine is to unity, as the entire revolution of the axis wheel is to that portion of it which it moves during a complete turn of the winch;

the

the radii of the barrel and of the winch being considered in this case equal. To illustrate the above, let the primary wheel be called A, Fig. 1, (Plate XIII.), the double wheels B and D, and the axis wheel C. B and D, being fixed upon the same axis, revolve together, about the common axis F, of A and C. Suppose in the first place, all these four wheels to be what are technically called spur-wheels, and that the double wheels revolve round the primary and axis wheels; suppose also A to be immoveable, and A and B to be similar in the number of their teeth, and C and D to be the same; then whatever motion is gained by B and D from their connexion with A, will only have. a tendency to keep C at rest with respect to A, consequently C will have no motion; but if there be a disproportion in the teeth or dimensions, viz. let A be as 30, B and D also each as 30, and C as 31, the equ ation in this case will be incorrect. The disproportion being 1-31, then the winch must turn 31 times in order to turn the axis wheel once round, and the power is consequently 31. If 30:30 :: 30:33, be the disproportion, the power in like manner will be 11. If a fraction be the difference, let A=30. B 31. C-31. D=32; the difference then is 1-31 part of 31 or 1-961, the power therefore equals 961. The same effects may be produced by using face united with spur wheels, or by using bevelled or other wheels; but the machine will be less compact from the projection of the teeth of the wheels; also cylinders or polygons connected by chains or bands will produce the same effects if made according to the above arrangements. Suppose again the double wheels to revolve within the primary and axis wheels, let the same letters represent the primary, &c. wheels as in the former case, the result will be the same, except that the double wheels cannot have so great a proportion to the primary and axis

wheels,

wheels, and consequently the power gained by making the difference a fraction, will not be so great in proportion to the number of teeth in the primary and axis wheels. The power in this instance may be increased by applying a wheel in the centre, which may be called the centre wheel, which runs unconnected with its axis, and is occasionally attached to the winch, which in that case is by a bolt or catch K disengaged from the frame M, and fixed into the wheel E, or into a projection from it (see Figs 2, 3, 4). To gain the greatest possible power, the difference being unity, let the primary and axis wheel differ 1, and let the double wheels be equal; viz. Let A and C have 84 and 85, and B and C any convenient equal number of teeth, the power will then be about 84. To acquire the greatest possible power, the difference being a fraction, let the double wheels be very nearly an aliquot part of the wheels in which they act, viz. one-half or one-third. In using the latter proportion the power may be raised still higher by employing the central wheel. In all the above cases I have supposed the primary wheel to be immoveably fixed, but by adding a wheel V to the edge of the primary wheel, and connecting it with the barrel by the intervention of wheels or other contrivances, a motion will be given to the primary wheel contrary to the direction of the winch, which by allowing it to recede as the double wheels advance, will very much increase the power. Or a motion will be given to it in the same direction which will increase the velocity; Figs. 2 and 3 explain how this may be effected with a great variety of powers. Let the wheel V on the edge of the primary wheel be connected with the spindle N, by means of the wheel Q, Figs. 2 and 3 ; upon this spindle let any convenient number of wheels be fixed in such a manner as to have a sliding motion upon it, but pre

vented from turning round except when it also turns; let these wheels be capable of uniting with the wheels L L, which are fixed upon a frame R, moving truly upon or about the centre F of the axis, and connected with a wheel I, fixed upon the barrel. The frame R may be fixed by the pin S, so as to admit the connexion at pleasure of H or L L with G 1, G 2, or G 3; the moveable wheels on the spindle N, which will add twelve different powers to the machine; H, when connected with G, produces a high power, and L L a low one, as the latter impels A forwards, and the other inverts the motion. The catch T, which fixes A to the frame of the machine, must be released when the spindle N is engaged with the barrel wheel I. In the above illustration the machine is supposed to act as a crane, but it is applicable to various mechanical purposes, as a capstan, windlas, jack for lifting timber, &c. steering-wheel, rolling-press, engine for dividing astronomical instruments, &c. and various other purposes to which the known mechanical powers have been heretofore applied. By means of a hollow axis a winch may be applied to each side of the barrel; it is represented by the dotted line TT, passing through the axis FF in Fig. 3; its advantages are, first, that the weight will be sustained in any part of its progress, without the aid of a catch or any other contrivance, for the effort of the weight to run down is to the exertion required to raise it, as the difference of the radii of A and C to the whole radii of C; supposing, therefore, the power to be only ten, the difference of these radii will be onetenth; and if the friction be less than one-tenth, the weight will merely make an effort to run down equal to one-tenth, subtracting the friction; that is, suppose the weight on the winch to be 60lbs. the effort to run down in this case would be 6lb. if there was no friction; but sup

pose

pose the friction equal to four pounds, the effort to run down would be two pounds. This applies only to the action of the double wheels in connexion with the pri-' mary and axis wheels, for whether the power be increased afterwards by the application of the central wheel E, or the segment wheel H, or decreased by the use of the segment wheels L L, the above advantage is not affected; second, another advantage is, that the power (contrary to the ordinary crane) does not depend upon the disproportion between the wheel and pinion, the greatest power being that which is produced by four wheels as nearly as possible, equal or proportional, without being exactly so. All the wheels, therefore, being of considerable dimensions, the teeth when in contact lie nearly in the same plane, consequently the equal friction occasioned by the oblique action of the teeth upon each other, inseparable from the use of very small pinions, is avoided; third, this machine also admits of being made four or five times or more (if necessary) as strong as other cranes, &c. of the same dimensions; for the double wheels may be increased to any number, which can be applied to the axis and primary wheels, and also from their size the points of contact will be multiplied. This strictly applies only to those instances in which the primary wheel is fixed, as in Figs. 1 and 4, where four pair of double wheels are shewn at B, B, B, B; fourthly, a very high mechanical power may be acquired in much less space than by the known mode of repeating the wheel and pinion; fifth, if used in the division of philosophical instruments, the greatest accuracy may be acquired, for supposing the wheels to be A 59, B 60, C 60, D 61, (see Fig. 1) the power will then be 60 × 60 or 3600 each, of which 3600 divisions is formed by a complete revolution of the winch, and all the teeth excepting one-sixty

VOL. XXXIV.-SECOND SERIES. Xx fourth