350:
58:
416:
605:
630:
237:, a lever with a narrow slit on the end through which the balance spring passes. This holds the part of the spring behind the slit stationary. Moving the lever slides the slit up and down the balance spring, changing its effective length, and thus the resonant vibration rate of the balance. Since the regulator interferes with the spring's action, chronometers and some precision watches have "free sprung" balances with no regulator, such as the
528:
38:
497:, making it harder for the balance spring to accelerate. The two effects of increasing temperature on physical dimensions of the spring and the balance, the strengthening of the balance spring and the increase in rotational inertia of the balance, have opposing effects and to an extent cancel each other. The major effect of temperature which affects the rate of a watch is the weakening of the balance spring with increasing temperature.
367:
432:
watch without balance spring, the drive force provides both the force that accelerates the wheel and also the force that slows it down and reverses it. If the drive force is increased, both acceleration and deceleration are increased, this results in the wheel getting pushed back and forth faster. This made the timekeeping strongly dependent on the force applied by the escapement. In a watch the drive force provided by the
488:. The strength of a spring, the restoring force it produces in response to a deflection, is proportional to its breadth and the cube of its thickness, and inversely proportional to its length. An increase in temperature would actually make a spring stronger if it affected only its physical dimensions. However, a much larger effect in a balance spring made of plain steel is that the
249:
often have a rate of 4 beats per second (14,400 BPH). Watches made prior to the 1970s usually had a rate of 5 beats per second (18,000 BPH). Current watches have rates of 6 (21,600 BPH), 8 (28,800 BPH) and a few have 10 beats per second (36,000 BPH). Audemars Piguet currently produces a watch with a very high balance vibration rate of 12 beats/s (43,200 BPH). During
390:, an early inertial timekeeper consisting of a straight bar pivoted in the center with weights on the ends, which oscillates back and forth. The foliot weights could be slid in or out on the bar, to adjust the rate of the clock. The first clocks in northern Europe used foliots, while those in southern Europe used balance wheels. As clocks were made smaller, first as
663:, 'invariable elasticity') an alloy whose elasticity is unchanged over a wide temperature range, for balance springs. A solid Invar balance with a spring of Elinvar was largely unaffected by temperature, so it replaced the difficult-to-adjust bimetallic balance. This led to a series of improved low temperature coefficient alloys for balances and springs.
436:, applied to the escapement through the timepiece's gear train, declined during the watch's running period as the mainspring unwound. Without some means of equalizing the drive force, the watch slowed down during the running period between windings as the spring lost force, causing it to lose time. This is why all pre-balance spring watches required
667:
effect of the steel hairspring, but still required a bimetal compensated balance wheel, known as a
Guillaume balance wheel. This design was mostly fitted in high precision chronometers destined for competition in observatories. The quadratic coefficient is defined by its place in the equation of expansion of a material;
616:
To mitigate this problem, chronometer makers adopted various 'auxiliary compensation' schemes, which reduced error below 1 second per day. Such schemes consisted for example of small bimetallic arms attached to the inside of the balance wheel. Such compensators could only bend in one direction toward
248:
are also used. The length of a beat is one swing of the balance wheel, between reversals of direction, so there are two beats in a complete cycle. Balances in precision watches are designed with faster beats, because they are less affected by motions of the wrist. Alarm clocks and kitchen timers
531:
Bimetallic temperature-compensated balance wheel, from an early 1900s pocket watch. 17 mm dia. (1) Moving opposing pairs of weights closer to the ends of the arms increases temperature compensation. (2) Unscrewing pairs of weights near the spokes slows the oscillation rate. Adjusting a single
586:
construction bend toward the steel side when they are warmed, because the thermal expansion of brass is greater than steel. The rim was cut open at two points next to the spokes of the wheel, so it resembled an S-shape (see figure) with two circular bimetallic "arms". These wheels are sometimes
595:
can reduce her moment of inertia by pulling in her arms. This reduction in the moment of inertia compensated for the reduced torque produced by the weaker balance spring. The amount of compensation is adjusted by moveable weights on the arms. Marine chronometers with this type of balance had
431:
until the verge flag that was in contact with a tooth on the escape wheel slipped past the tip of the tooth ("escaped") and the action of the escapement reversed, pushing the wheel back the other way. In such an "inertial" wheel, the acceleration is proportional to the drive force. In a clock or
666:
Before developing
Elinvar, Guillaume also invented an alloy to compensate for middle temperature error in bimetallic balances by endowing it with a negative quadratic temperature coefficient. This alloy, named anibal, is a slight variation of invar. It almost completely negated the temperature
612:
The standard
Earnshaw compensation balance dramatically reduced error due to temperature variations, but it didn't eliminate it. As first described by J. G. Ulrich, a compensated balance adjusted to keep correct time at a given low and high temperature will be a few seconds per day fast at
492:
of the spring's metal decreases significantly as the temperature increases, the net effect being that a plain steel spring becomes weaker with increasing temperature. An increase in temperature also increases diameter of a steel or brass balance wheel, increasing its rotational inertia, its
617:
the center of the balance wheel, but bending outward would be blocked by the wheel itself. The blocked movement causes a non-linear temperature response that could slightly better compensate the elasticity changes in the spring. Most of the chronometers that came in first in the annual
471:
or "beat" and resisted changes in its vibration rate caused by friction or changing drive force. This crucial innovation greatly increased the accuracy of watches, from several hours per day to perhaps 10 minutes per day, changing them from expensive novelties into useful timekeepers.
22:
480:
After the balance spring was added, a major remaining source of inaccuracy was the effect of temperature changes. Early watches had balance springs made of plain steel and balances of brass or steel, and the influence of temperature on these noticeably affected the rate.
613:
intermediate temperatures. The reason is that the moment of inertia of the balance varies as the square of the radius of the compensation arms, and thus of the temperature. But the elasticity of the spring varies linearly with temperature.
219:. Older balance wheels used weight screws around the rim to adjust the poise (balance), but modern wheels are computer-poised at the factory, using a laser to burn a precise pit in the rim to make them balanced. Balance wheels rotate about
747:
552:"compensation curb" on the spring, in the first successful marine chronometers, H4 and H5. These achieved an accuracy of a fraction of a second per day, but the compensation curb was not further used because of its complexity.
116:
into impulses delivered to the balance wheel. Each swing of the wheel (called a "tick" or "beat") allows the gear train to advance a set amount, moving the hands forward. The balance wheel and hairspring together form a
215:. The two alloys are matched so their residual temperature responses cancel out, resulting in even lower temperature error. The wheels are smooth, to reduce air friction, and the pivots are supported on precision
1612:
1263:
Construction nouvelle de trois montres portatives, d'un nouveau balancier en forme de croix,... d'un gnomon spéculaire... et autres curiositez, par M. l'abbé de Haute-Feuille. [Orléans, juin 1722.]
398:
and then as the first large watches after 1500, balance wheels began to be used in place of foliots. Since more of its weight is located on the rim away from the axis, a balance wheel could have a larger
500:
In a watch that is not compensated for the effects of temperature, the weaker spring takes longer to return the balance wheel back toward the center, so the "beat" gets slower and the watch loses time.
344:
837:
444:) to equalize the force from the mainspring reaching the escapement, to achieve even minimal accuracy. Even with these devices, watches prior to the balance spring were very inaccurate.
782:
386:
The balance wheel appeared with the first mechanical clocks, in 14th century Europe, but it seems unknown exactly when or where it was first used. It is an improved version of the
882:
859:
806:
906:
582:
To accomplish this, the outer rim of the balance was made of a "sandwich" of two metals; a layer of steel on the inside fused to a layer of brass on the outside. Strips of this
1183:"Brittens Old Clocks & Watches" Edited by Cecil Clutton, G H Baillie & C A Ilbert, Ninth Edition Revised and Enlarged by Cecil Clutton. Bloomsbury Books London 1986
137:
or "tick" very constant, accounting for its nearly universal use as the timekeeper in mechanical watches to the present. From its invention in the 14th century until
575:
balance wheel. The key was to make the balance wheel change size with temperature. If the balance could be made to shrink in diameter as it got warmer, the smaller
1604:
1277:
960:
1311:
253:, Elgin produced a very precise stopwatch for US Air Force bomber crews that ran at 40 beats per second (144,000 BPH), earning it the nickname 'Jitterbug'.
673:
447:
The idea of the balance spring was inspired by observations that springy hog bristle curbs, added to limit the rotation of the wheel, increased its accuracy.
1649:. Technical article on construction of watch balance wheels, starting with compensation balances, by a professional watchmaker, on a watch repair website.
587:
referred to as "Z-balances". A temperature increase makes the arms bend inward toward the center of the wheel, and the shift of mass inward reduces the
1011:
1303:
505:
found in 1773 that an ordinary brass balance and steel hairspring, subjected to a 60 °F (33 °C) temperature increase, loses 393 seconds (
378:, built 1364, Padua, Italy. The balance wheel (crown shape, top) had a beat of 2 seconds. Tracing of an illustration from his 1364 clock treatise,
256:
The precision of the best balance wheel watches on the wrist is around a few seconds per day. The most accurate balance wheel timepieces made were
233:
turns with each swing, that is, about 270° to each side of their center equilibrium position. The rate of the balance wheel is adjusted with the
1599:. Comprehensive 616 p. book by astronomy professor, good account of origin of clock parts, but historical research dated. Long bibliography.
621:
trials between 1850 and 1914 were auxiliary compensation designs. Auxiliary compensation was never used in watches because of its complexity.
1096:
403:
than a foliot of the same size, and keep better time. The wheel shape also had less air resistance, and its geometry partly compensated for
1336:
986:
1629:
930:
608:
Marine chronometer balance wheels from the mid-1800s, with various 'auxiliary compensation' systems to reduce middle temperature error
540:
during sea voyages drove many advances in balance technology in 18th century
Britain and France. Even a 1-second per day error in a
1592:
1536:
1403:
1122:
596:
errors of only 3–4 seconds per day over a wide temperature range. By the 1870s compensated balances began to be used in watches.
1728:
1188:
307:
1715:
Pictures of a private collection of antique watches from 1710 to 1908, showing many different varieties of balance wheel.
646:
244:
A balance's vibration rate is traditionally measured in beats (ticks) per hour, or BPH, although beats per second and
145:
movements became available in the 1960s, virtually every portable timekeeping device used some form of balance wheel.
1682:
1547:
1143:
813:
645:
The bimetallic compensated balance wheel was made obsolete in the early 20th century by advances in metallurgy.
560:
1703:
349:
94:. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral
1019:
758:
129:
or "beat", and resists oscillating at other rates. The combination of the mass of the balance wheel and the
57:
415:
865:
842:
789:
113:
1579:. Good engineering overview of development of clock and watch escapements, focusing on sources of error.
889:
618:
50:
423:
These early balance wheels were crude timekeepers because they lacked the other essential element: the
579:
would compensate for the weakening of the balance spring, keeping the period of oscillation the same.
537:
489:
459:
improved it to its present spiral form in 1674. The addition of the spring made the balance wheel a
452:
261:
130:
604:
1471:
460:
118:
1490:
1227:
188:
technology has taken over these applications, and the main remaining use is in quality mechanical
1665:
1271:
541:
502:
484:
An increase in temperature increases the dimensions of the balance spring and the balance due to
468:
456:
375:
257:
154:
126:
629:
283:
in seconds, the time required for one complete cycle (two beats), is determined by the wheel's
1588:
1532:
1399:
1332:
1184:
1118:
1092:
990:
588:
576:
494:
485:
404:
400:
371:
284:
21:
1348:
1637:
1559:
1202:
1155:
938:
583:
549:
527:
437:
387:
79:
37:
742:{\displaystyle \ell _{\theta }=\ell _{0}\left(1+\alpha \theta +\beta \theta ^{2}\right)\,}
564:
291:
544:
could result in a 17-mile (27 km) error in ship's position after a 2-month voyage.
366:
424:
295:
234:
100:
95:
91:
62:
46:
30:
1722:
1042:
556:
545:
395:
391:
216:
1331:
A.L. Rawlings, Timothy
Treffry, The Science of Clocks and Watches, Publisher: BHI,
448:
250:
185:
142:
26:
1509:
1370:
1261:
1451:
1062:
548:
was first to apply temperature compensation to a balance wheel in 1753, using a
173:
138:
134:
42:
1712:
1704:"Monochrome-Watches A technical perspective the regulating organ of the watch"
1661:
592:
441:
433:
428:
158:
109:
1624:. Detailed illustrations of parts of a modern watch, on watch repair website
519:
minutes) per day, of which 312 seconds is due to spring elasticity decrease.
1708:
Monochrome-Watches A technical perspective the regulating organ of the watch
1567:
1523:. Detailed section on balance temperature error and auxiliary compensation.
1163:
277:
265:
200:
181:
161:
122:
1686:
1677:
Video of antique mid-19th century watch showing the balance wheel turning
196:
169:
87:
211:, with springs of a low thermal coefficient of elasticity alloy such as
654:
268:. By World War II they had achieved accuracies of 0.1 second per day.
238:
212:
153:
Until the 1980s balance wheels were the timekeeping technology used in
1563:
1159:
638:
634:
204:
177:
650:
628:
603:
526:
464:
414:
365:
348:
245:
189:
83:
56:
20:
1018:. Professional Watches magazine. 19 January 2009. Archived from
208:
165:
419:
Early balance wheel with spring in an 18th-century French watch
241:. Their rate is adjusted by weight screws on the balance rim.
370:
Perhaps the earliest existing drawing of a balance wheel, in
653:, a nickel steel alloy with very low thermal expansion, and
633:
Low-temperature-coefficient alloy balance and spring, in an
427:. Early balance wheels were pushed in one direction by the
1260:
Hautefeuille, Jean de (1647-1724) Auteur du texte (1722).
784:
is the length of the sample at some reference temperature
1485:. Has detailed account of development of balance spring.
451:
first applied a metal spring to the balance in 1658 and
195:
Modern (2007) watch balance wheels are usually made of
1012:"Jules Audemars Watch with Audemars Piguet Escapement"
893:
869:
846:
817:
793:
762:
1548:"Origin and Evolution of the Anchor Clock Escapement"
1144:"Origin and Evolution of the Anchor Clock Escapement"
892:
868:
845:
816:
792:
761:
676:
339:{\displaystyle T=2\pi {\sqrt {\frac {I}{\kappa }}}\,}
310:
112:, which transforms the rotating motion of the watch
1529:
1396:
1339:, Edition: 1993, 3rd enlarged and revised edition.
900:
876:
853:
831:
800:
776:
741:
338:
125:oscillates preferentially at a certain rate, its
987:"Does faster mean more accurate?, TimeZone.com"
1662:"William Simcock Massey Type III pocket watch"
1312:National Institute of Standards and Technology
591:of the balance, similar to the way a spinning
555:A simpler solution was devised around 1765 by
467:. This means the wheel vibrated at a natural
8:
832:{\displaystyle \scriptstyle \ell _{\theta }}
658:
649:won a Nobel prize for the 1896 invention of
1276:: CS1 maint: numeric names: authors list (
839:is the length of the sample at temperature
1698:History of watches, on commercial website.
1531:. London: J. D. Potter. pp. 176–177.
1137:
1135:
45:, the Apollo, by Lux Mfg. Co. showing the
1473:On the Springing and Adjusting of Watches
1204:On the Springing and Adjusting of Watches
908:is the quadratic coefficient of expansion
891:
867:
844:
822:
815:
791:
767:
760:
738:
727:
694:
681:
675:
335:
323:
309:
133:of the spring keep the time between each
264:, as a precise time source to determine
36:
1298:
1296:
924:
922:
918:
1269:
884:is the linear coefficient of expansion
808:is the temperature above the reference
777:{\displaystyle \scriptstyle \ell _{0}}
290:in kilogram-meter and the stiffness (
1089:Medieval Technology and Social Change
532:weight changes the poise, or balance.
523:Temperature-compensated balance wheel
357:from De Vick clock, built 1379, Paris
7:
877:{\displaystyle \scriptstyle \alpha }
854:{\displaystyle \scriptstyle \theta }
801:{\displaystyle \scriptstyle \theta }
78:, is the timekeeping device used in
1458:. Encyclopædia Britannica Inc. 2007
1069:. Encyclopædia Britannica Inc. 2007
901:{\displaystyle \scriptstyle \beta }
536:The need for an accurate clock for
199:, a low thermal expansion alloy of
1476:. New York: Spon & Chamberlain
1207:. New York: Spon & Chamberlain
407:error due to temperature changes.
14:
1615:from the original on 14 June 2007
1546:Headrick, Michael (April 2002).
1142:Headrick, Michael (April 2002).
1668:from the original on 2021-12-12
260:, which were used on ships for
1636:. TimeZone.com. Archived from
1630:"The Balance Wheel of a Watch"
1470:Britten, Frederick J. (1898).
1456:Encyclopædia Britannica online
1201:Britten, Frederick J. (1898).
1067:Encyclopædia Britannica online
937:. TimeZone.com. Archived from
931:"The Balance Wheel of a Watch"
1:
1492:Time Telling through the Ages
1304:"A Revolution in Timekeeping"
1229:Time Telling through the Ages
355:(horizontal bar with weights)
301:in newton-meters per radian:
1043:"The Elgin Collector's Site"
463:, the basis of every modern
1685:. Atmos Man. Archived from
1489:Brearley, Harry C. (1919).
1226:Brearley, Harry C. (1919).
641:Co. watch made in the 1950s
1747:
1583:Milham, Willis I. (1945).
1113:Milham, Willis I. (1945).
411:Addition of balance spring
61:Modern balance wheel in a
1660:Choi, Fred (2007-05-26).
1611:. TimeZone Watch School.
1527:Gould, Rupert T. (1923).
1514:. London: Cassel & Co
1394:Gould, Rupert T. (1923).
1375:. London: Cassel & Co
647:Charles Édouard Guillaume
41:Balance wheel in a 1950s
1683:"The History of Watches"
1605:"Balance Wheel Assembly"
1398:. London: J. D. Potter.
1087:White, Lynn Jr. (1966).
961:"Balance Wheel Assembly"
600:Middle temperature error
1609:Glossary of Watch Parts
1587:. New York: MacMillan.
1508:Glasgow, David (1885).
1419:Gould 1923, pp. 265–266
1369:Glasgow, David (1885).
1117:. New York: MacMillan.
1041:Schlitt, Wayne (2002).
985:Arnstein, Walt (2007).
967:. TimeZone Watch School
965:Glossary of Watch Parts
1729:Timekeeping components
1702:Markl, Xavier (2016).
1511:Watch and Clock Making
1372:Watch and Clock Making
1016:Audemars press release
902:
878:
855:
833:
802:
778:
743:
659:
642:
609:
533:
420:
383:
358:
340:
108:. It is driven by the
65:
54:
34:
16:Time measuring device
1495:. New York: Doubleday
1232:. New York: Doubleday
903:
879:
856:
834:
803:
779:
744:
660:élasticité invariable
637:1280 movement from a
632:
619:Greenwich Observatory
607:
530:
418:
380:Il Tractatus Astrarii
369:
352:
341:
278:period of oscillation
272:Period of oscillation
60:
40:
24:
1681:Costa, Alan (1998).
1628:Odets, Walt (2007).
1603:Odets, Walt (2005).
1585:Time and Timekeepers
1552:IEEE Control Systems
1452:"Marine Chronometer"
1148:IEEE Control Systems
1115:Time and Timekeepers
1063:"Marine Chronometer"
959:Odets, Walt (2005).
929:Odets, Walt (2007).
890:
866:
843:
814:
790:
759:
674:
538:celestial navigation
453:Jean de Hautefeuille
308:
262:celestial navigation
86:, analogous to the
1428:Milham 1945, p. 234
1359:Milham 1945, p. 233
1349:Britten 1898, p. 37
1308:A Walk Through Time
1290:Milham 1945, p. 226
1250:Milham 1945, p. 224
461:harmonic oscillator
440:(or in a few cases
258:marine chronometers
119:harmonic oscillator
25:Balance wheel in a
898:
897:
874:
873:
851:
850:
829:
828:
798:
797:
774:
773:
739:
643:
610:
559:, and improved by
542:marine chronometer
534:
503:Ferdinand Berthoud
469:resonant frequency
457:Christiaan Huygens
421:
384:
376:astronomical clock
359:
336:
276:A balance wheel's
127:resonant frequency
80:mechanical watches
66:
55:
35:
33:is visible at top.
1713:The Watch Cabinet
1564:10.1109/37.993314
1160:10.1109/37.993314
1098:978-0-19-500266-9
589:moment of inertia
577:moment of inertia
495:moment of inertia
486:thermal expansion
476:Temperature error
405:thermal expansion
401:moment of inertia
372:Giovanni de Dondi
333:
332:
285:moment of inertia
1736:
1707:
1697:
1695:
1694:
1676:
1674:
1673:
1648:
1646:
1645:
1623:
1621:
1620:
1598:
1578:
1576:
1575:
1566:. Archived from
1542:
1522:
1520:
1519:
1503:
1501:
1500:
1484:
1482:
1481:
1466:
1464:
1463:
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1426:
1420:
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1409:
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1340:
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1223:
1217:
1215:
1213:
1212:
1198:
1192:
1181:
1175:
1174:
1172:
1171:
1162:. Archived from
1139:
1130:
1128:
1110:
1104:
1102:
1091:. Oxford Press.
1084:
1078:
1077:
1075:
1074:
1059:
1053:
1052:
1050:
1049:
1038:
1032:
1031:
1029:
1027:
1008:
1002:
1001:
999:
998:
989:. Archived from
982:
976:
975:
973:
972:
956:
950:
949:
947:
946:
926:
907:
905:
904:
899:
883:
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875:
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858:
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838:
836:
835:
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827:
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772:
771:
748:
746:
745:
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737:
733:
732:
731:
699:
698:
686:
685:
662:
625:Better materials
518:
517:
513:
510:
345:
343:
342:
337:
334:
325:
324:
232:
231:
227:
224:
1746:
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1739:
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1735:
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1733:
1719:
1718:
1701:
1692:
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1680:
1671:
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1656:
1643:
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1627:
1618:
1616:
1602:
1595:
1582:
1573:
1571:
1545:
1539:
1526:
1517:
1515:
1507:
1498:
1496:
1488:
1479:
1477:
1469:
1461:
1459:
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1447:
1442:
1441:
1436:
1432:
1427:
1423:
1418:
1414:
1406:
1393:
1392:
1388:
1378:
1376:
1368:
1367:
1363:
1358:
1354:
1347:
1343:
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1326:
1317:
1315:
1302:
1301:
1294:
1289:
1285:
1268:
1259:
1258:
1254:
1249:
1245:
1235:
1233:
1225:
1224:
1220:
1210:
1208:
1200:
1199:
1195:
1182:
1178:
1169:
1167:
1141:
1140:
1133:
1125:
1112:
1111:
1107:
1099:
1086:
1085:
1081:
1072:
1070:
1061:
1060:
1056:
1047:
1045:
1040:
1039:
1035:
1025:
1023:
1010:
1009:
1005:
996:
994:
984:
983:
979:
970:
968:
958:
957:
953:
944:
942:
928:
927:
920:
915:
888:
887:
864:
863:
841:
840:
818:
812:
811:
788:
787:
763:
757:
756:
723:
704:
700:
690:
677:
672:
671:
627:
602:
565:Thomas Earnshaw
525:
515:
511:
508:
506:
478:
413:
364:
306:
305:
292:spring constant
274:
229:
225:
222:
220:
151:
121:, which due to
98:, known as the
68:
67:
17:
12:
11:
5:
1744:
1743:
1740:
1732:
1731:
1721:
1720:
1717:
1716:
1711:Oliver Mundy,
1709:
1699:
1678:
1655:
1654:External links
1652:
1651:
1650:
1640:on 6 July 2007
1634:The Horologium
1625:
1600:
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1580:
1543:
1537:
1524:
1505:
1486:
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1440:
1439:
1437:Gould, p. 201.
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1123:
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941:on 6 July 2007
935:The Horologium
917:
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914:
911:
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909:
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821:
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766:
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749:
736:
730:
726:
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719:
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713:
710:
707:
703:
697:
693:
689:
684:
680:
626:
623:
601:
598:
524:
521:
477:
474:
425:balance spring
412:
409:
396:lantern clocks
392:bracket clocks
363:
360:
347:
346:
331:
328:
322:
319:
316:
313:
296:balance spring
273:
270:
217:jewel bearings
150:
147:
101:balance spring
96:torsion spring
92:pendulum clock
63:watch movement
47:balance spring
31:balance spring
19:
18:
15:
13:
10:
9:
6:
4:
3:
2:
1742:
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1689:on 2007-07-17
1688:
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1601:
1596:
1594:0-7808-0008-7
1590:
1586:
1581:
1570:on 2009-10-25
1569:
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1549:
1544:
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1538:0-907462-05-7
1534:
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1337:0 9509621 3 9
1334:
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1166:on 2009-10-25
1165:
1161:
1157:
1153:
1149:
1145:
1138:
1136:
1132:
1126:
1124:0-7808-0008-7
1120:
1116:
1109:
1106:
1100:
1094:
1090:
1083:
1080:
1068:
1064:
1058:
1055:
1044:
1037:
1034:
1022:on 2009-12-28
1021:
1017:
1013:
1007:
1004:
993:on 2007-06-08
992:
988:
981:
978:
966:
962:
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847:
823:
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764:
755:
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734:
728:
724:
720:
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695:
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631:
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620:
614:
606:
599:
597:
594:
590:
585:
580:
578:
574:
570:
566:
562:
558:
557:Pierre Le Roy
553:
551:
547:
546:John Harrison
543:
539:
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522:
520:
504:
498:
496:
491:
487:
482:
475:
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368:
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351:
329:
326:
320:
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293:
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128:
124:
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115:
111:
107:
103:
102:
97:
93:
89:
85:
81:
77:
73:
72:balance wheel
64:
59:
52:
48:
44:
39:
32:
29:. The spiral
28:
23:
1691:. Retrieved
1687:the original
1670:. Retrieved
1642:. Retrieved
1638:the original
1633:
1617:. Retrieved
1608:
1584:
1572:. Retrieved
1568:the original
1558:(2): 41–52.
1555:
1551:
1528:
1516:. Retrieved
1510:
1497:. Retrieved
1491:
1478:. Retrieved
1472:
1460:. Retrieved
1455:
1433:
1424:
1415:
1395:
1389:
1377:. Retrieved
1371:
1364:
1355:
1344:
1327:
1316:. Retrieved
1307:
1286:
1262:
1255:
1246:
1234:. Retrieved
1228:
1221:
1209:. Retrieved
1203:
1196:
1179:
1168:. Retrieved
1164:the original
1154:(2): 41–52.
1151:
1147:
1114:
1108:
1088:
1082:
1071:. Retrieved
1066:
1057:
1046:. Retrieved
1036:
1024:. Retrieved
1020:the original
1015:
1006:
995:. Retrieved
991:the original
980:
969:. Retrieved
964:
954:
943:. Retrieved
939:the original
934:
751:
665:
644:
615:
611:
581:
573:compensating
572:
568:
554:
535:
499:
483:
479:
449:Robert Hooke
446:
422:
385:
379:
354:
298:
287:
280:
275:
255:
251:World War II
243:
194:
174:alarm clocks
155:chronometers
152:
105:
99:
75:
71:
69:
27:mantel clock
1664:. YouTube.
1410:pp. 176–177
1241:pp. 108–109
561:John Arnold
442:stackfreeds
182:stopwatches
139:tuning fork
135:oscillation
43:alarm clock
1693:2007-06-19
1672:2008-04-26
1644:2007-06-15
1619:2007-06-15
1574:2007-06-06
1518:2008-04-16
1499:2008-04-16
1480:2008-04-20
1462:2007-06-15
1445:References
1379:2008-04-16
1318:2022-10-13
1236:2008-04-16
1211:2008-04-16
1189:0906223695
1170:2007-06-06
1073:2007-06-15
1048:2007-06-20
1026:15 October
997:2007-06-15
971:2007-06-15
945:2007-06-16
593:ice skater
584:bimetallic
550:bimetallic
490:elasticity
434:mainspring
429:escapement
176:, kitchen
162:time locks
159:bank vault
131:elasticity
114:gear train
110:escapement
106:hairspring
82:and small
1272:cite book
1103:, p. 124
913:Footnotes
895:β
871:α
848:θ
824:θ
820:ℓ
795:θ
765:ℓ
725:θ
721:β
715:θ
712:α
692:ℓ
683:θ
679:ℓ
330:κ
321:π
294:) of its
266:longitude
235:regulator
201:beryllium
170:munitions
123:resonance
51:regulator
1723:Category
1666:Archived
1613:Archived
569:Earnshaw
197:Glucydur
149:Overview
88:pendulum
49:(1) and
1191:page 16
1129:, p. 92
752:where:
655:Elinvar
514:⁄
362:History
353:Foliot
239:Gyromax
228:⁄
213:Nivarox
190:watches
164:, time
76:balance
1591:
1535:
1402:
1384:p. 227
1335:
1314:. 2004
1187:
1121:
1095:
657:(from
639:Benrus
567:: the
563:, and
438:fusees
388:foliot
205:copper
186:quartz
184:, but
178:timers
143:quartz
84:clocks
651:Invar
465:clock
166:fuzes
90:in a
74:, or
1589:ISBN
1533:ISBN
1400:ISBN
1333:ISBN
1278:link
1216:p. 9
1185:ISBN
1119:ISBN
1093:ISBN
1028:2020
455:and
394:and
209:iron
207:and
180:and
168:for
141:and
1560:doi
1156:doi
635:ETA
571:or
374:'s
104:or
53:(2)
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