409:
400:
346:
382:
373:
20:
418:
364:
319:
355:
57:
391:
33:
310:
256:
292:
283:
337:
301:
274:
69:
45:
1135:
North
America would experience a summer/winter temperature variation of around 14 °C (25 °F) resulting in an error rate of 6.8 seconds per day. Wood has a smaller CTE of 4.9 x 10 per °C thus a pendulum with a wood rod will have a smaller thermal error of 0.21 sec per day per °C, so wood pendulum rods were often used in quality domestic clocks. The wood had to be varnished to protect it from the atmosphere as
138:
328:
265:
193:
adjusted by having a section of the central rod which is partly brass and partly steel. These overlap (like a sandwich) and are joined by a pin which passes through both metals. A number of holes for the pin are made in both parts and moving the pin up or down the rod changes how much of the combined rod is brass and how much is steel.
177:
bottom bridge drops relative to the suspension, and the bob drops relative to the middle bridge. However, the middle bridge rises relative to the bottom one because the greater expansion of the zinc rods pushes the middle bridge, and therefore the bob, upward to match the combined drop caused by the expanding steel.
1134:
Steel has a CTE of 11.5 x 10 per °C so a pendulum with a steel rod will have a thermal error rate of 5.7 parts per million or 0.5 seconds per day per degree
Celsius (0.9 seconds per day per degree Fahrenheit). Before 1900 most buildings were unheated, so clocks in temperate climates like Europe and
220:
Scientists in the 1800s found that the gridiron pendulum had disadvantages that made it unsuitable for the highest-precision clocks. The friction of the rods sliding in the holes in the frame caused the rods to adjust to temperature changes in a series of tiny jumps, rather than with a smooth motion.
176:
rods, one on each side of the central rod, which reach down to, and are fixed to, the bottom bridge just above the bob. The bottom bridge clears the central rod and connects to two further steel rods which run back up to the top bridge attached to the suspension. As the steel rods expand in heat, the
128:
employed as time standards in factories, laboratories, office buildings, railroad stations and post offices to schedule work and set other clocks. The gridiron became so associated with accurate timekeeping that by the turn of the 20th century many clocks had pendulums with decorative fake gridirons,
2494:
To allow the use of metals with a lower ratio of expansion coefficients, such as brass and steel, a greater proportion of the suspension length must be the high expansion metal, so a construction with more high expansion rods must be used. In the 9 rod gridiron, there are two high expansion rods on
1884:
of the pendulum must be somewhat longer to give the correct period. This factor is hard to calculate accurately. Another minor factor is that if the pendulum bob is supported at bottom by a nut on the pendulum rod, as is typical, the rise in center of gravity due to thermal expansion of the bob has
149:
The gridiron pendulum is constructed so the high thermal expansion (zinc or brass) rods make the pendulum shorter when they expand, while the low expansion steel rods make the pendulum longer. By using the correct ratio of lengths, the greater expansion of the zinc or brass rods exactly compensate
1168:
is equal to the sum of the changes of the rods that make it up. It is designed so with an increase in temperature the high expansion rods on each side push the pendulum bob up, in the opposite direction to the low expansion rods which push it down, so the net change in length is the difference
192:
rods (pure zinc not being available then); these required more rods because brass does not expand as much as zinc does. Instead of one high expansion rod on each side, two are needed on each side, requiring a total of 9 rods, five steel and four brass. The exact degree of compensation can be
2966:
2742:
1370:
1458:
2349:
912:
1020:
1675:
2112:
1596:
180:
In simple terms, the upward expansion of the zinc counteracts the combined downward expansion of the steel (which has a greater total length). The rod lengths are calculated so that the effective length of the zinc rods multiplied by zinc's
2843:
100:
of the pendulum's swing depends on its length, so a pendulum clock's rate varied with changes in ambient temperature, causing inaccurate timekeeping. The gridiron pendulum consists of alternating parallel rods of two metals with different
1797:
3127:
113:. The rods are connected by a frame in such a way that their different thermal expansions (or contractions) compensate for each other, so that the overall length of the pendulum, and thus its period, stays constant with temperature.
200:
developed a tubular version of the zinc gridiron in which the four outer rods were replaced by two concentric tubes which were linked by a tubular nut which could be screwed up and down to alter the degree of compensation.
1231:
1126:
2854:
1147:
A gridiron pendulum is symmetrical, with two identical linkages of suspension rods, one on each side, suspending the bob from the pivot. Within each suspension chain, the total change in length of the pendulum
2484:
2636:
455:, so uncompensated pendulum rods get longer with a temperature increase, causing the clock to slow down, and get shorter with a temperature decrease, causing the clock to speed up. The amount depends on the
3036:= 1.68 times steel. So while brass/steel cannot be used in 5 rod gridirons, it can be used in the 9 rod version. So the compensation condition for a brass/steel gridiron using brass with the above CTE is
1288:
2254:
3034:
2417:
1068:
1376:
1860:
0.9936 m and then correct the clock's period with the adjustment nut. But in a gridiron pendulum, the gridiron constitutes a significant part of the mass of the pendulum. This changes the
581:
2265:
809:
2195:
2155:
815:
946:
1602:
652:
2034:
3206:
3397:
3242:
1521:
3436:
1491:
221:
This caused the rate of the pendulum, and therefore the clock, to change suddenly with each jump. Later it was found that zinc is not very stable dimensionally; it is subject to
2747:
Since to fit in the frame each of the two high expansion rods must be as short as or shorter than each of the high expansion rods, the geometrical condition for construction is
754:
1885:
to be taken into account. Clockmakers of the 19th century usually used recommended lengths for gridiron rods that had been found by master clockmakers by trial and error.
1280:
938:
702:
540:
3472:
2628:
2601:
2574:
2547:
2520:
2026:
1999:
1972:
1945:
1918:
1683:
In order to calculate the length of the individual rods, this equation is solved along with equation (2) giving the total length of pendulum needed for the correct period
1529:
2753:
1257:
725:
679:
3271:
3170:
2992:
2375:
517:
477:
453:
1708:
3300:
3042:
1828:
1523:
is the sum of the lengths of the high expansion rods in the suspension chain from the bob to the pivot. The condition for zero length change with temperature is
1858:
212:), in which the brass rods as they expanded with increasing temperature pressed against levers which lifted the bob. The Ellicott pendulum did not see much use.
3501:
3358:
3329:
1882:
1701:
1166:
608:
497:
1175:
479:
of the material they are composed of. CTE is usually given in parts per million per degree
Celsius. The expansion or contraction of a rod of length
1076:
185:
coefficient equals the effective length of the steel rods multiplied by iron's expansion coefficient, thereby keeping the pendulum the same length.
2961:{\displaystyle {\alpha _{\text{high}} \over \alpha _{\text{low}}}={L_{\text{1}}+L_{\text{3}}+L_{\text{5}} \over L_{\text{2}}+L_{\text{4}}}\geq 1.5}
96:
around 1726. It was used in precision clocks. In ordinary clock pendulums, the pendulum rod expands and contracts with changes in temperature. The
1131:
So the fractional change in an uncompensated pendulum's period is equal to one-half the coefficient of expansion times the change in temperature.
153:
The simplest form of gridiron pendulum, introduced as an improvement to
Harrison's around 1750 by John Smeaton, consists of five rods, 3 of
2737:{\displaystyle {\alpha _{\text{high}} \over \alpha _{\text{low}}}={L_{\text{1}}+L_{\text{3}}+L_{\text{5}} \over L_{\text{2}}+L_{\text{4}}}}
3827:"A letter concerning the inventor of the contrivance in a pendulum of a clock to prevent the irregularities of its motion by heat or cold"
1681:
In other words, the ratio of thermal expansion coefficients of the two metals must be equal to the inverse ratio of the total rod lengths.
2427:
1365:{\displaystyle \Delta L=\sum \alpha _{\text{low}}L_{\text{low}}\Delta \theta -\sum \alpha _{\text{high}}L_{\text{high}}\Delta \theta }
2259:
Therefore the 5 rod gridiron can only be made with metals whose expansion coefficients have a ratio greater than or equal to two
2203:
2997:
2380:
1026:
1837:
is near the center of the bob, so it was usually accurate enough to make the length from the pivot to the center of the bob
727:. Since the expansion coefficient is so small, the length changes due to temperature are very small, parts per million, so
236:
By 1900, the highest-precision astronomical regulator clocks used pendulum rods of low thermal expansion materials such as
150:
for the greater length of the low expansion steel rods, and the pendulum stays the same length with temperature changes.
1453:{\displaystyle \Delta L=(\alpha _{\text{low}}\sum L_{\text{low}}-\alpha _{\text{high}}\sum L_{\text{high}})\Delta \theta }
2344:{\displaystyle {\alpha _{\text{high}} \over \alpha _{\text{low}}}={L_{\text{1}}+L_{\text{3}} \over L_{\text{2}}}\geq 2}
3568:
907:{\displaystyle \qquad ={d \over dL}{\Big (}2\pi {\sqrt {L \over g}}{\Big )}\Delta L=\pi {\Delta L \over {\sqrt {gL}}}}
3783:
3661:
3578:
3546:
548:
3603:
1015:{\displaystyle \qquad =\pi {\alpha L\Delta \theta \over {\sqrt {gL}}}=\alpha \pi {\sqrt {L \over g}}\Delta \theta }
762:
408:
2848:
Therefore the 9 rod gridiron can be made with metals with a ratio of thermal expansion coefficients exceeding 1.5.
2160:
2120:
1670:{\displaystyle {\alpha _{\text{high}} \over \alpha _{\text{low}}}={\sum L_{\text{low}} \over \sum L_{\text{high}}}}
456:
2117:
Since to fit in the frame the high expansion rod must be equal to or shorter than each of the low expansion rods
399:
3864:
2107:{\displaystyle {\alpha _{\text{high}} \over \alpha _{\text{low}}}={L_{\text{1}}+L_{\text{3}} \over L_{\text{2}}}}
616:
3536:
3804:
3707:
3184:
1864:
so the center of oscillation is somewhat higher, above the bob in the gridiron. Therefore the total length
3815:
3727:
3372:
3220:
1496:
3826:
3411:
1466:
345:
3747:
3684:
3681:
The total lengths should be inversely proportional to the coefficients of expansion for the metals used
730:
230:
205:
197:
1262:
920:
684:
522:
1591:{\displaystyle \alpha _{\text{low}}\sum L_{\text{low}}-\alpha _{\text{high}}\sum L_{\text{high}}=0}
381:
3450:
2606:
2579:
2552:
2525:
2498:
2004:
1977:
1950:
1923:
1896:
19:
2838:{\displaystyle L_{\text{1}}+L_{\text{3}}+L_{\text{5}}\geq {3 \over 2}(L_{\text{2}}+L_{\text{2}})}
917:
Substituting equation (1), the change in the pendulum's period caused by a change in temperature
417:
3651:
363:
1792:{\displaystyle L=\sum L_{\text{low}}-\sum L_{\text{high}}=g{\big (}{T \over 2\pi }{\big )}^{2}}
372:
3773:
1239:
707:
661:
3256:
3155:
3122:{\displaystyle {L_{\text{1}}+L_{\text{3}}+L_{\text{5}} \over L_{\text{2}}+L_{\text{4}}}=1.68}
2977:
2360:
1834:
502:
462:
438:
172:
At that point a cross-piece (middle bridge) extends from the central rod and connects to two
117:
3285:
1809:
8:
222:
1840:
3859:
3486:
3343:
3314:
1867:
1686:
1151:
593:
482:
3779:
3657:
3574:
3542:
1861:
182:
102:
226:
1803:
354:
1833:
In an ordinary uncompensated pendulum, which has most of its mass in the bob, the
318:
2419:= 2.28 times steel, so the zinc/steel combination can be used in 5 rod pendulums.
2028:
down to support the bob. So from equation (3) the condition for compensation is
756:
and the change in period can be approximated to first order as a linear function
390:
1806:', in which the period was two seconds. The length of the seconds pendulum was
56:
1893:
In the 5 rod gridiron, there is one high expansion rod on each side, of length
1226:{\displaystyle \Delta L=\sum \Delta L_{\text{low}}-\sum \Delta L_{\text{high}}}
121:
1121:{\displaystyle \quad {\Delta T \over T}={\alpha \Delta \theta \over 2}\quad }
32:
3853:
166:
93:
3213:
Coefficient of thermal expansion of the high expansion (brass or zinc) rods
241:
610:
of the pendulum (the time interval for a right swing and a left swing) is
309:
255:
208:
designed a version that only required 3 rods, two brass and one steel (
3365:
Length of pendulum rod from the pivot to center of gravity of the bob
282:
588:
336:
300:
97:
1493:
is the sum of the lengths of all the low expansion (steel) rods and
68:
44:
3249:
Coefficient of thermal expansion of the low expansion (steel) rods
2479:{\displaystyle {L_{\text{1}}+L_{\text{3}} \over L_{\text{2}}}=2.28}
1136:
291:
225:. Therefore, another type of temperature-compensated pendulum, the
89:
3610:. Vol. 6. The Encyclopaedia Brittanica Co. 1910. p. 539
3508:
Period of the pendulum (time for a complete cycle of two swings)
273:
137:
327:
264:
3817:
A Rudimentary
Treatise on Clocks and Watches and Bells, 6th Ed
3729:
A Rudimentary
Treatise on Clocks and Watches and Bells, 6th Ed
2197:
the geometrical condition for construction of the gridiron is
2971:
1802:
Most of the precision pendulum clocks with gridirons used a '
237:
189:
162:
154:
110:
106:
86:
2354:
2249:{\displaystyle L_{\text{1}}+L_{\text{3}}\geq 2L_{\text{2}}}
1677: (3)
654: (2)
583: (1)
173:
158:
3029:{\displaystyle \alpha _{\text{high}}/\alpha _{\text{low}}}
2412:{\displaystyle \alpha _{\text{high}}/\alpha _{\text{low}}}
2630:. So from equation (3) the condition for compensation is
1063:{\displaystyle \Delta T={\alpha T\Delta \theta \over 2}}
2421:
The compensation condition for a zinc/steel gridiron is
3404:
Sum of the lengths of the high expansion gridiron rods
3443:
Sum of the lengths of the low expansion gridiron rods
435:
All substances expand with an increase in temperature
3535:
Turner, Anthony; Nye, James; Betts, Jonathan (2022).
3489:
3453:
3414:
3375:
3346:
3317:
3288:
3259:
3223:
3187:
3177:
Coefficient of thermal expansion of the pendulum rod
3158:
3045:
3000:
2980:
2857:
2756:
2639:
2609:
2582:
2555:
2528:
2501:
2430:
2383:
2363:
2268:
2206:
2163:
2123:
2037:
2007:
1980:
1953:
1926:
1899:
1870:
1843:
1812:
1711:
1689:
1605:
1532:
1499:
1469:
1379:
1291:
1265:
1242:
1178:
1154:
1079:
1029:
949:
923:
818:
765:
733:
710:
687:
664:
619:
596:
551:
525:
505:
485:
465:
441:
62:
Tubular version, with zinc and steel concentric tubes
3809:. Edinburgh: James Clarke and Co. pp. 363–371.
2549:, flanked by three low expansion rods with lengths
3495:
3466:
3430:
3391:
3352:
3323:
3294:
3265:
3236:
3200:
3164:
3121:
3028:
2986:
2960:
2837:
2736:
2622:
2595:
2568:
2541:
2514:
2478:
2411:
2369:
2343:
2248:
2189:
2149:
2106:
2020:
1993:
1966:
1939:
1912:
1876:
1852:
1822:
1791:
1695:
1669:
1590:
1515:
1485:
1452:
1364:
1274:
1251:
1225:
1160:
1120:
1062:
1014:
932:
906:
803:
748:
719:
696:
673:
646:
602:
575:
534:
511:
491:
471:
447:
1920:, flanked by two low expansion rods with lengths
1259:of a gridiron pendulum with a temperature change
865:
840:
129:which had no temperature compensating qualities.
3851:
16:Pendulum mechanism that adjusts with temperature
3831:Philosophical Transactions of the Royal Society
3772:Baker, Gregory L.; Blackburn, James A. (2005).
576:{\displaystyle \Delta L=\alpha L\Delta \theta }
3771:
3534:
1974:, one from the pivot to support the bottom of
804:{\displaystyle \Delta T={dT \over dL}\Delta L}
2190:{\displaystyle L_{\text{3}}\geq L_{\text{2}}}
2150:{\displaystyle L_{\text{1}}\geq L_{\text{2}}}
1778:
1755:
3705:
3598:
3596:
3594:
3592:
3590:
233:, was used in the highest-precision clocks.
3820:. London: Lockwood & Co. p. 50-60.
3814:Beckett, Edmund (Lord Grimsthorpe) (1874).
3767:
3765:
3763:
3761:
3759:
3732:. London: Lockwood & Co. p. 59-60.
3726:Beckett, Edmund (Lord Grimsthorpe) (1874).
3573:. Oxford University Press. pp. 79–82.
3562:
3560:
3558:
3837:(LXXXVIII). London: Royal Society: 517–525
3675:
3673:
3656:. Oxford University Press. pp. 8–10.
3645:
3132:
647:{\displaystyle T=2\pi {\sqrt {L \over g}}}
116:The gridiron pendulum was used during the
3741:
3739:
3721:
3719:
3643:
3641:
3639:
3637:
3635:
3633:
3631:
3629:
3627:
3625:
3587:
1819:
23:Wall clock with a 5-rod gridiron pendulum
3756:
3706:Kater, Henry; Lardner, Dionysus (1831).
3555:
3541:. Oxford University Press. p. 321.
3530:
3528:
3526:
3524:
425:
136:
18:
3813:
3745:
3725:
3701:
3699:
3697:
3695:
3670:
3649:
457:linear coefficient of thermal expansion
3852:
3736:
3716:
3622:
3824:
3775:The Pendulum: A Case Study in Physics
3566:
3521:
3201:{\displaystyle \alpha _{\text{high}}}
3802:
3692:
3392:{\displaystyle \sum L_{\text{high}}}
3237:{\displaystyle \alpha _{\text{low}}}
2489:
1888:
1516:{\displaystyle \sum L_{\text{high}}}
1139:could also cause changes in length.
430:
3431:{\displaystyle \sum L_{\text{low}}}
3307:Mathematical constant (3.14159...)
1486:{\displaystyle \sum L_{\text{low}}}
13:
3806:Treatise on Clock and Watch Making
3796:
1444:
1380:
1356:
1324:
1292:
1266:
1243:
1210:
1191:
1179:
1105:
1084:
1048:
1030:
1006:
966:
924:
885:
870:
795:
766:
734:
711:
704:will cause a change in the period
688:
665:
567:
552:
526:
188:Harrison's original pendulum used
74:Ellicott pendulum, another version
14:
3876:
3608:Encyclopaedia Britannica, 11th Ed
2001:, the other goes from the top of
749:{\displaystyle \Delta T<<T}
3689:, Cassell and Co., London, p.289
3479:Length of the n-th gridiron rod
1830:0.9936 meters (39.12 inches).
499:with a coefficient of expansion
416:
407:
398:
389:
380:
371:
362:
353:
344:
335:
326:
317:
308:
299:
290:
281:
272:
263:
254:
215:
67:
55:
50:Brass-steel gridiron with 9 rods
43:
31:
2994:= 19.3 x 10 per °C, a ratio of
2377:= 26.2 x 10 per °C, a ratio of
1142:
1117:
1080:
950:
819:
519:caused by a temperature change
132:
92:invented by British clockmaker
38:Zinc-steel gridiron with 5 rods
3712:. Philadelphia: Carey and Lea.
2832:
2806:
1441:
1389:
1275:{\displaystyle \Delta \theta }
1236:From (1) the change in length
933:{\displaystyle \Delta \theta }
697:{\displaystyle \Delta \theta }
535:{\displaystyle \Delta \theta }
85:was a temperature-compensated
1:
3538:A General History of Horology
3514:
196:In the late 19th century the
3467:{\displaystyle L_{\text{n}}}
2623:{\displaystyle L_{\text{5}}}
2596:{\displaystyle L_{\text{3}}}
2569:{\displaystyle L_{\text{1}}}
2542:{\displaystyle L_{\text{4}}}
2515:{\displaystyle L_{\text{2}}}
2021:{\displaystyle L_{\text{2}}}
1994:{\displaystyle L_{\text{2}}}
1967:{\displaystyle L_{\text{3}}}
1940:{\displaystyle L_{\text{1}}}
1913:{\displaystyle L_{\text{2}}}
681:due to a temperature change
7:
3778:. Oxford University Press.
3650:Matthys, Robert J. (2004).
3570:Seven Tales of the Pendulum
10:
3881:
3567:Baker, Gregory L. (2011).
247:
3752:. London: Cassell and Co.
169:to the suspension pivot.
124:, particularly precision
3683:" Glasgow, David (1885)
3653:Accurate Clock Pendulums
3336:Acceleration of gravity
1252:{\displaystyle \Delta L}
1169:between these changes
720:{\displaystyle \Delta T}
674:{\displaystyle \Delta L}
204:In the 1730s clockmaker
3746:Glasgow, David (1885).
3709:A Treatise on Mechanics
3266:{\displaystyle \theta }
3165:{\displaystyle \alpha }
3133:Definition of variables
2987:{\displaystyle \alpha }
2370:{\displaystyle \alpha }
512:{\displaystyle \alpha }
472:{\displaystyle \alpha }
448:{\displaystyle \theta }
3865:Timekeeping components
3749:Watch and Clock Making
3686:Watch and Clock Making
3497:
3468:
3432:
3393:
3354:
3325:
3296:
3267:
3238:
3202:
3166:
3123:
3030:
2988:
2962:
2839:
2738:
2624:
2597:
2570:
2543:
2516:
2480:
2413:
2371:
2345:
2250:
2191:
2151:
2108:
2022:
1995:
1968:
1941:
1914:
1878:
1854:
1824:
1793:
1697:
1671:
1592:
1517:
1487:
1454:
1366:
1276:
1253:
1227:
1162:
1122:
1064:
1016:
934:
908:
805:
750:
721:
698:
675:
648:
604:
577:
536:
513:
493:
473:
449:
146:
105:coefficients, such as
24:
3825:Short, James (1753).
3803:Reid, Thomas (1826).
3498:
3469:
3433:
3394:
3355:
3326:
3297:
3268:
3239:
3203:
3167:
3124:
3031:
2989:
2963:
2840:
2739:
2625:
2598:
2571:
2544:
2517:
2495:each side, of length
2481:
2414:
2372:
2346:
2251:
2192:
2152:
2109:
2023:
1996:
1969:
1942:
1915:
1879:
1855:
1835:center of oscillation
1825:
1794:
1698:
1672:
1593:
1518:
1488:
1455:
1367:
1277:
1254:
1228:
1163:
1123:
1065:
1017:
935:
909:
806:
751:
722:
699:
676:
649:
605:
589:period of oscillation
578:
537:
514:
494:
474:
450:
426:Mathematical analysis
165:rod runs up from the
145:C: higher temperature
143:B: normal temperature
141:A: exterior schematic
140:
118:Industrial Revolution
22:
3487:
3451:
3412:
3373:
3344:
3315:
3295:{\displaystyle \pi }
3286:
3278:Ambient temperature
3257:
3221:
3185:
3156:
3043:
2998:
2978:
2974:has a CTE of around
2855:
2754:
2637:
2607:
2580:
2553:
2526:
2499:
2428:
2381:
2361:
2266:
2204:
2161:
2121:
2035:
2005:
1978:
1951:
1924:
1897:
1868:
1841:
1823:{\displaystyle L=\,}
1810:
1709:
1687:
1603:
1530:
1497:
1467:
1377:
1289:
1263:
1240:
1176:
1152:
1077:
1027:
947:
921:
816:
763:
731:
708:
685:
662:
617:
594:
549:
523:
503:
483:
463:
439:
229:invented in 1721 by
3138:
658:A change in length
3493:
3464:
3428:
3389:
3350:
3321:
3292:
3263:
3234:
3198:
3162:
3137:
3119:
3026:
2984:
2958:
2835:
2734:
2620:
2593:
2566:
2539:
2512:
2476:
2409:
2367:
2341:
2246:
2187:
2147:
2104:
2018:
1991:
1964:
1937:
1910:
1874:
1853:{\displaystyle L=}
1850:
1820:
1789:
1693:
1667:
1588:
1513:
1483:
1450:
1362:
1272:
1249:
1223:
1158:
1118:
1060:
1012:
930:
904:
801:
746:
717:
694:
671:
644:
600:
573:
532:
509:
489:
469:
445:
147:
25:
3512:
3511:
3496:{\displaystyle T}
3461:
3425:
3386:
3353:{\displaystyle L}
3324:{\displaystyle g}
3231:
3195:
3111:
3107:
3094:
3082:
3069:
3056:
3023:
3008:
2950:
2946:
2933:
2921:
2908:
2895:
2880:
2877:
2867:
2829:
2816:
2804:
2790:
2777:
2764:
2732:
2728:
2715:
2703:
2690:
2677:
2662:
2659:
2649:
2617:
2590:
2563:
2536:
2509:
2490:Nine rod gridiron
2468:
2465:
2454:
2441:
2406:
2391:
2333:
2330:
2319:
2306:
2291:
2288:
2278:
2243:
2227:
2214:
2184:
2171:
2144:
2131:
2102:
2099:
2088:
2075:
2060:
2057:
2047:
2015:
1988:
1961:
1934:
1907:
1889:Five rod gridiron
1877:{\displaystyle L}
1862:moment of inertia
1773:
1744:
1728:
1696:{\displaystyle T}
1665:
1661:
1646:
1628:
1625:
1615:
1579:
1566:
1553:
1540:
1510:
1480:
1438:
1425:
1412:
1399:
1353:
1343:
1321:
1311:
1220:
1201:
1161:{\displaystyle L}
1115:
1094:
1058:
1004:
1003:
983:
981:
902:
900:
861:
860:
836:
793:
642:
641:
603:{\displaystyle T}
492:{\displaystyle L}
431:Temperature error
183:thermal expansion
103:thermal expansion
83:gridiron pendulum
3872:
3846:
3844:
3842:
3821:
3810:
3790:
3789:
3769:
3754:
3753:
3743:
3734:
3733:
3723:
3714:
3713:
3703:
3690:
3677:
3668:
3667:
3647:
3620:
3619:
3617:
3615:
3600:
3585:
3584:
3564:
3553:
3552:
3532:
3502:
3500:
3499:
3494:
3473:
3471:
3470:
3465:
3463:
3462:
3459:
3437:
3435:
3434:
3429:
3427:
3426:
3423:
3398:
3396:
3395:
3390:
3388:
3387:
3384:
3359:
3357:
3356:
3351:
3330:
3328:
3327:
3322:
3301:
3299:
3298:
3293:
3272:
3270:
3269:
3264:
3243:
3241:
3240:
3235:
3233:
3232:
3229:
3207:
3205:
3204:
3199:
3197:
3196:
3193:
3171:
3169:
3168:
3163:
3139:
3136:
3128:
3126:
3125:
3120:
3112:
3110:
3109:
3108:
3105:
3096:
3095:
3092:
3085:
3084:
3083:
3080:
3071:
3070:
3067:
3058:
3057:
3054:
3047:
3035:
3033:
3032:
3027:
3025:
3024:
3021:
3015:
3010:
3009:
3006:
2993:
2991:
2990:
2985:
2967:
2965:
2964:
2959:
2951:
2949:
2948:
2947:
2944:
2935:
2934:
2931:
2924:
2923:
2922:
2919:
2910:
2909:
2906:
2897:
2896:
2893:
2886:
2881:
2879:
2878:
2875:
2869:
2868:
2865:
2859:
2844:
2842:
2841:
2836:
2831:
2830:
2827:
2818:
2817:
2814:
2805:
2797:
2792:
2791:
2788:
2779:
2778:
2775:
2766:
2765:
2762:
2743:
2741:
2740:
2735:
2733:
2731:
2730:
2729:
2726:
2717:
2716:
2713:
2706:
2705:
2704:
2701:
2692:
2691:
2688:
2679:
2678:
2675:
2668:
2663:
2661:
2660:
2657:
2651:
2650:
2647:
2641:
2629:
2627:
2626:
2621:
2619:
2618:
2615:
2602:
2600:
2599:
2594:
2592:
2591:
2588:
2575:
2573:
2572:
2567:
2565:
2564:
2561:
2548:
2546:
2545:
2540:
2538:
2537:
2534:
2521:
2519:
2518:
2513:
2511:
2510:
2507:
2485:
2483:
2482:
2477:
2469:
2467:
2466:
2463:
2457:
2456:
2455:
2452:
2443:
2442:
2439:
2432:
2418:
2416:
2415:
2410:
2408:
2407:
2404:
2398:
2393:
2392:
2389:
2376:
2374:
2373:
2368:
2350:
2348:
2347:
2342:
2334:
2332:
2331:
2328:
2322:
2321:
2320:
2317:
2308:
2307:
2304:
2297:
2292:
2290:
2289:
2286:
2280:
2279:
2276:
2270:
2255:
2253:
2252:
2247:
2245:
2244:
2241:
2229:
2228:
2225:
2216:
2215:
2212:
2196:
2194:
2193:
2188:
2186:
2185:
2182:
2173:
2172:
2169:
2156:
2154:
2153:
2148:
2146:
2145:
2142:
2133:
2132:
2129:
2113:
2111:
2110:
2105:
2103:
2101:
2100:
2097:
2091:
2090:
2089:
2086:
2077:
2076:
2073:
2066:
2061:
2059:
2058:
2055:
2049:
2048:
2045:
2039:
2027:
2025:
2024:
2019:
2017:
2016:
2013:
2000:
1998:
1997:
1992:
1990:
1989:
1986:
1973:
1971:
1970:
1965:
1963:
1962:
1959:
1946:
1944:
1943:
1938:
1936:
1935:
1932:
1919:
1917:
1916:
1911:
1909:
1908:
1905:
1883:
1881:
1880:
1875:
1859:
1857:
1856:
1851:
1829:
1827:
1826:
1821:
1804:seconds pendulum
1798:
1796:
1795:
1790:
1788:
1787:
1782:
1781:
1774:
1772:
1761:
1759:
1758:
1746:
1745:
1742:
1730:
1729:
1726:
1702:
1700:
1699:
1694:
1676:
1674:
1673:
1668:
1666:
1664:
1663:
1662:
1659:
1649:
1648:
1647:
1644:
1634:
1629:
1627:
1626:
1623:
1617:
1616:
1613:
1607:
1597:
1595:
1594:
1589:
1581:
1580:
1577:
1568:
1567:
1564:
1555:
1554:
1551:
1542:
1541:
1538:
1522:
1520:
1519:
1514:
1512:
1511:
1508:
1492:
1490:
1489:
1484:
1482:
1481:
1478:
1459:
1457:
1456:
1451:
1440:
1439:
1436:
1427:
1426:
1423:
1414:
1413:
1410:
1401:
1400:
1397:
1371:
1369:
1368:
1363:
1355:
1354:
1351:
1345:
1344:
1341:
1323:
1322:
1319:
1313:
1312:
1309:
1281:
1279:
1278:
1273:
1258:
1256:
1255:
1250:
1232:
1230:
1229:
1224:
1222:
1221:
1218:
1203:
1202:
1199:
1167:
1165:
1164:
1159:
1127:
1125:
1124:
1119:
1116:
1111:
1100:
1095:
1090:
1082:
1069:
1067:
1066:
1061:
1059:
1054:
1040:
1021:
1019:
1018:
1013:
1005:
996:
995:
984:
982:
974:
972:
958:
939:
937:
936:
931:
913:
911:
910:
905:
903:
901:
893:
891:
883:
869:
868:
862:
853:
852:
844:
843:
837:
835:
824:
810:
808:
807:
802:
794:
792:
784:
776:
755:
753:
752:
747:
726:
724:
723:
718:
703:
701:
700:
695:
680:
678:
677:
672:
653:
651:
650:
645:
643:
634:
633:
609:
607:
606:
601:
582:
580:
579:
574:
541:
539:
538:
533:
518:
516:
515:
510:
498:
496:
495:
490:
478:
476:
475:
470:
454:
452:
451:
446:
420:
411:
402:
393:
384:
375:
366:
357:
348:
339:
330:
321:
312:
303:
294:
285:
276:
267:
258:
227:mercury pendulum
126:regulator clocks
71:
59:
47:
35:
3880:
3879:
3875:
3874:
3873:
3871:
3870:
3869:
3850:
3849:
3840:
3838:
3799:
3797:Further reading
3794:
3793:
3786:
3770:
3757:
3744:
3737:
3724:
3717:
3704:
3693:
3678:
3671:
3664:
3648:
3623:
3613:
3611:
3602:
3601:
3588:
3581:
3565:
3556:
3549:
3533:
3522:
3517:
3488:
3485:
3484:
3458:
3454:
3452:
3449:
3448:
3422:
3418:
3413:
3410:
3409:
3383:
3379:
3374:
3371:
3370:
3345:
3342:
3341:
3316:
3313:
3312:
3287:
3284:
3283:
3258:
3255:
3254:
3228:
3224:
3222:
3219:
3218:
3192:
3188:
3186:
3183:
3182:
3157:
3154:
3153:
3135:
3104:
3100:
3091:
3087:
3086:
3079:
3075:
3066:
3062:
3053:
3049:
3048:
3046:
3044:
3041:
3040:
3020:
3016:
3011:
3005:
3001:
2999:
2996:
2995:
2979:
2976:
2975:
2943:
2939:
2930:
2926:
2925:
2918:
2914:
2905:
2901:
2892:
2888:
2887:
2885:
2874:
2870:
2864:
2860:
2858:
2856:
2853:
2852:
2826:
2822:
2813:
2809:
2796:
2787:
2783:
2774:
2770:
2761:
2757:
2755:
2752:
2751:
2725:
2721:
2712:
2708:
2707:
2700:
2696:
2687:
2683:
2674:
2670:
2669:
2667:
2656:
2652:
2646:
2642:
2640:
2638:
2635:
2634:
2614:
2610:
2608:
2605:
2604:
2587:
2583:
2581:
2578:
2577:
2560:
2556:
2554:
2551:
2550:
2533:
2529:
2527:
2524:
2523:
2506:
2502:
2500:
2497:
2496:
2492:
2462:
2458:
2451:
2447:
2438:
2434:
2433:
2431:
2429:
2426:
2425:
2420:
2403:
2399:
2394:
2388:
2384:
2382:
2379:
2378:
2362:
2359:
2358:
2327:
2323:
2316:
2312:
2303:
2299:
2298:
2296:
2285:
2281:
2275:
2271:
2269:
2267:
2264:
2263:
2240:
2236:
2224:
2220:
2211:
2207:
2205:
2202:
2201:
2181:
2177:
2168:
2164:
2162:
2159:
2158:
2141:
2137:
2128:
2124:
2122:
2119:
2118:
2096:
2092:
2085:
2081:
2072:
2068:
2067:
2065:
2054:
2050:
2044:
2040:
2038:
2036:
2033:
2032:
2012:
2008:
2006:
2003:
2002:
1985:
1981:
1979:
1976:
1975:
1958:
1954:
1952:
1949:
1948:
1931:
1927:
1925:
1922:
1921:
1904:
1900:
1898:
1895:
1894:
1891:
1869:
1866:
1865:
1842:
1839:
1838:
1811:
1808:
1807:
1783:
1777:
1776:
1775:
1765:
1760:
1754:
1753:
1741:
1737:
1725:
1721:
1710:
1707:
1706:
1688:
1685:
1684:
1682:
1658:
1654:
1650:
1643:
1639:
1635:
1633:
1622:
1618:
1612:
1608:
1606:
1604:
1601:
1600:
1576:
1572:
1563:
1559:
1550:
1546:
1537:
1533:
1531:
1528:
1527:
1507:
1503:
1498:
1495:
1494:
1477:
1473:
1468:
1465:
1464:
1435:
1431:
1422:
1418:
1409:
1405:
1396:
1392:
1378:
1375:
1374:
1350:
1346:
1340:
1336:
1318:
1314:
1308:
1304:
1290:
1287:
1286:
1264:
1261:
1260:
1241:
1238:
1237:
1217:
1213:
1198:
1194:
1177:
1174:
1173:
1153:
1150:
1149:
1145:
1129:
1101:
1099:
1083:
1081:
1078:
1075:
1074:
1041:
1039:
1028:
1025:
1024:
994:
973:
959:
957:
948:
945:
944:
922:
919:
918:
892:
884:
882:
864:
863:
851:
839:
838:
828:
823:
817:
814:
813:
785:
777:
775:
764:
761:
760:
732:
729:
728:
709:
706:
705:
686:
683:
682:
663:
660:
659:
632:
618:
615:
614:
595:
592:
591:
550:
547:
546:
524:
521:
520:
504:
501:
500:
484:
481:
480:
464:
461:
460:
440:
437:
436:
433:
428:
421:
412:
403:
394:
385:
376:
367:
358:
349:
340:
331:
322:
313:
304:
295:
286:
277:
268:
259:
250:
218:
144:
142:
135:
122:pendulum clocks
79:
78:
77:
76:
75:
72:
64:
63:
60:
52:
51:
48:
40:
39:
36:
17:
12:
11:
5:
3878:
3868:
3867:
3862:
3848:
3847:
3822:
3811:
3798:
3795:
3792:
3791:
3784:
3755:
3735:
3715:
3691:
3669:
3662:
3621:
3586:
3579:
3554:
3547:
3519:
3518:
3516:
3513:
3510:
3509:
3506:
3503:
3492:
3481:
3480:
3477:
3474:
3457:
3445:
3444:
3441:
3438:
3421:
3417:
3406:
3405:
3402:
3399:
3382:
3378:
3367:
3366:
3363:
3360:
3349:
3338:
3337:
3334:
3331:
3320:
3309:
3308:
3305:
3302:
3291:
3280:
3279:
3276:
3275:degree Celsius
3273:
3262:
3251:
3250:
3247:
3246:degree Celsius
3244:
3227:
3215:
3214:
3211:
3210:degree Celsius
3208:
3191:
3179:
3178:
3175:
3174:degree Celsius
3172:
3161:
3150:
3149:
3146:
3143:
3134:
3131:
3130:
3129:
3118:
3115:
3103:
3099:
3090:
3078:
3074:
3065:
3061:
3052:
3019:
3014:
3004:
2983:
2969:
2968:
2957:
2954:
2942:
2938:
2929:
2917:
2913:
2904:
2900:
2891:
2884:
2873:
2863:
2846:
2845:
2834:
2825:
2821:
2812:
2808:
2803:
2800:
2795:
2786:
2782:
2773:
2769:
2760:
2745:
2744:
2724:
2720:
2711:
2699:
2695:
2686:
2682:
2673:
2666:
2655:
2645:
2613:
2586:
2559:
2532:
2505:
2491:
2488:
2487:
2486:
2475:
2472:
2461:
2450:
2446:
2437:
2402:
2397:
2387:
2366:
2352:
2351:
2340:
2337:
2326:
2315:
2311:
2302:
2295:
2284:
2274:
2257:
2256:
2239:
2235:
2232:
2223:
2219:
2210:
2180:
2176:
2167:
2140:
2136:
2127:
2115:
2114:
2095:
2084:
2080:
2071:
2064:
2053:
2043:
2011:
1984:
1957:
1930:
1903:
1890:
1887:
1873:
1849:
1846:
1818:
1815:
1800:
1799:
1786:
1780:
1771:
1768:
1764:
1757:
1752:
1749:
1740:
1736:
1733:
1724:
1720:
1717:
1714:
1692:
1679:
1678:
1657:
1653:
1642:
1638:
1632:
1621:
1611:
1598:
1587:
1584:
1575:
1571:
1562:
1558:
1549:
1545:
1536:
1506:
1502:
1476:
1472:
1461:
1460:
1449:
1446:
1443:
1434:
1430:
1421:
1417:
1408:
1404:
1395:
1391:
1388:
1385:
1382:
1372:
1361:
1358:
1349:
1339:
1335:
1332:
1329:
1326:
1317:
1307:
1303:
1300:
1297:
1294:
1271:
1268:
1248:
1245:
1234:
1233:
1216:
1212:
1209:
1206:
1197:
1193:
1190:
1187:
1184:
1181:
1157:
1144:
1141:
1114:
1110:
1107:
1104:
1098:
1093:
1089:
1086:
1072:
1071:
1070:
1057:
1053:
1050:
1047:
1044:
1038:
1035:
1032:
1022:
1011:
1008:
1002:
999:
993:
990:
987:
980:
977:
971:
968:
965:
962:
956:
953:
929:
926:
915:
914:
899:
896:
890:
887:
881:
878:
875:
872:
867:
859:
856:
850:
847:
842:
834:
831:
827:
822:
811:
800:
797:
791:
788:
783:
780:
774:
771:
768:
745:
742:
739:
736:
716:
713:
693:
690:
670:
667:
656:
655:
640:
637:
631:
628:
625:
622:
599:
585:
584:
572:
569:
566:
563:
560:
557:
554:
531:
528:
508:
488:
468:
444:
432:
429:
427:
424:
423:
422:
415:
413:
406:
404:
397:
395:
388:
386:
379:
377:
370:
368:
361:
359:
352:
350:
343:
341:
334:
332:
325:
323:
316:
314:
307:
305:
298:
296:
289:
287:
280:
278:
271:
269:
262:
260:
253:
249:
246:
217:
214:
134:
131:
73:
66:
65:
61:
54:
53:
49:
42:
41:
37:
30:
29:
28:
27:
26:
15:
9:
6:
4:
3:
2:
3877:
3866:
3863:
3861:
3858:
3857:
3855:
3836:
3832:
3828:
3823:
3819:
3818:
3812:
3808:
3807:
3801:
3800:
3787:
3785:9780198567547
3781:
3777:
3776:
3768:
3766:
3764:
3762:
3760:
3751:
3750:
3742:
3740:
3731:
3730:
3722:
3720:
3711:
3710:
3702:
3700:
3698:
3696:
3688:
3687:
3682:
3676:
3674:
3665:
3663:9780198529712
3659:
3655:
3654:
3646:
3644:
3642:
3640:
3638:
3636:
3634:
3632:
3630:
3628:
3626:
3609:
3605:
3599:
3597:
3595:
3593:
3591:
3582:
3580:9780191004841
3576:
3572:
3571:
3563:
3561:
3559:
3550:
3548:9780192609366
3544:
3540:
3539:
3531:
3529:
3527:
3525:
3520:
3507:
3504:
3490:
3483:
3482:
3478:
3475:
3455:
3447:
3446:
3442:
3439:
3419:
3415:
3408:
3407:
3403:
3400:
3380:
3376:
3369:
3368:
3364:
3361:
3347:
3340:
3339:
3335:
3332:
3318:
3311:
3310:
3306:
3303:
3289:
3282:
3281:
3277:
3274:
3260:
3253:
3252:
3248:
3245:
3225:
3217:
3216:
3212:
3209:
3189:
3181:
3180:
3176:
3173:
3159:
3152:
3151:
3147:
3144:
3141:
3140:
3116:
3113:
3101:
3097:
3088:
3076:
3072:
3063:
3059:
3050:
3039:
3038:
3037:
3017:
3012:
3002:
2981:
2973:
2955:
2952:
2940:
2936:
2927:
2915:
2911:
2902:
2898:
2889:
2882:
2871:
2861:
2851:
2850:
2849:
2823:
2819:
2810:
2801:
2798:
2793:
2784:
2780:
2771:
2767:
2758:
2750:
2749:
2748:
2722:
2718:
2709:
2697:
2693:
2684:
2680:
2671:
2664:
2653:
2643:
2633:
2632:
2631:
2611:
2584:
2557:
2530:
2503:
2473:
2470:
2459:
2448:
2444:
2435:
2424:
2423:
2422:
2400:
2395:
2385:
2364:
2357:has a CTE of
2356:
2338:
2335:
2324:
2313:
2309:
2300:
2293:
2282:
2272:
2262:
2261:
2260:
2237:
2233:
2230:
2221:
2217:
2208:
2200:
2199:
2198:
2178:
2174:
2165:
2138:
2134:
2125:
2093:
2082:
2078:
2069:
2062:
2051:
2041:
2031:
2030:
2029:
2009:
1982:
1955:
1928:
1901:
1886:
1871:
1863:
1847:
1844:
1836:
1831:
1816:
1813:
1805:
1784:
1769:
1766:
1762:
1750:
1747:
1738:
1734:
1731:
1722:
1718:
1715:
1712:
1705:
1704:
1703:
1690:
1655:
1651:
1640:
1636:
1630:
1619:
1609:
1599:
1585:
1582:
1573:
1569:
1560:
1556:
1547:
1543:
1534:
1526:
1525:
1524:
1504:
1500:
1474:
1470:
1447:
1432:
1428:
1419:
1415:
1406:
1402:
1393:
1386:
1383:
1373:
1359:
1347:
1337:
1333:
1330:
1327:
1315:
1305:
1301:
1298:
1295:
1285:
1284:
1283:
1269:
1246:
1214:
1207:
1204:
1195:
1188:
1185:
1182:
1172:
1171:
1170:
1155:
1140:
1138:
1132:
1128:
1112:
1108:
1102:
1096:
1091:
1087:
1055:
1051:
1045:
1042:
1036:
1033:
1023:
1009:
1000:
997:
991:
988:
985:
978:
975:
969:
963:
960:
954:
951:
943:
942:
941:
927:
897:
894:
888:
879:
876:
873:
857:
854:
848:
845:
832:
829:
825:
820:
812:
798:
789:
786:
781:
778:
772:
769:
759:
758:
757:
743:
740:
737:
714:
691:
668:
638:
635:
629:
626:
623:
620:
613:
612:
611:
597:
590:
570:
564:
561:
558:
555:
545:
544:
543:
529:
506:
486:
466:
458:
442:
419:
414:
410:
405:
401:
396:
392:
387:
383:
378:
374:
369:
365:
360:
356:
351:
347:
342:
338:
333:
329:
324:
320:
315:
311:
306:
302:
297:
293:
288:
284:
279:
275:
270:
266:
261:
257:
252:
251:
245:
243:
239:
234:
232:
231:George Graham
228:
224:
216:Disadvantages
213:
211:
207:
206:John Ellicott
202:
199:
194:
191:
186:
184:
178:
175:
170:
168:
164:
161:. A central
160:
156:
151:
139:
130:
127:
123:
119:
114:
112:
108:
104:
99:
95:
94:John Harrison
91:
88:
84:
70:
58:
46:
34:
21:
3839:. Retrieved
3834:
3830:
3816:
3805:
3774:
3748:
3728:
3708:
3685:
3680:
3652:
3612:. Retrieved
3607:
3569:
3537:
3333:meter×second
2970:
2847:
2746:
2493:
2353:
2258:
2116:
1892:
1832:
1801:
1680:
1462:
1235:
1146:
1143:Compensation
1133:
1130:
1073:
916:
657:
586:
434:
242:fused quartz
235:
219:
209:
203:
198:Dent company
195:
187:
179:
171:
152:
148:
133:How it works
125:
115:
82:
80:
3148:Definition
210:see drawing
157:and two of
3854:Categories
3515:References
120:period in
3860:Pendulums
3416:∑
3377:∑
3290:π
3261:θ
3226:α
3190:α
3160:α
3018:α
3003:α
2982:α
2953:≥
2872:α
2862:α
2794:≥
2654:α
2644:α
2401:α
2386:α
2365:α
2336:≥
2283:α
2273:α
2231:≥
2175:≥
2135:≥
2052:α
2042:α
1770:π
1735:∑
1732:−
1719:∑
1652:∑
1637:∑
1620:α
1610:α
1570:∑
1561:α
1557:−
1544:∑
1535:α
1501:∑
1471:∑
1448:θ
1445:Δ
1429:∑
1420:α
1416:−
1403:∑
1394:α
1381:Δ
1360:θ
1357:Δ
1338:α
1334:∑
1331:−
1328:θ
1325:Δ
1306:α
1302:∑
1293:Δ
1270:θ
1267:Δ
1244:Δ
1211:Δ
1208:∑
1205:−
1192:Δ
1189:∑
1180:Δ
1109:θ
1106:Δ
1103:α
1085:Δ
1052:θ
1049:Δ
1043:α
1031:Δ
1010:θ
1007:Δ
992:π
989:α
970:θ
967:Δ
961:α
955:π
928:θ
925:Δ
886:Δ
880:π
871:Δ
849:π
796:Δ
767:Δ
735:Δ
712:Δ
692:θ
689:Δ
666:Δ
630:π
571:θ
568:Δ
562:α
553:Δ
530:θ
527:Δ
507:α
467:α
443:θ
1137:humidity
741:<<
90:pendulum
3604:"Clock"
248:Gallery
3841:9 July
3782:
3660:
3614:7 July
3577:
3545:
3505:second
3142:Symbol
1463:where
459:(CTE)
98:period
3476:meter
3440:meter
3401:meter
3362:meter
2972:Brass
238:invar
223:creep
190:brass
163:steel
155:steel
111:brass
107:steel
87:clock
3843:2024
3780:ISBN
3658:ISBN
3616:2024
3575:ISBN
3543:ISBN
3385:high
3304:none
3194:high
3145:Unit
3117:1.68
3007:high
2866:high
2648:high
2603:and
2522:and
2474:2.28
2390:high
2355:Zinc
2277:high
2157:and
2046:high
1947:and
1743:high
1660:high
1614:high
1578:high
1565:high
1509:high
1437:high
1424:high
1352:high
1342:high
1219:high
587:The
240:and
174:zinc
159:zinc
109:and
3424:low
3230:low
3022:low
2956:1.5
2876:low
2658:low
2405:low
2287:low
2056:low
1727:low
1645:low
1624:low
1552:low
1539:low
1479:low
1411:low
1398:low
1320:low
1310:low
1282:is
1200:low
940:is
542:is
167:bob
3856::
3835:47
3833:.
3829:.
3758:^
3738:^
3718:^
3694:^
3672:^
3624:^
3606:.
3589:^
3557:^
3523:^
2576:,
244:.
81:A
3845:.
3788:.
3679:"
3666:.
3618:.
3583:.
3551:.
3491:T
3460:n
3456:L
3420:L
3381:L
3348:L
3319:g
3114:=
3106:4
3102:L
3098:+
3093:2
3089:L
3081:5
3077:L
3073:+
3068:3
3064:L
3060:+
3055:1
3051:L
3013:/
2945:4
2941:L
2937:+
2932:2
2928:L
2920:5
2916:L
2912:+
2907:3
2903:L
2899:+
2894:1
2890:L
2883:=
2833:)
2828:2
2824:L
2820:+
2815:2
2811:L
2807:(
2802:2
2799:3
2789:5
2785:L
2781:+
2776:3
2772:L
2768:+
2763:1
2759:L
2727:4
2723:L
2719:+
2714:2
2710:L
2702:5
2698:L
2694:+
2689:3
2685:L
2681:+
2676:1
2672:L
2665:=
2616:5
2612:L
2589:3
2585:L
2562:1
2558:L
2535:4
2531:L
2508:2
2504:L
2471:=
2464:2
2460:L
2453:3
2449:L
2445:+
2440:1
2436:L
2396:/
2339:2
2329:2
2325:L
2318:3
2314:L
2310:+
2305:1
2301:L
2294:=
2242:2
2238:L
2234:2
2226:3
2222:L
2218:+
2213:1
2209:L
2183:2
2179:L
2170:3
2166:L
2143:2
2139:L
2130:1
2126:L
2098:2
2094:L
2087:3
2083:L
2079:+
2074:1
2070:L
2063:=
2014:2
2010:L
1987:2
1983:L
1960:3
1956:L
1933:1
1929:L
1906:2
1902:L
1872:L
1848:=
1845:L
1817:=
1814:L
1785:2
1779:)
1767:2
1763:T
1756:(
1751:g
1748:=
1739:L
1723:L
1716:=
1713:L
1691:T
1656:L
1641:L
1631:=
1586:0
1583:=
1574:L
1548:L
1505:L
1475:L
1442:)
1433:L
1407:L
1390:(
1387:=
1384:L
1348:L
1316:L
1299:=
1296:L
1247:L
1215:L
1196:L
1186:=
1183:L
1156:L
1113:2
1097:=
1092:T
1088:T
1056:2
1046:T
1037:=
1034:T
1001:g
998:L
986:=
979:L
976:g
964:L
952:=
898:L
895:g
889:L
877:=
874:L
866:)
858:g
855:L
846:2
841:(
833:L
830:d
826:d
821:=
799:L
790:L
787:d
782:T
779:d
773:=
770:T
744:T
738:T
715:T
669:L
639:g
636:L
627:2
624:=
621:T
598:T
565:L
559:=
556:L
487:L
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
