854:
952:
42:
473:
surface in the normal direction, namely the force to cause the drop to fly off from the surface. The measurement of both adhesion forms can be done with the
Centrifugal Adhesion Balance (CAB). The CAB uses a combination of centrifugal and gravitational forces to obtain any ratio of lateral and normal forces. For example, it can apply a normal force at zero lateral force for the drop to fly off away from the surface in the normal direction or it can induce a lateral force at zero normal force (simulating zero
1016:
809:
842:
988:
925:
870:
901:
577:
1000:
976:
913:
964:
797:
889:
685:
102:
785:
175:
937:
644:
110:
728:
fragment into smaller drops, effectively limiting the largest raindrops to about 6 mm diameter. However, drops up to 10 mm (equivalent in volume to a sphere of radius 4.5 mm) are theoretically stable and could be levitated in a wind tunnel. The largest recorded raindrop was 8.8 mm in diameter, located at the base of a
652:
The classic shape associated with a drop (with a pointy end in its upper side) comes from the observation of a droplet clinging to a surface. The shape of a drop falling through a gas is actually more or less spherical for drops less than 2 mm in diameter. Larger drops tend to be flatter on the
647:
Raindrops are not tear-shaped (â’¶); very small raindrops are almost spherical in shape (â’·), while larger raindrops are flattened at the bottom (â’¸). As raindrops increase in size they encounter progressively more air resistance as they fall, making them begin to become unstable (â’ą); in the case of the
472:
lateral adhesion is a more accurate term) and refers to the force required to slide a drop on the surface, namely the force to detach the drop from its position on the surface only to translate it to another position on the surface. Normal adhesion is the adhesion required to detach a drop from the
727:
Scientists traditionally thought that the variation in the size of raindrops was due to collisions on the way down to the ground. In 2009, French researchers succeeded in showing that the distribution of sizes is due to the drops' interaction with air, which deforms larger drops and causes them to
455:
This relationship is the basis of a convenient method of measuring surface tension, commonly used in the petroleum industry. More sophisticated methods are available to take account of the developing shape of the pendant as the drop grows. These methods are used if the surface tension is unknown.
131:
A simple way to form a drop is to allow liquid to flow slowly from the lower end of a vertical tube of small diameter. The surface tension of the liquid causes the liquid to hang from the tube, forming a pendant. When the drop exceeds a certain size it is no longer stable and detaches itself. The
680:
Using the capillary length we can define microdrops and macrodrops. Microdrops are droplets with radius smaller than the capillary length, where the shape of the droplet is governed by surface tension and they form a more or less spherical cap shape. If a droplet has a radius larger than the
115:
114:
111:
116:
113:
821:
853:
1015:
825:
829:
827:
824:
822:
828:
826:
381:
247:
333:
681:
capillary length, they are known as macrodrops and the gravitational forces will dominate. Macrodrops will be 'flattened' by gravity and the height of the droplet will be reduced.
841:
619:
trapped underwater. These oscillating bubbles are responsible for most liquid sounds, such as running water or splashes, as they actually consist of many drop-liquid collisions.
450:
112:
653:
bottom part due to the pressure of the gas they move through. As a result, as drops get larger, a concave depression forms which leads to the eventual breakup of the drop.
73:. A drop may form when liquid accumulates at the end of a tube or other surface boundary, producing a hanging drop called a pendant drop. Drops may also be formed by the
297:
411:
204:
951:
713:
186:. The force due to surface tension is proportional to the length of the boundary between the liquid and the tube, with the proportionality constant usually denoted
823:
50:
869:
595:
987:
773:. When smaller amounts are necessary (such as paediatrics), microdroppers or paediatric infusion sets are used, in which 1 millilitre = 60 microdrops.
627:
Reducing the surface tension of a body of liquid makes possible to reduce or prevent noise due to droplets falling into it. This would involve adding
724:
Raindrop sizes typically range from 0.5 mm to 4 mm, with size distributions quickly decreasing past diameters larger than 2-2.5 mm.
924:
1203:
1445:
1098:
594:
505:
relative to diameter; thus, a 50 ÎĽm droplet represents a dose in 65 pl and a 500 ÎĽm drop represents a dose in 65 nanolitres.
497:, droplets are usually described by their perceived size (i.e., diameter) whereas the dose (or number of infective particles in the case of
166:– is shown to be a liquid in this way. Pitch in a funnel slowly forms droplets, each droplet taking about 10 years to form and break off.
1362:
900:
1396:
1034:
999:
808:
393:
The limit of this formula, as α goes to 90°, gives the maximum weight of a pendant drop for a liquid with a given surface tension,
1624:
1130:
468:
to a solid can be divided into two categories: lateral adhesion and normal adhesion. Lateral adhesion resembles friction (though
784:
89:. Water vapor will condense into droplets depending on the temperature. The temperature at which droplets form is called the
1513:
1165:
F.K.Hansen; G. Rodsrun (1991). "Surface tension by pendant drop. A fast standard instrument using computer image analysis".
888:
975:
673:, and is directly responsible for the shape a droplet for a specific fluid will take. The capillary length stems from the
586:
521:. But above this size the distance to get to terminal velocity increases sharply. An example is a drop with a diameter of
796:
1660:
1273:
963:
1630:
936:
341:
206:. Since the length of this boundary is the circumference of the tube, the force due to surface tension is given by
35:
912:
31:
1347:
1322:
212:
513:
A droplet with a diameter of 3 mm has a terminal velocity of approximately 8 m/s. Drops smaller than
41:
1617:
302:
1655:
1586:
1058:
729:
1063:
1048:
494:
155:
145:
49:
546:
419:
1558:
1497:
1425:
1334:
1246:
1174:
1026:
554:
1237:; Oguz, Hasan N. (1993). "The impact of drops on liquid surfaces and the underwater noise of rain".
1210:
182:
In the pendant drop test, a drop of liquid is suspended from the end of a tube or by any surface by
1030:
101:
1455:
1234:
1068:
876:
759:
502:
736:
in July 1999. A raindrop of identical size was detected over northern Brazil in
September 1995.
684:
263:
of the drop hanging from the end of the tube can be found by equating the force due to gravity (
1299:"Scientists have finally come up with a solution for the world's most annoying household sound"
1441:
1402:
1392:
1094:
1088:
635:
or a similar substance to water. The reduced surface tension reduces the noise from dripping.
266:
396:
189:
1650:
1566:
1505:
1433:
1342:
1298:
1254:
1182:
674:
662:
538:
1366:
859:
A drop of water hitting a wet metal surface and ejecting more droplets, which become water
691:
1634:
1467:
1022:
733:
670:
648:
largest raindrops, air resistance will be enough to split them into smaller raindrops (â’ş).
183:
125:
82:
1562:
1525:
1501:
1429:
1338:
1258:
1250:
1178:
1141:
847:
A drop of water hitting a metal surface and crown formation due to splashing of droplet
1644:
1186:
616:
159:
498:
74:
70:
1482:
593:
770:
745:
174:
943:
860:
766:
643:
607:
550:
150:
Some substances that appear to be solid, can be shown to instead be extremely
1406:
489:
is a diminutive form of 'drop' – and as a guide is typically used for liquid
154:
liquids, because they form drops and display droplet behavior. In the famous
120:
Surface tension prevents water droplet from being cut by a hydrophobic knife.
1021:
Rain water flux from a canopy. Among the forces that govern drop formation:
632:
469:
151:
141:
90:
1612:
1204:"Numerical model for the fall speed of raindrops in a waterfall simulator"
1627:
1571:
1546:
1437:
1303:
762:
751:
490:
465:
17:
880:
755:
666:
562:
474:
299:) with the component of the surface tension in the vertical direction (
163:
1509:
615:
The major source of sound when a droplet hits a liquid surface is the
1420:
McFarquhar, Greg (2010). "Raindrop Size
Distribution and Evolution".
1323:"A Semi-Empirical Determination of the Shape of Cloud and Rain Drops"
66:
386:
where α is the angle of contact with the tube's front surface, and
683:
542:
173:
108:
100:
86:
78:
48:
40:
1623:(Greatly varying) calculation of water waste from dripping tap:
1053:
1006:
628:
558:
132:
falling liquid is also a drop held together by surface tension.
105:
Drop of water bouncing on a water surface subject to vibrations
517:
in diameter will attain 95% of their terminal velocity within
575:
30:"Droplet" and "raindrop" redirect here. For other uses, see
1391:. Silberzan, Pascal. (2nd ed.). Boston: Artech House.
1348:
10.1175/1520-0469(1971)028<0086:ASEDOT>2.0.CO;2
1131:"Surface Tension Measurements Using the Drop Shape Method"
1316:
1314:
1618:
Liquid Art – Galleries of fine art droplet photography
1481:
Emmanuel
Villermaux, Benjamin Bossa (September 2009).
993:
Fountain water droplets as seen in very short exposure
1483:"Single-drop fragmentation distribution of raindrops"
694:
422:
399:
344:
305:
269:
215:
192:
501:) is a function of their volume. This increases by
707:
444:
405:
375:
327:
291:
241:
198:
1278:The Physics of Bubbles, Antibubbles, and all That
1545:Hobbs, Peter V.; Rangno, Arthur L. (July 2004).
1114:Cutnell, John D.; Kenneth W. Johnson (2006).
1093:. Oxford University Press, USA. p. 196.
376:{\displaystyle \,mg=\pi d\gamma \sin \alpha }
69:, bounded completely or almost completely by
8:
957:Droplets of water refracting a small flower
930:Water droplets forming out of a shower head
790:Blue dye being dropped in a saucer of milk
242:{\displaystyle \,F_{\gamma }=\pi d\gamma }
1570:
1346:
1321:Pruppacher, H. R.; Pitter, R. L. (1971).
835:Rain droplets impacting and dripping down
699:
693:
423:
421:
398:
345:
343:
310:
304:
274:
268:
221:
216:
214:
191:
1198:
1196:
863:and skim across the surface of the water
665:is a length scaling factor that relates
642:
1209:. 2005-10-04. p. 2. Archived from
1079:
780:
328:{\displaystyle F_{\gamma }\sin \alpha }
124:Liquid forms drops because it exhibits
1463:
1453:
740:Standardized droplet sizes in medicine
605:
493:of less than 500 ÎĽm diameter. In
7:
1613:Liquid Sculpture – pictures of drops
390:is the acceleration due to gravity.
136:Viscosity and pitch drop experiments
1327:Journal of the Atmospheric Sciences
1259:10.1146/annurev.fl.25.010193.003045
906:Photo of a raindrop on a fern frond
677:, using the radius of the droplet.
1526:"Why raindrops come in many sizes"
758:and IV infusion sets which have a
754:, this property is used to create
162:– a substance somewhat like solid
25:
1424:. Vol. 191. pp. 49–60.
1297:Thompson, Rachel (25 June 2018).
445:{\displaystyle \,mg=\pi d\gamma }
178:The pendant drop test illustrated
1519:from the original on 2022-10-09.
1239:Annual Review of Fluid Mechanics
1014:
998:
986:
974:
962:
950:
935:
923:
911:
899:
887:
868:
852:
840:
819:
807:
795:
783:
606:Problems playing this file? See
591:
1389:Microfluidics for biotechnology
623:"Dripping tap" noise prevention
1524:Victoria Gill (20 July 2009).
1422:Rainfall: State of the Science
1090:The American Desk Encyclopedia
53:Water drops falling from a tap
1:
1272:Rankin, Ryan C. (June 2005).
1167:Colloid and Interface Science
894:A triple backjet after impact
1551:Geophysical Research Letters
1187:10.1016/0021-9797(91)90296-K
1035:Plateau–Rayleigh instability
617:resonance of excited bubbles
875:A drop of water on a leaf,
1677:
743:
715:against radii of a droplet
139:
36:Raindrops (disambiguation)
29:
802:Impact of a drop of water
587:Drops dripping into water
557:occur on the surfaces of
525:that may achieve this at
32:Droplets (disambiguation)
1620:(archived 19 March 2008)
814:Backjet from drop impact
460:Drop adhesion to a solid
292:{\displaystyle F_{g}=mg}
1547:"Super-large raindrops"
1387:Berthier, Jean (2010).
1059:Splash (fluid dynamics)
981:Water droplets on glass
765:, in such a way that 1
730:cumulus congestus cloud
406:{\displaystyle \gamma }
199:{\displaystyle \gamma }
942:A drop of water on an
716:
709:
649:
580:
446:
407:
377:
329:
293:
256:is the tube diameter.
243:
200:
179:
156:pitch drop experiments
121:
106:
54:
46:
1116:Essentials of Physics
1064:Water droplet erosion
1049:Pitch drop experiment
744:Further information:
710:
708:{\displaystyle L_{c}}
688:The capillary length
687:
646:
579:
537:Due to the different
447:
408:
378:
335:) giving the formula
330:
294:
244:
201:
177:
146:Pitch drop experiment
119:
104:
65:is a small column of
52:
45:Water drops on a leaf
44:
1572:10.1029/2004GL020167
1438:10.1029/2010GM000971
1087:Luck, Steve (1998).
969:A raindrop on a leaf
769:is equivalent to 20
692:
420:
397:
342:
303:
267:
213:
190:
85:of a larger mass of
27:Small unit of liquid
1661:Alcohol measurement
1563:2004GeoRL..3113102H
1502:2009NatPh...5..697V
1430:2010GMS...191...49M
1339:1971JAtS...28...86P
1251:1993AnRFM..25..577P
1235:Prosperetti, Andrea
1179:1991JCIS..141....1H
1138:First Ten Angstroms
1129:Roger P. Woodward.
1118:. Wiley Publishing.
1031:Van der Waals force
732:in the vicinity of
1633:2009-08-13 at the
1363:"Water Drop Shape"
1274:"Bubble Resonance"
1069:Dribbling (teapot)
877:hydrophobic effect
717:
705:
650:
581:
442:
403:
373:
325:
289:
239:
196:
180:
122:
107:
55:
47:
1510:10.1038/NPHYS1340
1447:978-0-87590-481-8
1100:978-0-19-521465-9
1005:Rain droplets on
830:
596:
495:spray application
170:Pendant drop test
117:
16:(Redirected from
1668:
1601:
1600:
1598:
1597:
1583:
1577:
1576:
1574:
1542:
1536:
1533:
1520:
1518:
1487:
1478:
1472:
1471:
1465:
1461:
1459:
1451:
1417:
1411:
1410:
1384:
1378:
1377:
1375:
1374:
1365:. Archived from
1359:
1353:
1352:
1350:
1318:
1309:
1308:
1294:
1288:
1287:
1285:
1284:
1269:
1263:
1262:
1231:
1225:
1224:
1222:
1221:
1215:
1208:
1200:
1191:
1190:
1162:
1156:
1155:
1153:
1152:
1146:
1140:. Archived from
1135:
1126:
1120:
1119:
1111:
1105:
1104:
1084:
1018:
1002:
990:
978:
966:
954:
939:
927:
915:
903:
891:
872:
856:
844:
832:
831:
811:
799:
787:
714:
712:
711:
706:
704:
703:
675:Laplace pressure
663:capillary length
657:Capillary length
598:
597:
578:
539:refractive index
528:
524:
520:
516:
503:a cubic function
451:
449:
448:
443:
412:
410:
409:
404:
382:
380:
379:
374:
334:
332:
331:
326:
315:
314:
298:
296:
295:
290:
279:
278:
248:
246:
245:
240:
226:
225:
205:
203:
202:
197:
118:
21:
1676:
1675:
1671:
1670:
1669:
1667:
1666:
1665:
1641:
1640:
1635:Wayback Machine
1609:
1604:
1595:
1593:
1585:
1584:
1580:
1544:
1543:
1539:
1523:
1516:
1485:
1480:
1479:
1475:
1462:
1452:
1448:
1419:
1418:
1414:
1399:
1386:
1385:
1381:
1372:
1370:
1361:
1360:
1356:
1320:
1319:
1312:
1296:
1295:
1291:
1282:
1280:
1271:
1270:
1266:
1233:
1232:
1228:
1219:
1217:
1213:
1206:
1202:
1201:
1194:
1164:
1163:
1159:
1150:
1148:
1144:
1133:
1128:
1127:
1123:
1113:
1112:
1108:
1101:
1086:
1085:
1081:
1077:
1045:
1038:
1023:surface tension
1019:
1010:
1003:
994:
991:
982:
979:
970:
967:
958:
955:
946:
940:
931:
928:
919:
916:
907:
904:
895:
892:
883:
873:
864:
857:
848:
845:
836:
833:
820:
815:
812:
803:
800:
791:
788:
779:
748:
742:
734:Kwajalein Atoll
722:
695:
690:
689:
671:surface tension
669:, density, and
659:
641:
625:
613:
612:
604:
602:
601:
600:
599:
592:
589:
582:
576:
571:
535:
526:
522:
518:
514:
511:
483:
462:
418:
417:
395:
394:
340:
339:
306:
301:
300:
270:
265:
264:
217:
211:
210:
188:
187:
184:surface tension
172:
148:
140:Main articles:
138:
126:surface tension
109:
99:
97:Surface tension
39:
28:
23:
22:
15:
12:
11:
5:
1674:
1672:
1664:
1663:
1658:
1656:Fluid dynamics
1653:
1643:
1642:
1639:
1638:
1621:
1615:
1608:
1607:External links
1605:
1603:
1602:
1578:
1557:(13): L13102.
1537:
1535:
1534:
1496:(9): 697–702.
1490:Nature Physics
1473:
1464:|journal=
1446:
1412:
1397:
1379:
1354:
1310:
1289:
1264:
1226:
1192:
1157:
1121:
1106:
1099:
1078:
1076:
1073:
1072:
1071:
1066:
1061:
1056:
1051:
1044:
1041:
1040:
1039:
1020:
1013:
1011:
1004:
997:
995:
992:
985:
983:
980:
973:
971:
968:
961:
959:
956:
949:
947:
941:
934:
932:
929:
922:
920:
918:Detaching drop
917:
910:
908:
905:
898:
896:
893:
886:
884:
874:
867:
865:
858:
851:
849:
846:
839:
837:
834:
818:
816:
813:
806:
804:
801:
794:
792:
789:
782:
778:
775:
741:
738:
721:
718:
702:
698:
658:
655:
640:
637:
624:
621:
603:
590:
585:
584:
583:
574:
573:
572:
570:
567:
534:
531:
510:
507:
482:
479:
470:tribologically
461:
458:
453:
452:
441:
438:
435:
432:
429:
426:
402:
384:
383:
372:
369:
366:
363:
360:
357:
354:
351:
348:
324:
321:
318:
313:
309:
288:
285:
282:
277:
273:
250:
249:
238:
235:
232:
229:
224:
220:
195:
171:
168:
137:
134:
98:
95:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1673:
1662:
1659:
1657:
1654:
1652:
1649:
1648:
1646:
1636:
1632:
1628:
1625:
1622:
1619:
1616:
1614:
1611:
1610:
1606:
1592:
1588:
1582:
1579:
1573:
1568:
1564:
1560:
1556:
1552:
1548:
1541:
1538:
1531:
1527:
1522:
1521:
1515:
1511:
1507:
1503:
1499:
1495:
1491:
1484:
1477:
1474:
1469:
1457:
1449:
1443:
1439:
1435:
1431:
1427:
1423:
1416:
1413:
1408:
1404:
1400:
1398:9781596934443
1394:
1390:
1383:
1380:
1369:on 2008-03-02
1368:
1364:
1358:
1355:
1349:
1344:
1340:
1336:
1332:
1328:
1324:
1317:
1315:
1311:
1306:
1305:
1300:
1293:
1290:
1279:
1275:
1268:
1265:
1260:
1256:
1252:
1248:
1244:
1240:
1236:
1230:
1227:
1216:on 2013-07-31
1212:
1205:
1199:
1197:
1193:
1188:
1184:
1180:
1176:
1172:
1168:
1161:
1158:
1147:on 2008-12-17
1143:
1139:
1132:
1125:
1122:
1117:
1110:
1107:
1102:
1096:
1092:
1091:
1083:
1080:
1074:
1070:
1067:
1065:
1062:
1060:
1057:
1055:
1052:
1050:
1047:
1046:
1042:
1036:
1032:
1028:
1024:
1017:
1012:
1008:
1001:
996:
989:
984:
977:
972:
965:
960:
953:
948:
945:
938:
933:
926:
921:
914:
909:
902:
897:
890:
885:
882:
878:
871:
866:
862:
855:
850:
843:
838:
817:
810:
805:
798:
793:
786:
781:
776:
774:
772:
768:
764:
761:
757:
753:
747:
739:
737:
735:
731:
725:
719:
700:
696:
686:
682:
678:
676:
672:
668:
664:
656:
654:
645:
638:
636:
634:
630:
622:
620:
618:
611:
609:
588:
568:
566:
564:
561:, leading to
560:
556:
552:
548:
544:
540:
532:
530:
508:
506:
504:
500:
499:biopesticides
496:
492:
488:
480:
478:
476:
471:
467:
459:
457:
439:
436:
433:
430:
427:
424:
416:
415:
414:
400:
391:
389:
370:
367:
364:
361:
358:
355:
352:
349:
346:
338:
337:
336:
322:
319:
316:
311:
307:
286:
283:
280:
275:
271:
262:
257:
255:
236:
233:
230:
227:
222:
218:
209:
208:
207:
193:
185:
176:
169:
167:
165:
161:
157:
153:
147:
143:
135:
133:
129:
127:
103:
96:
94:
92:
88:
84:
80:
76:
72:
71:free surfaces
68:
64:
60:
51:
43:
37:
33:
19:
1594:. Retrieved
1591:www6.dict.cc
1590:
1587:"Millilitre"
1581:
1554:
1550:
1540:
1529:
1493:
1489:
1476:
1421:
1415:
1388:
1382:
1371:. Retrieved
1367:the original
1357:
1333:(1): 86–94.
1330:
1326:
1302:
1292:
1281:. Retrieved
1277:
1267:
1242:
1238:
1229:
1218:. Retrieved
1211:the original
1170:
1166:
1160:
1149:. Retrieved
1142:the original
1137:
1124:
1115:
1109:
1089:
1082:
760:standardized
749:
726:
723:
679:
660:
651:
626:
614:
536:
512:
486:
484:
463:
454:
392:
387:
385:
260:
258:
253:
251:
181:
149:
130:
123:
75:condensation
62:
58:
56:
1245:: 577–602.
1173:(1): 1–12.
746:Drop (unit)
565:formation.
83:atomization
1645:Categories
1596:2018-08-30
1373:2008-03-08
1283:2006-12-09
1220:2013-06-28
1151:2008-11-05
1075:References
1009:plant leaf
944:Asteraceae
879:, partial
767:millilitre
608:media help
555:reflection
551:refraction
1466:ignored (
1456:cite book
1407:642685865
633:detergent
559:raindrops
491:particles
485:The term
464:The drop
440:γ
434:π
401:γ
371:α
368:
362:γ
356:π
323:α
320:
312:γ
259:The mass
237:γ
231:π
223:γ
194:γ
142:Viscosity
91:dew point
1631:Archived
1530:BBC News
1514:Archived
1304:Mashable
1043:See also
1027:cohesion
861:globules
763:diameter
756:droppers
752:medicine
466:adhesion
18:Raindrop
1651:Liquids
1559:Bibcode
1498:Bibcode
1426:Bibcode
1335:Bibcode
1247:Bibcode
1175:Bibcode
881:wetting
777:Gallery
667:gravity
563:rainbow
487:droplet
481:Droplet
475:gravity
164:bitumen
152:viscous
63:droplet
1444:
1405:
1395:
1097:
533:Optics
252:where
81:or by
67:liquid
1517:(PDF)
1486:(PDF)
1214:(PDF)
1207:(PDF)
1145:(PDF)
1134:(PDF)
771:drops
639:Shape
569:Sound
543:water
527:5.6 m
509:Speed
160:pitch
87:solid
79:vapor
77:of a
1468:help
1442:ISBN
1403:OCLC
1393:ISBN
1095:ISBN
1054:Rain
1007:rose
720:Size
661:The
629:soap
553:and
545:and
523:2 mm
515:1 mm
144:and
59:drop
34:and
1567:doi
1506:doi
1434:doi
1343:doi
1255:doi
1183:doi
1171:141
750:In
547:air
541:of
519:2 m
477:).
365:sin
317:sin
61:or
1647::
1626:,
1589:.
1565:.
1555:31
1553:.
1549:.
1528:.
1512:.
1504:.
1492:.
1488:.
1460::
1458:}}
1454:{{
1440:.
1432:.
1401:.
1341:.
1331:28
1329:.
1325:.
1313:^
1301:.
1276:.
1253:.
1243:25
1241:.
1195:^
1181:.
1169:.
1136:.
1033:,
1029:,
1025:,
631:,
549:,
529:.
413:.
158:,
128:.
93:.
57:A
1637:)
1629:(
1599:.
1575:.
1569::
1561::
1532:.
1508::
1500::
1494:5
1470:)
1450:.
1436::
1428::
1409:.
1376:.
1351:.
1345::
1337::
1307:.
1286:.
1261:.
1257::
1249::
1223:.
1189:.
1185::
1177::
1154:.
1103:.
1037:.
701:c
697:L
610:.
437:d
431:=
428:g
425:m
388:g
359:d
353:=
350:g
347:m
308:F
287:g
284:m
281:=
276:g
272:F
261:m
254:d
234:d
228:=
219:F
38:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
