43:
1853:
2002:
608:
108:
150:
675:, which requires a set of assumptions, including that the law of superposition holds true and that an object cannot be older than the materials of which it is composed. To illustrate the practical applications of superposition in scientific inquiry, sedimentary rock that has not been deformed by more than 90° will exhibit the oldest layers on the bottom, thus enabling
747:
or layers) are created by undercutting previous strata. An example would be that the silt back-fill of an underground drain would form some time after the ground immediately above it. Other examples of non vertical superposition would be modifications to standing structures such as the creation of
683:
to identify the relative ages of any fossils found within the strata, with the remains of the most archaic lifeforms confined to the lowest. These findings can inform the community on the fossil record covering the relevant strata, to determine which species coexisted temporally and which species
764:
Original stratification induced by natural processes can subsequently be disrupted or permutated by a number of factors, including animal interference and vegetation, as well as limestone crystallization.
768:
Stratification behaves in a different manner with surface-formed igneous depositions, such as lava flows and ash falls, and thus superposition may not always successfully apply under certain conditions.
739:
is slightly different as the processes involved in laying down archaeological strata are somewhat different from geological processes. Human-made intrusions and activity in the
743:
need not form chronologically from top to bottom or be deformed from the horizontal as natural strata are by equivalent processes. Some archaeological strata (often termed as
519:
72:
1786:
1482:
1158:
882:
by W. Kenneth
Hamblin, BYU, Provo, UT, Illus. William L. Chesser, Dennis Tasa, (Burgess Publishing Company, Minneapolis, Minnesota), c 1978, pg. 115,
638:
1827:
783:
308:
2031:
929:
524:
671:
will lie at the bottom of the sequence, while newer material stacks upon the surface to form new deposits over time. This is paramount to
1812:
798:
293:
1276:
1779:
1477:
1073:
902:
94:
1113:
1822:
793:
303:
1832:
887:
862:
841:
788:
313:
31:
1523:
1271:
631:
1772:
1266:
732:
712:
1456:
1326:
803:
423:
123:. Since there is no overturning, the rock at the bottom is older than the rock on the top by the law of superposition.
1666:
1646:
1837:
1656:
1628:
1240:
753:
318:
165:
55:
1723:
922:
736:
624:
65:
59:
51:
1611:
897:
Principles of
Archaeological Stratigraphy. 40 figs. 1 pl. 136 pp. London & New York: Academic Press
2026:
1661:
1398:
1245:
1561:
1362:
1108:
1007:
744:
76:
2036:
1163:
740:
1596:
1949:
1906:
1537:
1508:
1623:
1518:
1461:
1436:
1426:
1201:
1098:
1088:
915:
551:
483:
262:
189:
180:
1964:
1748:
1728:
1606:
1591:
1576:
1498:
1297:
1261:
1063:
813:
541:
451:
442:
400:
372:
185:
170:
112:
1977:
1954:
1886:
1556:
1352:
1347:
1191:
1027:
898:
858:
837:
591:
581:
512:
464:
1842:
1753:
1702:
1618:
1566:
1342:
1320:
1186:
1083:
586:
566:
546:
498:
493:
323:
227:
222:
175:
131:
1601:
1939:
1929:
1686:
1651:
1638:
1548:
1406:
1301:
1235:
1196:
1033:
672:
556:
242:
716:
667:. In its plainest form, it states that in undeformed stratigraphic sequences, the oldest
1852:
2006:
1934:
1896:
1876:
1871:
1586:
1384:
1372:
1316:
1311:
1305:
1230:
1153:
1078:
612:
488:
213:
107:
756:
and in this sense superposition in archaeology is more dynamic and multi-dimensional.
2020:
1921:
1881:
1503:
1421:
1416:
1367:
1357:
1118:
997:
778:
701:
689:
390:
362:
1764:
2001:
1987:
1911:
1804:
1581:
1379:
1093:
1068:
1053:
1019:
979:
808:
676:
664:
607:
576:
352:
283:
217:
149:
17:
1281:
1178:
1140:
1123:
1058:
1039:
972:
952:
749:
715:, who used it to produce the first geologic map of Britain. It is the first of
680:
660:
405:
704:, and is present as one of his major theses in the groundbreaking seminal work
1944:
1901:
1891:
1048:
1043:
938:
395:
357:
252:
1863:
1738:
1718:
1451:
1411:
1148:
957:
700:
The law of superposition was first proposed in 1669 by the Danish scientist
685:
571:
447:
367:
1733:
1571:
1215:
1128:
233:
116:
752:
requires a degree of interpretation to correctly identify chronological
1982:
1972:
1795:
1743:
967:
962:
668:
656:
561:
257:
208:
140:
247:
120:
1168:
1102:
984:
1768:
911:
711:
In the
English-language literature, the law was popularized by
1002:
36:
907:
1851:
884:"The Principle of Superposition and Original Horizontality;"
880:
The Earth's
Dynamic Systems: A Textbook in Physical Geology,
855:
The
Chronologers' Quest: The Search for the Age of the Earth
655:
is an axiom that forms one of the bases of the sciences of
890:, "The Principle of Crosscutting Relations;" pg 116-17:
760:
Other limitations to stratification and superposition
27:
Law stating that newer strata stack above older ones
1963:
1920:
1862:
1803:
1711:
1695:
1679:
1637:
1547:
1536:
1491:
1483:
Global
Boundary Stratotype Section and Point (GSSP)
1470:
1444:
1435:
1397:
1335:
1290:
1254:
1223:
1214:
1177:
1139:
1018:
993:
945:
748:new doors and windows in a wall. Superposition in
520:Lists of geological features of the Solar System
64:but its sources remain unclear because it lacks
731:Superposition in archaeology and especially in
1780:
923:
632:
8:
663:, and other fields pertaining to geological
111:Layer upon layer of rocks on north shore of
1787:
1773:
1765:
1544:
1441:
1220:
1015:
930:
916:
908:
639:
625:
126:
95:Learn how and when to remove this message
1828:Principle of cross-cutting relationships
1478:Global Standard Stratigraphic Age (GSSA)
784:Principle of cross-cutting relationships
309:Principle of cross-cutting relationships
106:
825:
138:
1838:Principle of inclusions and components
319:Principle of inclusions and components
7:
525:Geology of solar terrestrial planets
1813:Principle of original horizontality
894:(as in the Steno discussion above).
857:, Cambridge University Press, 2006
799:Principle of original horizontality
719:, which were formally published in
684:existed successively in perhaps an
294:Principle of original horizontality
1277:Adoption of the Gregorian calendar
25:
836:, p. 153, Cengage Learning, 2005
2000:
606:
148:
41:
1823:Principle of lateral continuity
1159:English and British regnal year
794:Principle of lateral continuity
304:Principle of lateral continuity
1833:Principle of faunal succession
789:Principle of faunal succession
314:Principle of faunal succession
32:Superposition (disambiguation)
1:
1272:Old Style and New Style dates
892:"The Principle of Inclusion,"
727:Archaeological considerations
1224:Pre-Julian / Julian
888:The Law of Faunal Succession
832:David Thomas, Robert Kelly,
721:Strata Identified by Fossils
2032:Geological history of Earth
1457:Geological history of Earth
1327:Astronomical year numbering
804:Stratification (archeology)
424:Geological history of Earth
2053:
276:Laws, principles, theories
155:Science of the solid Earth
29:
1996:
1849:
1629:Thermoluminescence dating
1524:Samarium–neodymium dating
1922:Geomorphologic processes
1805:Stratigraphic principles
1798:principles and processes
1343:Chinese sexagenary cycle
706:Dissertationis prodromus
284:Stratigraphic principles
50:This article includes a
1557:Amino acid racemisation
79:more precise citations.
1988:Mass wasting processes
1856:
1562:Archaeomagnetic dating
1074:Era of Caesar (Iberia)
853:Patrick Wyse Jackson,
713:William "Strata" Smith
124:
1864:Petrologic principles
1855:
1462:Geological time units
741:archaeological record
110:
1950:Marine transgression
1818:Law of superposition
1514:Law of superposition
1509:Isotope geochemistry
673:stratigraphic dating
653:law of superposition
299:Law of superposition
30:For other uses, see
1647:Fluorine absorption
1624:Luminescence dating
1519:Luminescence dating
1427:Milankovitch cycles
1267:Proleptic Gregorian
1099:Hindu units of time
443:Branches of geology
382:Landform structures
263:Geologic time scale
2007:Geology portal
1965:Sediment transport
1857:
1749:Terminus post quem
1729:Synchronoptic view
1696:Linguistic methods
1657:Obsidian hydration
1592:Radiometric dating
1577:Incremental dating
1499:Chronostratigraphy
814:Structural geology
613:Geology portal
533:By planet and body
401:Structural Geology
373:Structure of Earth
125:
52:list of references
18:Layer (archeology)
2014:
2013:
1983:Glacial processes
1978:Aeolian processes
1973:Fluvial processes
1955:Marine regression
1762:
1761:
1675:
1674:
1532:
1531:
1393:
1392:
1348:Geologic Calendar
1210:
1209:
649:
648:
513:Planetary geology
465:Geological survey
105:
104:
97:
16:(Redirected from
2044:
2005:
2004:
1789:
1782:
1775:
1766:
1754:ASPRO chronology
1703:Glottochronology
1619:Tephrochronology
1567:Dendrochronology
1545:
1442:
1241:Proleptic Julian
1231:Pre-Julian Roman
1221:
1016:
932:
925:
918:
909:
866:
851:
845:
830:
690:phylogenetically
641:
634:
627:
611:
610:
415:Geologic history
152:
127:
100:
93:
89:
86:
80:
75:this article by
66:inline citations
45:
44:
37:
21:
2052:
2051:
2047:
2046:
2045:
2043:
2042:
2041:
2017:
2016:
2015:
2010:
1999:
1992:
1959:
1940:Tectonic uplift
1930:Plate tectonics
1916:
1858:
1847:
1799:
1793:
1763:
1758:
1707:
1691:
1687:Molecular clock
1680:Genetic methods
1671:
1652:Nitrogen dating
1639:Relative dating
1633:
1602:Potassium–argon
1549:Absolute dating
1539:
1528:
1487:
1466:
1431:
1407:Cosmic Calendar
1399:Astronomic time
1389:
1331:
1286:
1250:
1236:Original Julian
1206:
1173:
1135:
1034:Ab urbe condita
1012:
989:
941:
936:
878:Hamblin, W.K.
875:
873:General sources
870:
869:
852:
848:
831:
827:
822:
775:
762:
729:
698:
677:paleontologists
645:
605:
598:
597:
596:
537:
529:
515:
505:
504:
503:
478:
470:
469:
456:
438:
430:
429:
428:
419:
411:
410:
386:
378:
377:
348:
340:
338:
330:
329:
328:
289:
279:
277:
269:
268:
267:
243:Plate tectonics
238:
203:
195:
157:
101:
90:
84:
81:
70:
56:related reading
46:
42:
35:
28:
23:
22:
15:
12:
11:
5:
2050:
2048:
2040:
2039:
2034:
2029:
2027:Dating methods
2019:
2018:
2012:
2011:
1997:
1994:
1993:
1991:
1990:
1985:
1980:
1975:
1969:
1967:
1961:
1960:
1958:
1957:
1952:
1947:
1942:
1937:
1935:Salt tectonics
1932:
1926:
1924:
1918:
1917:
1915:
1914:
1909:
1904:
1899:
1897:Soil formation
1894:
1889:
1884:
1879:
1874:
1868:
1866:
1860:
1859:
1850:
1848:
1846:
1845:
1840:
1835:
1830:
1825:
1820:
1815:
1809:
1807:
1801:
1800:
1794:
1792:
1791:
1784:
1777:
1769:
1760:
1759:
1757:
1756:
1751:
1746:
1741:
1736:
1731:
1726:
1724:New Chronology
1721:
1715:
1713:
1712:Related topics
1709:
1708:
1706:
1705:
1699:
1697:
1693:
1692:
1690:
1689:
1683:
1681:
1677:
1676:
1673:
1672:
1670:
1669:
1664:
1659:
1654:
1649:
1643:
1641:
1635:
1634:
1632:
1631:
1626:
1621:
1616:
1615:
1614:
1609:
1604:
1599:
1589:
1587:Paleomagnetism
1584:
1579:
1574:
1569:
1564:
1559:
1553:
1551:
1542:
1534:
1533:
1530:
1529:
1527:
1526:
1521:
1516:
1511:
1506:
1501:
1495:
1493:
1489:
1488:
1486:
1485:
1480:
1474:
1472:
1468:
1467:
1465:
1464:
1459:
1454:
1448:
1446:
1439:
1433:
1432:
1430:
1429:
1424:
1419:
1414:
1409:
1403:
1401:
1395:
1394:
1391:
1390:
1388:
1387:
1385:New Earth Time
1382:
1377:
1376:
1375:
1370:
1360:
1355:
1350:
1345:
1339:
1337:
1333:
1332:
1330:
1329:
1324:
1314:
1309:
1294:
1292:
1288:
1287:
1285:
1284:
1279:
1274:
1269:
1264:
1258:
1256:
1252:
1251:
1249:
1248:
1246:Revised Julian
1243:
1238:
1233:
1227:
1225:
1218:
1212:
1211:
1208:
1207:
1205:
1204:
1199:
1194:
1189:
1183:
1181:
1175:
1174:
1172:
1171:
1166:
1164:Lists of kings
1161:
1156:
1154:Canon of Kings
1151:
1145:
1143:
1137:
1136:
1134:
1133:
1132:
1131:
1126:
1121:
1116:
1106:
1096:
1091:
1086:
1081:
1079:Before present
1076:
1071:
1066:
1061:
1056:
1051:
1046:
1037:
1030:
1024:
1022:
1013:
1011:
1010:
1005:
1000:
994:
991:
990:
988:
987:
982:
977:
976:
975:
965:
960:
955:
949:
947:
943:
942:
937:
935:
934:
927:
920:
912:
906:
905:
895:
874:
871:
868:
867:
846:
824:
823:
821:
818:
817:
816:
811:
806:
801:
796:
791:
786:
781:
774:
771:
761:
758:
733:stratification
728:
725:
697:
694:
692:relevant way.
686:evolutionarily
681:paleobotanists
647:
646:
644:
643:
636:
629:
621:
618:
617:
616:
615:
600:
599:
595:
594:
589:
584:
579:
574:
569:
564:
559:
554:
549:
544:
538:
536:
535:
528:
527:
522:
516:
511:
510:
507:
506:
502:
501:
496:
491:
486:
480:
479:
476:
475:
472:
471:
468:
467:
462:
455:
454:
445:
439:
436:
435:
432:
431:
427:
426:
420:
418:
417:
409:
408:
403:
398:
393:
387:
385:
384:
376:
375:
370:
365:
360:
355:
349:
347:
346:
339:
336:
335:
332:
331:
327:
326:
321:
316:
311:
306:
301:
296:
290:
288:
287:
278:
275:
274:
271:
270:
266:
265:
260:
255:
250:
245:
239:
237:
236:
231:
225:
220:
211:
205:
204:
202:Key components
201:
200:
197:
196:
194:
193:
183:
178:
173:
168:
162:
159:
158:
153:
145:
144:
136:
135:
103:
102:
60:external links
49:
47:
40:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2049:
2038:
2035:
2033:
2030:
2028:
2025:
2024:
2022:
2009:
2008:
2003:
1995:
1989:
1986:
1984:
1981:
1979:
1976:
1974:
1971:
1970:
1968:
1966:
1962:
1956:
1953:
1951:
1948:
1946:
1943:
1941:
1938:
1936:
1933:
1931:
1928:
1927:
1925:
1923:
1919:
1913:
1910:
1908:
1905:
1903:
1900:
1898:
1895:
1893:
1890:
1888:
1885:
1883:
1880:
1878:
1875:
1873:
1870:
1869:
1867:
1865:
1861:
1854:
1844:
1843:Walther's law
1841:
1839:
1836:
1834:
1831:
1829:
1826:
1824:
1821:
1819:
1816:
1814:
1811:
1810:
1808:
1806:
1802:
1797:
1790:
1785:
1783:
1778:
1776:
1771:
1770:
1767:
1755:
1752:
1750:
1747:
1745:
1742:
1740:
1737:
1735:
1732:
1730:
1727:
1725:
1722:
1720:
1717:
1716:
1714:
1710:
1704:
1701:
1700:
1698:
1694:
1688:
1685:
1684:
1682:
1678:
1668:
1665:
1663:
1660:
1658:
1655:
1653:
1650:
1648:
1645:
1644:
1642:
1640:
1636:
1630:
1627:
1625:
1622:
1620:
1617:
1613:
1610:
1608:
1605:
1603:
1600:
1598:
1595:
1594:
1593:
1590:
1588:
1585:
1583:
1580:
1578:
1575:
1573:
1570:
1568:
1565:
1563:
1560:
1558:
1555:
1554:
1552:
1550:
1546:
1543:
1541:
1538:Chronological
1535:
1525:
1522:
1520:
1517:
1515:
1512:
1510:
1507:
1505:
1504:Geochronology
1502:
1500:
1497:
1496:
1494:
1490:
1484:
1481:
1479:
1476:
1475:
1473:
1469:
1463:
1460:
1458:
1455:
1453:
1450:
1449:
1447:
1443:
1440:
1438:
1437:Geologic time
1434:
1428:
1425:
1423:
1422:Metonic cycle
1420:
1418:
1417:Galactic year
1415:
1413:
1410:
1408:
1405:
1404:
1402:
1400:
1396:
1386:
1383:
1381:
1378:
1374:
1371:
1369:
1366:
1365:
1364:
1361:
1359:
1358:ISO week date
1356:
1354:
1351:
1349:
1346:
1344:
1341:
1340:
1338:
1334:
1328:
1325:
1322:
1318:
1315:
1313:
1310:
1307:
1303:
1299:
1296:
1295:
1293:
1289:
1283:
1280:
1278:
1275:
1273:
1270:
1268:
1265:
1263:
1260:
1259:
1257:
1253:
1247:
1244:
1242:
1239:
1237:
1234:
1232:
1229:
1228:
1226:
1222:
1219:
1217:
1213:
1203:
1200:
1198:
1195:
1193:
1190:
1188:
1185:
1184:
1182:
1180:
1176:
1170:
1167:
1165:
1162:
1160:
1157:
1155:
1152:
1150:
1147:
1146:
1144:
1142:
1138:
1130:
1127:
1125:
1122:
1120:
1117:
1115:
1112:
1111:
1110:
1107:
1104:
1100:
1097:
1095:
1092:
1090:
1087:
1085:
1082:
1080:
1077:
1075:
1072:
1070:
1067:
1065:
1064:Byzantine era
1062:
1060:
1057:
1055:
1052:
1050:
1047:
1045:
1041:
1038:
1036:
1035:
1031:
1029:
1026:
1025:
1023:
1021:
1020:Calendar eras
1017:
1014:
1009:
1006:
1004:
1001:
999:
996:
995:
992:
986:
983:
981:
978:
974:
971:
970:
969:
966:
964:
961:
959:
956:
954:
951:
950:
948:
944:
940:
933:
928:
926:
921:
919:
914:
913:
910:
904:
903:0-12-326650-5
900:
896:
893:
889:
885:
881:
877:
876:
872:
864:
860:
856:
850:
847:
843:
839:
835:
829:
826:
819:
815:
812:
810:
807:
805:
802:
800:
797:
795:
792:
790:
787:
785:
782:
780:
779:Harris matrix
777:
776:
772:
770:
766:
759:
757:
755:
751:
746:
742:
738:
734:
726:
724:
723:(1816–1819).
722:
718:
714:
709:
707:
703:
702:Nicolas Steno
695:
693:
691:
687:
682:
678:
674:
670:
666:
662:
658:
654:
642:
637:
635:
630:
628:
623:
622:
620:
619:
614:
609:
604:
603:
602:
601:
593:
590:
588:
585:
583:
580:
578:
575:
573:
570:
568:
565:
563:
560:
558:
555:
553:
550:
548:
545:
543:
540:
539:
534:
531:
530:
526:
523:
521:
518:
517:
514:
509:
508:
500:
497:
495:
492:
490:
487:
485:
482:
481:
474:
473:
466:
463:
461:
458:
457:
453:
449:
446:
444:
441:
440:
434:
433:
425:
422:
421:
416:
413:
412:
407:
404:
402:
399:
397:
394:
392:
391:Geomorphology
389:
388:
383:
380:
379:
374:
371:
369:
366:
364:
363:Sedimentology
361:
359:
356:
354:
351:
350:
345:
342:
341:
334:
333:
325:
324:Walther's law
322:
320:
317:
315:
312:
310:
307:
305:
302:
300:
297:
295:
292:
291:
286:
285:
281:
280:
273:
272:
264:
261:
259:
256:
254:
251:
249:
246:
244:
241:
240:
235:
232:
229:
226:
224:
221:
219:
215:
212:
210:
207:
206:
199:
198:
191:
187:
184:
182:
179:
177:
174:
172:
169:
167:
164:
163:
161:
160:
156:
151:
147:
146:
143:
142:
137:
133:
129:
128:
122:
118:
114:
109:
99:
96:
88:
78:
74:
68:
67:
61:
57:
53:
48:
39:
38:
33:
19:
2037:Stratigraphy
1998:
1912:Metamorphism
1817:
1667:Stratigraphy
1612:Uranium–lead
1582:Lichenometry
1513:
1380:Winter count
1363:Mesoamerican
1291:Astronomical
1109:Mesoamerican
1094:Sothic cycle
1069:Seleucid era
1054:Bosporan era
1042: /
1032:
980:Paleontology
891:
883:
879:
854:
849:
833:
828:
809:Stratigraphy
767:
763:
730:
720:
717:Smith's laws
710:
705:
699:
665:stratigraphy
652:
650:
532:
477:Applications
459:
414:
381:
353:Geochemistry
343:
298:
282:
154:
139:
91:
82:
71:Please help
63:
1887:Exfoliation
1607:Radiocarbon
1282:Dual dating
1141:Regnal year
1119:Short Count
1059:Bostran era
1040:Anno Domini
973:Big History
953:Archaeology
865:, pp.127-8.
834:Archaeology
750:archaeology
735:use during
661:archaeology
484:Engineering
406:Volcanology
344:Composition
228:Metamorphic
223:Sedimentary
77:introducing
2021:Categories
1945:Subsidence
1907:Compaction
1902:Diagenesis
1892:Weathering
1202:Vietnamese
1114:Long Count
1049:Anno Mundi
1044:Common Era
946:Key topics
939:Chronology
863:1139457578
842:0155058991
820:References
737:excavation
708:(1669).
396:Glaciology
358:Mineralogy
253:Weathering
85:March 2015
1877:Extrusive
1872:Intrusive
1739:Year zero
1719:Chronicle
1662:Seriation
1597:Lead–lead
1471:Standards
1452:Deep time
1412:Ephemeris
1298:Lunisolar
1262:Gregorian
1255:Gregorian
1216:Calendars
1179:Era names
1149:Anka year
1028:Human Era
958:Astronomy
886:pg. 116:
754:sequences
494:Forensics
448:Geologist
368:Petrology
1882:Volcanic
1796:Geologic
1734:Timeline
1572:Ice core
1445:Concepts
1192:Japanese
1124:Tzolk'in
1089:Egyptian
773:See also
745:contexts
499:Military
437:Research
234:Sediment
209:Minerals
190:Timeline
181:Glossary
176:Category
132:a series
130:Part of
117:Svalbard
1744:Floruit
1492:Methods
1353:Iranian
1321:Islamic
1187:Chinese
998:Periods
968:History
963:Geology
696:History
657:geology
542:Mercury
460:Methods
258:Erosion
218:Igneous
186:History
171:Outline
141:Geology
113:Isfjord
73:improve
1540:dating
1336:Others
1302:Hebrew
1197:Korean
1008:Epochs
901:
861:
840:
669:strata
592:Charon
582:Triton
489:Mining
337:Topics
248:Strata
121:Norway
1373:Aztec
1317:Lunar
1312:Solar
1306:Hindu
1169:Limmu
1129:Haab'
1084:Hijri
587:Pluto
577:Titan
567:Ceres
562:Vesta
547:Venus
452:List)
166:Index
58:, or
1368:Maya
1103:Yuga
1003:Eras
985:Time
899:ISBN
859:ISBN
838:ISBN
679:and
651:The
557:Mars
552:Moon
214:Rock
688:or
2023::
1304:,
659:,
572:Io
134:on
119:,
115:,
62:,
54:,
1788:e
1781:t
1774:v
1323:)
1319:(
1308:)
1300:(
1105:)
1101:(
931:e
924:t
917:v
844:.
640:e
633:t
626:v
450:(
230:)
216:(
192:)
188:(
98:)
92:(
87:)
83:(
69:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.