974

THEORY AND PRACTICE OF ENGINEERING.

Book II.

their edges, or by a strap or chain, or finally by teeth: if they act either by friction or byteeth, the rotation round the two axes will be in contrary directions; but if they act by astrap or chain, the rotation will be in the same direction, if the strap be crossed, butotherwise in opposite directions.

Fig. 1400. represents a watch escapement in-vented by Breguet to prevent the spring frombeing overwound or running down to its full ex-tent. In these watches the fusee is suppressed;the barrel A, which contains the spring, has atoothed wheel which transmits the action of thespring to the pinion of the first wheel of the watch ;the spring is fixed by one of its extremities to theaxle rd , and by the other to the inner and concavesurface of the barrel. The length of the spring issuch that, supposing it entirely unwound, the axlerd can make about twelve turns before it arrivesat its maximum of tension; in general the meantension of the spring is only employed, i. e. thatwhich results from four turns ; the axle rd has aratchet-wheel which prevents the axle from turn-ing in a direction contrary to that which thespring tends to communicate to the barrel. Tothe axle r d a toothed wheel Bis fixed, engaginganother C, which enters freely in a cylinder risingfrom the upper part of the drum; a large-headedscrew keeps the wheel in its place; the diameter ofthe wheels C and B are in the proportion of four tofive, the wheel B makes four turns, and C fivebefore the same teeth return to the same relativeposition. Suppose that the spring contained inthe barrel A be entirely down, and that the axledr with the wheel B is turned eight times, it will produce the maximum of the action ofthe spring, and prevent the axle rd from continuing to turn. If the distance de bedivided into two equal parts, and the semicircle dfe be drawn, it is evident that the stopsto produce the desired effect in the most advantageous manner should be placed in one ofthe points of this semicircle ; another condition is moreover requisite, from the moment thatthe wheel B is stopped, C turns, impelled by the barrel, and supposing that the proportionof the diameter of the wheel C to the diameter of the wheel B is as n 1 to n, the wheel Ccannot return to the point where it is found after having made a number ri of revolutionsround the wheel B, because it previously meets the stops, whatever point of the semicircledfe be chosen for the point of contact; but they will meet under different angles, which doesnot answer the end proposed. It is necessary that the stops should meet at right anglesbefore the wheel C terminates the nth revolution round the wheel B : let/be the pointrequired, the length of the arc ab must be equal to the arc ac, for if the barrel be turnedin the wrong direction, the point b will meet and tall on the point c, and when the centre eof the wheel c arrives at g , the angle def will be equal to the angle dgf and all the con-ditions will be fulfilled.

In watches with turning barrels there is nothing to indicate the state of the spring, con-sequently they stop or are wound up unnecessarily: M. Breguet, to obviate this, cuts thepart mn of the axis rd in a screw fitted with a nut st in form of a truncated cone ; one ortwo rods u rise above the surface of the barrel, and pass through the nut, without affectingits motion, in the direction of the axis rd. When the watch is wound up, since the screwturns without changing its place, and the nut cannot turn by reason of the rod w, it movesin the direction of the screw or axle rd: while the watch is in motion the nut turns andpasses over the same space in the opposite direction; an alternate rectilinear motion is theresult, which is transformed to alternate circular by a bent lever a' b' c'd', whose lesser arm c.' d‘rests on the conical surface of the nut, and the greater arm a f V marks on the dial plate thetension of the spring.

There can be no doubt that we are greatly indebted to the mechanists, who have appliedthemselves to the improvement of machinery for the measurement of time : from the periodof Richard of Walingford, abbot of St. Alban’s in 1326, we have continued to improvein the manufacture of clocks, which perhaps had their origin in the time of Pope Syl-vester II., who made one at Magdeburg as early as the year 996. Toothed-wheels werecertainly known 1300 years before, as we have them applied to the clepsydra: onTrajan’s column at Rome they are also represented, and we are not astonished that,when observed by an intelligent mind, like Gerbert, afterwards Sylvester II. , they shouldbe again brought into use. The history of clock-making would afford us the best method

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Fig. 1400.