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increased pressure on both surfaces of the cylinder retards its motion.

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The upper part of the first marginal diagram exhibits the anchor recoil; the lower Graham's dead-beat escapement.

The second diagram represents Mr. Arnold's watch escapement. The pin A, projecting from the verge or axis of the balance, moving towards B, carries before it the spring B, and with it the stiffer spring c, so as to set at liberty the tooth D, which rests on a pallet projecting from the spring. The angle E of the principal pallet has then just passed the tooth F, and is impelled by it until the tooth G arrives at the detent. In the return of the balance, the pin a passes

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easily by the detent, by forcing back the spring B. The screw H serves to adjust the position of the detent, which presses against it.

38. The escapement can render those vibrations only isochronal, whose inequality proceeds from the maintaining power, and not such as are produced by external agitations.

39. The effect of external agitations on the balance may be counteracted by the double escapement.

In this escapement, two equal balances are so connected, that they vibrate through equal angles, but in contrary directions; by which means, the one must always be accelerated as much as the other is retarded by any external agitation. But as Mr. Cummins observes, when balances are connected by means of teeth, there arises a resistance which, however small, when applied in this most delicate part, will tend to diminish the momentum of the balances.

40. That escapement is best in which the duration of the action of the balance-wheel on the pallets is least with respect to the time of vibration.

Hence the detached escapement is the best, which appears

to have been the invention of the ingenious artist, Mr. Thomas Mudge, who made a watch on this construction for the late King of Spain, Ferdinand VI., in the year 1755.

41. The time of the vibration of the balance is increased by heat, and diminished by cold.

First, because the length of the spiral spring is increased by heat, and therefore its force diminished, and the contrary by cold. 2dly. The diameter of the balance is increased by heat, and therefore also the time of vibration; and the contrary by cold.

42. That balance is the most perfect which, without the compensation of a thermometer, is most subject to the influence of heat and cold.

Because the obstructions from oil and friction act as a compensation to the expansion or contraction of the spring and balance; therefore that balance which is most affected, is freest from the influence of oil and friction.

43. The errors in the going of a watch, arising from the change of temperature, may be corrected by varying the length of the balance spring.

Nevertheless, as it is extremely difficult to form an isochronal spiral, any variation in its length is dangerous, because we shall thus probably lose that point which determines its isochronism.

44. The errors in the going of a watch, occasioned by the variation of temperature, may be corrected by varying the diameter of the balance.

This may be effected by dividing the rim of the balance into two or more separate parts, G D, I F, H E, each of which is composed of two plates of metal of different expansibility, riveted together, the least expansible being nearest the centre N, and carrying at one end D, F, E, a weight; whilst the other is connected either with the rim of the balance, or one of its radii. Now if the temperature increase, the exterior plate expanding more than the interior, the compound will become more concave towards the centre; and consequently the end which carries the weight will approach the centre of the balance, and on that account the vibrations will be rendered quicker. At the root of each thermometer, there is a screw G, I, H, by which the diameter of the balance may be increased or diminished, so as to alter the time kept by the chronometer, without interfering with the adjustment for heat and cold; and if the magnitude and position of

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the weights be properly regulated, they will correct the error arising from the variation of the diameter of the balance caused by the variation of temperature. (M. Young's Analysis.) The reader who wishes to acquire practical knowledge on this subject, may advantageously consult Hatton's Introduction to the Mechanical part of Clock and Watch Work.

Select Mechanical Expedients.

Although a full account of the principal contrivances for transmitting motion, and changing its rate, its direction, or its character, would carry us much beyond the assigned limits; yet it seems advisable to give a few of these, which are, therefore, here presented.

1. Spiral Gear. In the ordinary cases, the teeth of wheels are cut across their circumferences in a direction parallel to the axis. But, in the spiral gear, now used a little in this country, and still more in the American states, (especially in cottonmills,) the teeth are cut obliquely, so that if they were continued they would pass round the axis like the threads of a screw. By reason of this disposition, the teeth come in contact only in the line of the centres, and thus operate, in great measure, without friction. It must, however, be remarked, that the action of these wheels is compounded of two forces, one of which acts in the direction of the plane of the wheel, the other in the direction of its axis.

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This spiral gearing is sometimes applied to clock-work, and has this peculiarity, that it admits of a smaller pinion than any other gearing.

2. Change of rotatory velocity. It is sometimes necessary that a machine should be propelled with a velocity which is not equable, but continually changes in a given ratio. Thus, in cotton-mills, it is necessary that the speed of certain parts of the machinery should continually decrease from the beginning to the end of an operation. To accomplish this, two conical drums of equal size are placed with their axes parallel

to each other, and with their larger diameters in opposite directions. They are connected by a belt, which is so regulated by proper mechanism, that it is gradually moved from one extremity of the conic frustums or drums to the other; and thus acting upon circles of different diameter, causes a continual change of velocity in the driven cone with relation to that which drives it.

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Thus, if the drum on the axis a b drives the wheel on the axis A B, and the belt commences its operation at the ends a s; the driven conic frustum will first revolve slower than that which drives it, and will continue to move slower until the belt has reached the middle of both, when the rotatory motions of both will be equal: after that, the cone which is driven will turn quickest, and will so continue, turning quicker and quicker both with respect to the other, and, in fact, until the belt reaches the ends b, B.

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A change of rotatory velocity, upon the same general principle, is sometimes effected thus. A decreasing series of toothed wheels is placed in the order of their size upon a common axis, and fixed upon it. A corresponding series, but in an inverted order, are placed upon another axis, and not fixed, but capable of revolving about the axis like loose pulleys. The axis of this second series is hollow, and contains a moveable rod, which has a tooth projecting through a longitudinal slit in one side of the axis; and this tooth serves to lock any one of the wheels by entering a notch cut for its reception. Thus, however, only one wheel can be locked at a time, the others remaining loose. Hence, the driven axis will revolve with a velocity which is due to the relative size of the wheel which is locked and that which drives it. Suppose, for example, that the diameters of the wheels are as 1, 2, 3, 4, and 5, upon the driving axis, and the corresponding wheels, upon the driven axis, are as the numbers 5, 4, 3, 2, 1. Then, when the wheel 1 drives the wheel I, the rotatory velocity of the latter will be one-fifth of that of the former. When 2 drives II, the rotatory velocity communicated will be half that of the wheel 2. When 3 drives III, the velocities will be equal. When 4 drives IV, the rotatory velocity of the latter will be double that of the former. And, when 5 drives V, the velocity of the latter will be five times that of the former. Different proportions in the diameters of the wheels will, of course, give different proportions in the velocities.

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We owe this beautiful contrivance to the late Mr. Bramah. It is sometimes requisite that a wheel or axis should move with different velocities in different parts of one and the same revolution. This may be accomplished by an eccentric crown wheel acting upon and driving a long pinion. Thus, if the crown wheel in the margin rotates uniformly upon a centre of motion c,

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which is not the centre of the wheel, and the teeth of this crown wheel play into the leaves of the long pinion p q, since the portions of the crown wheel pass in contact with the pinion with different velocities, as their distances from the centre of motion c vary, the pinion p q will turn with an unequable or varying velocity, depending upon the eccentricity of the centre of motion c.

3. Cams and Wipers. These are contrivances by means of which beams placed vertically, or inclined aslant upwards, may be made to advance over a small space in the direction of their length, and then recede in the opposite direction; and so on alternately. Eccentric eircles, hearts, ellipses, portions of circles, and projecting epicycloids, serve to communicate these kinds of motions. Thus, in the first of the figures below, the circular eccentric cam, being put into uniform rotation, the sliding or reciprocating part A B of the machinery, will ascend and descend with a gentle, smooth motion; being never at rest, unless at the very moment of changing its direction. In the quadrant cam, represented in the second figure, the reciprocating part A' B' will remain at rest on the periphery of the cam during the first quarter of the revolution, while, during the second, it will descend to

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the axis of motion; during the third it will be at rest upon the axis; and during the fourth it will return to its original situation. The elliptical cam, in the third figure, turning upon

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