122:
668:
2320:
2380:
25:
2242:
1056:
2569:
1437:
1929:
798:
1602:
545:
1207:
2237:{\displaystyle {\begin{aligned}V_{G}&=\left({R_{2} \over {R_{1}+R_{2}}}-{R_{x} \over {R_{x}+R_{3}}}\right)V_{s}\\R_{x}&={{R_{2}\cdot V_{s}-(R_{1}+R_{2})\cdot V_{G}} \over {R_{1}\cdot V_{s}+(R_{1}+R_{2})\cdot V_{G}}}R_{3}\end{aligned}}}
1731:
1051:{\displaystyle {\begin{aligned}{\frac {V_{DC}}{V_{AD}}}&={\frac {V_{BC}}{V_{AB}}}\\\Rightarrow {\frac {I_{2}R_{2}}{I_{1}R_{1}}}&={\frac {I_{x}R_{x}}{I_{3}R_{3}}}\\\Rightarrow R_{x}&={\frac {R_{2}}{R_{1}}}\cdot R_{3}\end{aligned}}}
1192:
1460:
2329:
The
Wheatstone bridge is the fundamental bridge, but there are other modifications that can be made to measure various kinds of resistances when the fundamental Wheatstone bridge is not suitable. Some of the modifications are:
409:
803:
1934:
414:
1881:
2286:
was specially adapted from the
Wheatstone bridge for measuring very low resistances. In many cases, the significance of measuring the unknown resistance is related to measuring the impact of some
1465:
1212:
1081:
254:, one leg of which includes the unknown component. The primary benefit of the circuit is its ability to provide extremely accurate measurements (in contrast with something like a simple
1432:{\displaystyle {\begin{aligned}(I_{3}\cdot R_{3})-(I_{G}\cdot R_{G})-(I_{1}\cdot R_{1})&=0\\(I_{x}\cdot R_{x})-(I_{2}\cdot R_{2})+(I_{G}\cdot R_{G})&=0\end{aligned}}}
1613:
2266:
The
Wheatstone bridge illustrates the concept of a difference measurement, which can be extremely accurate. Variations on the Wheatstone bridge can be used to measure
1076:
2466:
Wheatstone, Charles (1843). "XIII. The
Bakerian lecture.—An account of several new instruments and processes for determining the constants of a voltaic circuit".
1597:{\displaystyle {\begin{aligned}I_{3}\cdot R_{3}&=I_{1}\cdot R_{1}\quad {\text{(1)}}\\I_{x}\cdot R_{x}&=I_{2}\cdot R_{2}\quad {\text{(2)}}\end{aligned}}}
540:{\displaystyle {\begin{aligned}{\frac {R_{2}}{R_{1}}}&={\frac {R_{x}}{R_{3}}}\\\Rightarrow R_{x}&={\frac {R_{2}}{R_{1}}}\cdot R_{3}\end{aligned}}}
2494:
2626:
2414:
259:
2290:(such as force, temperature, pressure, etc.) which thereby allows the use of Wheatstone bridge in measuring those elements indirectly.
42:
108:
2573:
89:
2804:
1815:
61:
2794:
46:
659:
measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.
2619:
2409:
638:
is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of
68:
2716:
2453:"Circuits in Practice: The Wheatstone Bridge, What It Does, and Why It Matters", as discussed in this MIT ES.333 class
2799:
1198:
648:
2784:
75:
35:
2789:
2612:
355:
between the two midpoints (B and D) will be zero. Therefore the ratio of the two resistances in the known leg
57:
1919:), or the supply voltage from all four resistor values. To do so, one has to work out the voltage from each
1067:
2551:
2519:
2429:
656:
266:
2344:
247:
2537:
2737:
2364:
2358:
2275:
352:
1726:{\displaystyle R_{x}={{R_{2}\cdot I_{2}\cdot I_{3}\cdot R_{3}} \over {R_{1}\cdot I_{1}\cdot I_{x}}}}
2696:
2334:
2298:
2294:
2287:
2711:
2585:
2523:
2385:
270:
243:
2579:
1607:
Then, equation (1) is divided by equation (2) and the resulting equation is rearranged, giving:
1187:{\displaystyle {\begin{aligned}I_{3}-I_{x}+I_{G}&=0\\I_{1}-I_{2}-I_{G}&=0\end{aligned}}}
82:
2691:
2419:
1920:
2509:
2475:
685:
2670:
2403:
2397:
667:
255:
126:
2742:
792:
Dividing the last two equations by members and using the above currents equalities, then
2367:, for measuring the self-inductance of the circuit, an advanced form of Maxwell's bridge
2732:
2706:
2701:
2635:
2350:
251:
2778:
2649:
2340:
2323:
2308:
2283:
274:
2591:
2319:
2758:
2434:
2393:
2279:
2278:
and other quantities, such as the amount of combustible gases in a sample, with an
652:
551:
340:
2675:
2354:
2267:
24:
2379:
391:. If the bridge is unbalanced, the direction of the current indicates whether
121:
2454:
2375:
2271:
1886:
On the other hand, if the resistance of the galvanometer is high enough that
339:
is adjusted until the bridge is "balanced" and no current flows through the
2513:
2479:
2568:
269:(sometimes spelled "Christy") in 1833 and improved and popularized by Sir
2763:
2424:
2599:
681:
2604:
2318:
373:
is equal to the ratio of the two resistances in the unknown leg
2608:
2526:'s contributions, and why the bridge carries Wheatstone's name.
273:
in 1843. One of the
Wheatstone bridge's initial uses was for
18:
1923:
and subtract one from the other. The equations for this are:
1908:
from the three other resistor values and the supply voltage (
1201:
is used for finding the voltage in the loops ABDA and BCDB:
2542:
1798:
cancels out of the above equation. The desired value of
688:
between the two midpoints (B and D) are zero. Therefore,
590:
can be measured to high precision. Very small changes in
1876:{\displaystyle R_{x}={{R_{3}\cdot R_{2}} \over {R_{1}}}}
321:
are resistors of known resistance and the resistance of
554:
can be done to extremely high precision. Therefore, if
1454:, so the second set of equations can be rewritten as:
294:
is the fixed, yet unknown, resistance to be measured.
1932:
1818:
1616:
1463:
1210:
1079:
801:
412:
2751:
2725:
2684:
2663:
2642:
1070:is used to find the currents in junctions B and D:
49:. Unsourced material may be challenged and removed.
2236:
1875:
1725:
1596:
1431:
1186:
1050:
539:
2538:"A dynamical theory of the electromagnetic field"
1770:being proportional from Kirchhoff's First Law,
1062:Full derivation using Kirchhoff's circuit laws
599:disrupt the balance and are readily detected.
2620:
2258:is the voltage of node D relative to node B.
8:
258:). Its operation is similar to the original
671:Directions of currents arbitrarily assigned
175:is 0, both legs have equal voltage ratios:
2627:
2613:
2605:
2502:Engineering Science and Education Journal
2224:
2211:
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2031:
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1965:
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1933:
1931:
1897:is negligible, it is possible to compute
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1859:
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1714:
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1138:
1114:
1101:
1088:
1080:
1078:
1038:
1023:
1013:
1007:
994:
974:
964:
952:
942:
935:
919:
909:
897:
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862:
849:
843:
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812:
806:
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800:
527:
512:
502:
496:
483:
464:
454:
448:
433:
423:
417:
413:
411:
166:is adjustable. When the measured voltage
109:Learn how and when to remove this message
666:
120:
2446:
16:System to measure electrical resistance
2550:Maxwell's bridge used a battery and a
2495:"The Genesis of the Wheatstone Bridge"
265:The Wheatstone bridge was invented by
2587:Lessons In Electric Circuits Vol 1 DC
2311:in British Patent no. 323,037, 1928.
7:
2415:Potentiometer (measuring instrument)
47:adding citations to reliable sources
2406:– a circuit using a balanced bridge
651:. This setup is frequently used in
1442:When the bridge is balanced, then
680:At the point of balance, both the
581:are known to high precision, then
14:
2337:, for measuring small resistances
2315:Modifications of the basic bridge
2567:
2378:
2301:in 1865 and further improved as
23:
1584:
1521:
138:is to be measured; resistances
34:needs additional citations for
2493:Ekelof, Stig (February 2001).
2201:
2175:
2131:
2105:
1412:
1386:
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1354:
1348:
1322:
1305:
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1247:
1241:
1215:
987:
877:
550:Detecting zero current with a
476:
330:is adjustable. The resistance
1:
2410:Post office box (electricity)
1809:is now known to be given as:
2717:Transformer ratio arm bridge
2664:Resistance–Capacitance
2593:Lessons In Electric Circuits
2293:The concept was extended to
1061:
676:Quick derivation at balance
250:by balancing two legs of a
246:used to measure an unknown
2823:
2536:Maxwell, J. Clerk (1865).
403:At the point of balance,
129:. The unknown resistance
649:Kirchhoff's circuit laws
400:is too high or too low.
2805:Impedance measurements
2552:ballistic galvanometer
2480:10.1098/rstl.1843.0014
2430:Resistance thermometer
2343:, for measuring small
2326:
2238:
1877:
1727:
1598:
1433:
1199:Kirchhoff's second law
1188:
1052:
672:
657:resistance thermometer
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267:Samuel Hunter Christie
235:
2795:Measuring instruments
2514:10.1049/esej:20010106
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2239:
1878:
1728:
1599:
1434:
1189:
1068:Kirchhoff's first law
1053:
670:
542:
351:. At this point, the
248:electrical resistance
124:
2581:DC Metering Circuits
2576:at Wikimedia Commons
1930:
1816:
1614:
1461:
1208:
1077:
799:
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353:potential difference
43:improve this article
2697:Carey Foster bridge
2574:Wheatstone's bridge
2554:. See pp. 475–477.
2468:Phil. Trans. R. Soc
2335:Carey Foster bridge
2299:James Clerk Maxwell
2295:alternating current
2288:physical phenomenon
58:"Wheatstone bridge"
2800:English inventions
2712:Murray loop bridge
2386:Electronics portal
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271:Charles Wheatstone
244:electrical circuit
236:
125:Wheatstone bridge
2785:Electrical meters
2772:
2771:
2738:Anderson's bridge
2692:Bridged T circuit
2655:Wheatstone bridge
2572:Media related to
2420:Potential divider
2365:Anderson's bridge
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1996:
1921:potential divider
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240:Wheatstone bridge
159:are known, where
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772:
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721:
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610:
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531:
519:
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471:
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468:
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440:
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428:
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399:
390:
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350:
338:
329:
320:
311:
302:
293:
277:and comparison.
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100:
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51:
27:
19:
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2790:Bridge circuits
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2671:Schering bridge
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2638:
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2404:Phantom circuit
2400:– diode bridges
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2377:
2374:
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2304:Blumlein bridge
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2256:
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1498:
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1468:
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1443:
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1415:
1402:
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1318:
1308:
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1250:
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1205:
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764:
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729:
723:
720:
711:
705:
702:
695:
689:
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665:
644:
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629:are known, but
627:
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582:
579:
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570:
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285:In the figure,
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233:
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127:circuit diagram
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2707:Lattice filter
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2702:Fontana bridge
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2562:External links
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1577:
1573:
1568:
1564:
1560:
1557:
1555:
1551:
1547:
1543:
1538:
1534:
1530:
1529:
1518:
1514:
1510:
1505:
1501:
1497:
1494:
1492:
1488:
1484:
1480:
1475:
1471:
1467:
1466:
1447:
1440:
1439:
1424:
1421:
1418:
1416:
1414:
1409:
1405:
1401:
1396:
1392:
1388:
1385:
1382:
1377:
1373:
1369:
1364:
1360:
1356:
1353:
1350:
1345:
1341:
1337:
1332:
1328:
1324:
1321:
1320:
1317:
1314:
1311:
1309:
1307:
1302:
1298:
1294:
1289:
1285:
1281:
1278:
1275:
1270:
1266:
1262:
1257:
1253:
1249:
1246:
1243:
1238:
1234:
1230:
1225:
1221:
1217:
1214:
1213:
1195:
1194:
1179:
1176:
1173:
1171:
1167:
1163:
1159:
1154:
1150:
1146:
1141:
1137:
1133:
1132:
1129:
1126:
1123:
1121:
1117:
1113:
1109:
1104:
1100:
1096:
1091:
1087:
1083:
1082:
1063:
1060:
1059:
1058:
1041:
1037:
1033:
1026:
1022:
1016:
1012:
1006:
1003:
1001:
997:
993:
989:
986:
985:
977:
973:
967:
963:
955:
951:
945:
941:
934:
931:
929:
922:
918:
912:
908:
900:
896:
890:
886:
879:
876:
875:
868:
865:
861:
855:
852:
848:
842:
839:
837:
831:
828:
824:
818:
815:
811:
805:
804:
785:
778:
769:
762:
753:
746:
734:
727:
716:
709:
700:
693:
677:
674:
664:
661:
642:
634:
625:
616:
607:
594:
585:
577:
568:
559:
548:
547:
530:
526:
522:
515:
511:
505:
501:
495:
492:
490:
486:
482:
478:
475:
474:
467:
463:
457:
453:
447:
444:
442:
436:
432:
426:
422:
416:
415:
396:
386:
378:
368:
361:
346:
335:
326:
317:
308:
299:
289:
282:
279:
252:bridge circuit
231:
224:
218:
209:
202:
193:
186:
179:
170:
163:
156:
149:
142:
133:
117:
116:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
2818:
2817:
2806:
2803:
2801:
2798:
2796:
2793:
2791:
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2786:
2783:
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2744:
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2736:
2734:
2731:
2730:
2728:
2724:
2718:
2715:
2713:
2710:
2708:
2705:
2703:
2700:
2698:
2695:
2693:
2690:
2689:
2687:
2683:
2677:
2674:
2672:
2669:
2668:
2666:
2662:
2656:
2653:
2651:
2650:Kelvin bridge
2648:
2647:
2645:
2641:
2637:
2630:
2625:
2623:
2618:
2616:
2611:
2610:
2607:
2601:
2600:Test Set I-49
2598:
2595:
2594:
2589:
2588:
2584:chapter from
2583:
2582:
2578:
2575:
2570:
2566:
2565:
2561:
2553:
2547:
2543:
2539:
2532:
2529:
2525:
2521:
2515:
2511:
2507:
2503:
2496:
2489:
2486:
2481:
2477:
2473:
2469:
2462:
2459:
2456:
2450:
2447:
2440:
2436:
2433:
2431:
2428:
2426:
2423:
2421:
2418:
2416:
2413:
2411:
2408:
2405:
2402:
2399:
2398:product mixer
2395:
2392:
2391:
2387:
2381:
2376:
2371:
2366:
2363:
2360:
2356:
2352:
2349:
2346:
2345:four-terminal
2342:
2341:Kelvin bridge
2339:
2336:
2333:
2332:
2331:
2325:
2324:Kelvin bridge
2321:
2314:
2312:
2310:
2309:Alan Blumlein
2300:
2296:
2291:
2289:
2285:
2284:Kelvin bridge
2281:
2277:
2273:
2269:
2261:
2259:
2255:
2251:
2225:
2221:
2212:
2208:
2204:
2196:
2192:
2188:
2183:
2179:
2172:
2167:
2163:
2159:
2154:
2150:
2142:
2138:
2134:
2126:
2122:
2118:
2113:
2109:
2102:
2097:
2093:
2089:
2084:
2080:
2073:
2071:
2064:
2060:
2050:
2046:
2041:
2032:
2028:
2024:
2019:
2015:
2008:
2004:
1998:
1990:
1986:
1982:
1977:
1973:
1966:
1962:
1955:
1951:
1949:
1942:
1938:
1926:
1925:
1924:
1922:
1916:
1912:
1905:
1901:
1894:
1890:
1865:
1861:
1853:
1849:
1845:
1840:
1836:
1829:
1824:
1820:
1812:
1811:
1810:
1806:
1802:
1793:
1787:
1780:
1774:
1765:
1758:
1751:
1747:
1740:
1715:
1711:
1707:
1702:
1698:
1694:
1689:
1685:
1677:
1673:
1669:
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1660:
1656:
1651:
1647:
1643:
1638:
1634:
1627:
1622:
1618:
1610:
1609:
1608:
1579:
1575:
1571:
1566:
1562:
1558:
1556:
1549:
1545:
1541:
1536:
1532:
1516:
1512:
1508:
1503:
1499:
1495:
1493:
1486:
1482:
1478:
1473:
1469:
1457:
1456:
1455:
1450:
1446:
1422:
1419:
1417:
1407:
1403:
1399:
1394:
1390:
1383:
1375:
1371:
1367:
1362:
1358:
1351:
1343:
1339:
1335:
1330:
1326:
1315:
1312:
1310:
1300:
1296:
1292:
1287:
1283:
1276:
1268:
1264:
1260:
1255:
1251:
1244:
1236:
1232:
1228:
1223:
1219:
1204:
1203:
1202:
1200:
1177:
1174:
1172:
1165:
1161:
1157:
1152:
1148:
1144:
1139:
1135:
1127:
1124:
1122:
1115:
1111:
1107:
1102:
1098:
1094:
1089:
1085:
1073:
1072:
1071:
1069:
1039:
1035:
1031:
1024:
1020:
1014:
1010:
1004:
1002:
995:
991:
975:
971:
965:
961:
953:
949:
943:
939:
932:
930:
920:
916:
910:
906:
898:
894:
888:
884:
866:
863:
859:
853:
850:
846:
840:
838:
829:
826:
822:
816:
813:
809:
795:
794:
793:
790:
784:
777:
768:
761:
752:
745:
739:
733:
726:
719:
715:
708:
699:
692:
687:
683:
675:
669:
662:
660:
658:
654:
650:
645:
633:
624:
615:
606:
600:
597:
588:
576:
567:
558:
553:
528:
524:
520:
513:
509:
503:
499:
493:
491:
484:
480:
465:
461:
455:
451:
445:
443:
434:
430:
424:
420:
406:
405:
404:
401:
395:
385:
381:
367:
360:
354:
349:
342:
334:
325:
316:
307:
298:
292:
280:
278:
276:
275:soil analysis
272:
268:
263:
261:
260:potentiometer
257:
253:
249:
245:
241:
230:
223:
217:
212:
208:
201:
196:
192:
185:
178:
173:
169:
162:
155:
148:
141:
136:
132:
128:
123:
113:
110:
102:
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
2759:Diode bridge
2743:Hay's bridge
2654:
2592:
2586:
2580:
2545:
2541:
2531:
2508:(1): 37–40.
2505:
2501:
2488:
2471:
2467:
2461:
2449:
2435:Strain gauge
2394:Diode bridge
2328:
2292:
2280:explosimeter
2265:
2262:Significance
2253:
2249:
2246:
1914:
1910:
1903:
1899:
1892:
1888:
1885:
1804:
1800:
1791:
1785:
1778:
1772:
1763:
1756:
1749:
1745:
1738:
1735:
1606:
1448:
1444:
1441:
1196:
1065:
791:
782:
775:
766:
759:
750:
743:
740:
731:
724:
717:
713:
706:
697:
690:
679:
653:strain gauge
640:
631:
622:
613:
604:
601:
592:
583:
574:
565:
556:
552:galvanometer
549:
402:
393:
383:
376:
365:
358:
344:
341:galvanometer
332:
323:
314:
305:
296:
287:
284:
264:
239:
237:
228:
221:
215:
210:
206:
199:
194:
190:
183:
176:
171:
167:
160:
153:
146:
139:
134:
130:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
2676:Wien bridge
2474:: 303–327.
2355:Wien bridge
2347:resistances
2268:capacitance
741:Because of
2779:Categories
2726:Inductance
2643:Resistance
2548:: 459–512.
2524:Wheatstone
2520:Christie's
2518:discusses
2441:References
2361:components
2272:inductance
663:Derivation
99:March 2019
69:newspapers
2276:impedance
2205:⋅
2160:⋅
2135:⋅
2103:−
2090:⋅
1999:−
1846:⋅
1708:⋅
1695:⋅
1670:⋅
1657:⋅
1644:⋅
1572:⋅
1542:⋅
1509:⋅
1479:⋅
1400:⋅
1368:⋅
1352:−
1336:⋅
1293:⋅
1277:−
1261:⋅
1245:−
1229:⋅
1158:−
1145:−
1095:−
1032:⋅
988:⇒
878:⇒
521:⋅
477:⇒
281:Operation
2764:H-bridge
2425:Ohmmeter
2372:See also
2359:reactive
684:and the
647:, using
2685:General
2596:series.
2282:. The
1736:Due to
1066:First,
757:, then
686:current
682:voltage
214:=
189:=
83:scholar
2353:, and
2247:where
1197:Then,
620:, and
572:, and
312:, and
242:is an
85:
78:
71:
64:
56:
2752:Other
2498:(PDF)
2455:video
90:JSTOR
76:books
2522:and
1754:and
773:and
655:and
205:and
152:and
62:news
2546:155
2510:doi
2476:doi
2472:133
2307:by
1587:(2)
1524:(1)
1452:= 0
45:by
2781::
2544:.
2540:.
2506:10
2504:.
2500:.
2470:.
2396:,
2274:,
2270:,
1762:=
1744:=
789:.
786:AB
781:=
779:AD
770:BC
765:=
763:DC
749:=
738:.
730:=
722:,
712:=
704:,
696:=
611:,
563:,
303:,
262:.
238:A
145:,
2628:e
2621:t
2614:v
2516:.
2512::
2482:.
2478::
2254:G
2250:V
2226:3
2222:R
2213:G
2209:V
2202:)
2197:2
2193:R
2189:+
2184:1
2180:R
2176:(
2173:+
2168:s
2164:V
2155:1
2151:R
2143:G
2139:V
2132:)
2127:2
2123:R
2119:+
2114:1
2110:R
2106:(
2098:s
2094:V
2085:2
2081:R
2074:=
2065:x
2061:R
2051:s
2047:V
2042:)
2033:3
2029:R
2025:+
2020:x
2016:R
2009:x
2005:R
1991:2
1987:R
1983:+
1978:1
1974:R
1967:2
1963:R
1956:(
1952:=
1943:G
1939:V
1915:S
1911:V
1904:x
1900:R
1893:G
1889:I
1866:1
1862:R
1854:2
1850:R
1841:3
1837:R
1830:=
1825:x
1821:R
1805:x
1801:R
1795:x
1792:I
1789:1
1786:I
1784:/
1782:2
1779:I
1776:3
1773:I
1767:2
1764:I
1760:1
1757:I
1750:x
1746:I
1742:3
1739:I
1716:x
1712:I
1703:1
1699:I
1690:1
1686:R
1678:3
1674:R
1665:3
1661:I
1652:2
1648:I
1639:2
1635:R
1628:=
1623:x
1619:R
1580:2
1576:R
1567:2
1563:I
1559:=
1550:x
1546:R
1537:x
1533:I
1517:1
1513:R
1504:1
1500:I
1496:=
1487:3
1483:R
1474:3
1470:I
1449:G
1445:I
1423:0
1420:=
1413:)
1408:G
1404:R
1395:G
1391:I
1387:(
1384:+
1381:)
1376:2
1372:R
1363:2
1359:I
1355:(
1349:)
1344:x
1340:R
1331:x
1327:I
1323:(
1316:0
1313:=
1306:)
1301:1
1297:R
1288:1
1284:I
1280:(
1274:)
1269:G
1265:R
1256:G
1252:I
1248:(
1242:)
1237:3
1233:R
1224:3
1220:I
1216:(
1178:0
1175:=
1166:G
1162:I
1153:2
1149:I
1140:1
1136:I
1128:0
1125:=
1116:G
1112:I
1108:+
1103:x
1099:I
1090:3
1086:I
1040:3
1036:R
1025:1
1021:R
1015:2
1011:R
1005:=
996:x
992:R
976:3
972:R
966:3
962:I
954:x
950:R
944:x
940:I
933:=
921:1
917:R
911:1
907:I
899:2
895:R
889:2
885:I
867:B
864:A
860:V
854:C
851:B
847:V
841:=
830:D
827:A
823:V
817:C
814:D
810:V
783:V
776:V
767:V
760:V
754:B
751:V
747:D
744:V
735:B
732:V
728:D
725:V
718:x
714:I
710:3
707:I
701:2
698:I
694:1
691:I
643:x
641:R
635:2
632:R
626:3
623:R
617:2
614:R
608:1
605:R
595:x
593:R
586:x
584:R
578:3
575:R
569:2
566:R
560:1
557:R
529:3
525:R
514:1
510:R
504:2
500:R
494:=
485:x
481:R
466:3
462:R
456:x
452:R
446:=
435:1
431:R
425:2
421:R
397:2
394:R
389:)
387:3
384:R
379:x
377:R
375:(
371:)
369:1
366:R
362:2
359:R
357:(
347:g
345:V
336:2
333:R
327:2
324:R
318:3
315:R
309:2
306:R
300:1
297:R
290:x
288:R
234:.
232:1
229:R
227:/
225:2
222:R
219:3
216:R
211:x
207:R
203:3
200:R
198:/
195:x
191:R
187:1
184:R
182:/
180:2
177:R
172:G
168:V
164:2
161:R
157:3
154:R
150:2
147:R
143:1
140:R
135:x
131:R
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
