ment for time, as well as compensation for temperature, are by means of heavy screws, which form a part of the moving balance. In these more perfect machines, the length of the spring, which is now made helical or cylindrical, is first determined such, that the long and short vibrations are performed in the same time, and this is called the isochronal lengths, which is not afterwards altered by subsequent adjust ments. The last portion of the watch which demands our explanation is the dialwork, for producing the hours and minutes; this will be easily understood by reference to figs. 502 and 507. When the pinion called the cannon pinion, seen near the minute-hand in fig. 502, is inserted on the arbor d the hour or centre wheel, to which it fits rather tight by friction, it revolve therewith in an hour, and receives the minute or hour hand on its protruding squared end; then this pinion drives the wheel a round a stud on the pillar plate, and with it a pinion w made fast to its centre; which pinion again drives a second wheel, v, round the tube of the cannon-pinion in twelve hours; and to this the hour-hand is attached. This diminution of twelve revolutions from the cannon-pinion to the hour-wheel might be effected by one pinion driving a single wheel of twelve times its number of teeth; but as the motion must be brought back to the centre of the dial again, twe more wheels, or a wheel and pinion, are necessary to be introduced, and these are therefore made a part of the train, and no large wheel or small pinion is wanted, for the ratio 12; 1 may be more conveniently obtained by two factors, viz. 4:1 and 3: 1; thus, suppose the cannon-pinion to have 15 leaves, its wheel may have 4x15-60 teeth for wheels, and if wheel v be the same, its pinion will be 20, and the train 60 60 360 72 60 12 or = 5 1 60 3 or 12; so that when the pinions are fixed 15 20 30 6 A TABLE OF TRAINS FOR WATCHES; Showing the Number of Turns on the Fusee and Teeth in the Balance wheel, with the Beats in an Hour, and the number of Seconds in which the Contrate or Fourth Wheel revolves; for the easy Timing of Watches by the Vibrations of the Pendulum. 17,550 17,828 17,194 17,238 17,191 17,168 17,464 17,160 17,115 17,717 16,900 48 17,160 16,673 17,403 50 17,316 17,400 15,600 12,480 15,600 15,600 17,160 18,954 442 523 484 60 60 60 50 60 60 60 443 58 7 60 6 48 6 70 7 50 6 50 6 54 7 64 8 64 8 If we divide double the product of all the four wheels by the product of all the three pinions, the quotient will be the number of beats, as given in any of the trains contained in this table; also, if we take the second and third wheels, and their pinions respectively, as a compound fraction of an hour, they will give the seconds in which the contrate-wheel, attached to the latter pinion, will revolve: thus. off of sou 160, which numbers are consequently proper for a watch that indicates the seconds; and if the beats be 18,000, or 14,400, there will be five or four beats respectively in a second, which are the best trains for measuring fractional parts of a second. CHRONOMETERS. CHRONOMETERS differ from an ordinary watch principally in the escapement and balance. These machines deserve more than usual attention, as well from their practical utility in navigation, as from the principles on which they are constructed, in which the irregular forces both of impulse and resistance are greatly diminished by the exactness of form and dimension. In the reign of queen Anne, the British parliament passed an act, offering a reward of 10,000l. for any method of determining the longitude within the accuracy of one degree of a great circle; of 15,000l. within the limit of forty geographical miles; and of 20,000l. within the limit of thirty such miles, or half of a degree; provided such method should extend more than eighty miles from the coast. The hope of obtaining this reward stimulated a watch-maker named Harrison to be indefatigable in his endeavours to effect the required improvement, which eventually led him to apply the principle of the apposite expansions of different metals to a watch to effect a self-regulating curb, for limiting the effective length of the spiral pendulum-spring to correspond to the successive changes of heat and cold, which changes were now known to alter the force of this spring, and the momentum of the balance. After Harrison had by his industry and perseverance obtained the large reward, the act was repealed, and another substituted, offering separate rewards to any person who should invent a practicable method of determining, within circumscribed limits, the longitude of a ship at sea; for a time-keeper, the reward held forth to the public is 5,000l. for determining the longitude to or within one degree; 7,500l. for determining the same to forty geographical miles; and 10,000l. for a determination at or within half a degree. This act, notwithstanding its abridged limits and diminished reward, has produced several candidates; of whom Mudge, the two Arnolds, and Earnshaw, have had their labours crowned with partial success. Although, in respect to Mudge's time-keeper, great expectations were at first raised, it has, from the complexity of the machinery, and consequent expense attendant upon making it, gradually fallen into disrepute, and is now seldom or ever made. Such of our readers who wish to see its manner of construction and performance, we must refer to "The Description of Mr. Mudge's Time-keeper," published in 1799, by Thomas Mudge, jun. The chronometer we purpose to lay before our readers is that constructed by Mr. Earnshaw, as we are strongly disposed to conclude, from various documents we have seen, and from the similarity so evident in the construction of the escapement, that Mr. Arnold derived the knowledge of his e principle from Mr. Earnshaw. In Mr. Earnshaw's chronometer the escapement is detached, which is the best for the equal measurement of time, because the vibrations of the balance are free from the friction of the wheels, excepting about one-twelfth part of the circle, while the scape-wheel is acting on the pallet to keep up the motion t of the balance, which is done with considerably more powe and less friction than by any other escapement, as it receives but one blow from the wheel, whilst other escapements receive two; it has also an equal advantage of the same quickness of train, and when the impulse is given to the balance by the wheel, it is given in a similar direction, and not in opposition, as most escapements are which produce a recoil. The pivots of the balance-axis should be the size of the verge-pivots of a good sized pocketwatch, and of the annexed shape, which will greatly add to their strength, the extreme end, or acting part, only being straight; the jewel-hole should be as shallow as possible, so as not to endanger cutting the pivot, and the part of the action of the hole made quite back, with only a very shallow chamber behind to retain the oil; deep holes are very bad, for when the oil becomes glutinous, it will make the pivots stick, so as to prevent the balance from its usual vibration. The pallet should be half the diameter of the wheel, or a little larger, for if smaller, or one-fourth the diameter, as is the case in Arnold's, the wheel will have too much action on it, which will increase friction most considerably, and likewise cause the balance to swing so much farther to clear the wheel; consequently, a check in the motion of the balance may stop the watch, and cause time-keepers so constructed to stop. The face of the pallet should run in a line of equal distance between the centre of the pallet and its extremity, and not in a right line to its centre, as this causes an increase of friction, and a loss of that power which is obtained by the wheel, acting on the extremity of the pallet. The scape-wheel teeth should form the same direction as the face of the pallet, under-cut for |