delivered the opinion of the Court. †
This litigation was instituted in August 1977, pursuant to Art. Ill, §2, cl. 2, of the United States Constitution and 28 U. S. C. § 1251(a)(1) (1976 ed.), by the presentation to this Court of a motion by the State of Georgia for leave to file a complaint against the State of South Carolina. The suit wasthe culmination of a prolonged dispute between the two States over the location of their boundary along the lower reaches of the Savannah River (that is, downstream from the city of Savannah) and at the river’s mouth. The two States also are in disagreement as to their lateral seaward boundary.
We granted leave to Georgia to file its complaint. 434 U. S. 917 (1977). The Honorable Walter E. Hoffman, Senior Judge of the United States District Court for the Eastern District of Virginia, was appointed Special Master with the authority customarily granted in litigation of this kind. 434 U. S. 1057 (1978). South Carolina, in due course, filed its answer and counterclaims.
*380The Special Master submitted his First Report (1 Rep.) to this Court eight years later on March 20, 1986. That report dealt with the issues other than the lateral seaward boundary. The Master and the parties moved that we defer action on the First Report until he had ruled on the seaward boundary. We complied with that request. The Special Master’s Second and Final Report (2 Rep.) was filed April 24, 1989. The Court fixed the time for the filing of exceptions. See 490 U. S. 1033 (1989). Each State filed exceptions and each responded to the exceptions of the other. Briefs were submitted and oral argument followed.
I
Background
On June 9, 1732, nearly 260 years ago, King George II, describing himself as King of Great Britain, France, and Ireland, issued letters patent constituting the Charter of the Colony of Georgia. These letters described the boundary between that colony and the existing Colony of South Carolina as “the most northern part of a stream or river there, commonly called the Savannah.” See F. Van Zandt, Boundaries of the United States and the Several States (Geological Survey Professional Paper 909) 100 (1976).
The precise location of segments of the boundary, however, proved to be a matter of continuing dispute between South Carolina and Georgia. Much of the controversy originally concerned navigation rights on the river. Shortly after the United States emerged as a Nation, commissioners appointed by each of the States met at Beaufort, S. C., and produced a Convention known as the Treaty of Beaufort of April 28, 1787 (hereinafter Treaty). See Van Zandt, supra, at 99; see also Georgia v. South Carolina, 257 U. S. 516, 518 (1922). The Treaty stated that the boundary was the “most northern branch or stream of the river Savannah ... , reserving all the islands in the said rive[r] Savannah ... to *381Georgia 1 The Treaty was ratified in due course by the legislature of each State and by the Continental Congress. See 33 Journals of the Continental Congress 467 (1936).2
*382Past Litigation
The very existence of the present suit, of course, demonstrates that the Treaty of Beaufort did not resolve all river-*383boundary questions between South Carolina and Georgia. Indeed, this is not the first, but the third, occasion that some issue concerning that boundary has come before this Court.
The first case is South Carolina v. Georgia, 93 U. S. 4 (1876). South Carolina filed a bill in equity for an injunction restraining Georgia and certain federal officials from “obstructing or interrupting” navigation on the Savannah River. This Court dismissed the bill. It ruled that the 1787 Treaty had no effect upon the power of Congress to regulate commerce among the several States. Congress’ power over the river was the same as it possessed over other navigable waters. Thus, Congress could close one of the several channels in the river if, in its judgment, navigation thereby would be improved.
The second case is Georgia v. South Carolina, 257 U. S. 516, decided in 1922. There, the Treaty of Beaufort was central to the controversy. The Court held, among other things, that (1) where there is no island in the Savannah River, the boundary is midway between the banks when the water is at ordinary stage, (2) where an island is present, the boundary is midway between the island bank and the South Carolina shore, with the water at ordinary stage, (3) where a navigable or nonnavigable river is the boundary between the two States, and the navigable channel is not involved, then, in the absence of contrary agreement, each State takes to the middle of the stream, and (4) the location of the boundary under the Treaty was unaffected by the thalweg doctrine because of the Treaty’s provision that each State shall have *384equal rights of navigation. The ensuing decree is set forth at 259 U. S. 572 (1922).3
It is to be noted that this Court did not discuss the problem of emerging islands, that navigability was not itself a factor in determining the boundary, and that no map or chart illuminated the Court’s reported opinion.
Neither of these cases bears directly upon the specific issues presently before us. The 1876 case, however, illustrates the type of boundary problem the Savannah River is capable of producing, and the 1922 case reveals generally this Court’s approach to the Treaty of Beaufort.
The decision in United States v. 450 Acres of Land, More or Less in Chatham County, 220 F. 2d 353 (CA5), cert. denied, 350 U. S. 826 (1955), must be mentioned. This was a condemnation proceeding instituted by the Federal Government in the United States District Court for the Southern District of Georgia to acquire an easement to enter upon “Barnwell Island,” one of the islands of a group discussed in Part III hereof, for the deposit of spoil excavated from Savannah Harbor. The complaint was served upon E. B. Pinckney, who claimed ownership of the island, and upon certain Beaufort County,,S. C., officials. Only Pinckney made an appearance. He moved to dismiss the complaint for lack of jurisdiction on the ground that the land was in South Carolina. The motion was granted, and the Government’s complaint was dismissed. Georgia then was allowed to intervene. The Court of Appeals for the Fifth Circuit reversed. It observed:
*385“The boundary line between Georgia and South Carolina is not in dispute as between these sovereigns. . . .
“There is, there can be, no doubt that the land here involved is in the State of Georgia. Article I of the Beaufort Convention specifically reserved to Georgia all the islands in the Savannah River and the Supreme Court by its decision and decree in State of Georgia v. South Carolina, 257 U. S. 516 . . . confirmed that reservation.” 220 F. 2d, at 356.
Although South Carolina did not participate in that case, it sought leave to file an original-jurisdiction complaint in this Court to confirm its claimed sovereignty over the Barnwell Islands. Leave to file was denied. South Carolina v. Georgia, 350 U. S. 812 (1955). This took place while Pinckney’s petition for certiorari, noted above, in the Fifth Circuit case was pending in this Court. Later, another application by South Carolina for leave to file also was denied. South Carolina v. Georgia, 352 U. S. 1030 (1957).
II
The Special Master’s Reports and the Exceptions
The Special Master’s two reports concern, as he listed them, (1) a small unnamed island upstream, or west, of Pennyworth Island, (2) an unnamed island east of Pennyworth, referred to as “Tidegate,” (3) the Barnwell Islands, that is, Rabbit Island, Hog Island, Long Island, and Barnwell No. 3, (4) Southeastern Denwill, (5) Jones Island, (6) Horseshoe Shoal and Oyster Bed Island, (7) the mouth of the river, and (8) the lateral seaward boundary.
The Special Master himself, “[f Jor the convenience of the Court and counsel,” described the “major legal issues” covered by his First Report in this way:
“1. Did the Treaty of 1787, in reserving all islands in the Savannah River to Georgia, intend to include not only the then existing islands, but also all islands thereafter emerging by natural processes on the South Caro*386lina side of the river? If the answer is in the affirmative, how can the 1922 decision of this Court be reconciled?
“2. Is the Special Master correct in determining that the right-angle principle should be invoked by the de-marcator in drawing the boundary line around islands on the South Carolina side of the ‘thread’ of the Savannah River, because of the ‘special circumstances’ existing by reason of the preclusive effect of the 1922 Supreme Court decision as it interpreted the Treaty of 1787?
“3. Has the Special Master correctly ruled that Rabbit Island accreted to the State of South Carolina, and whether the ‘Island Rule’ is applicable?
“4. Has the Special Master correctly decided that Hog Island and Long Island have been acquired by the State of South Carolina under the doctrine of prescription and acquiescence? The Special Master notes that, even though Hog Island (in existence in 1787) was acquired by South Carolina under the doctrine of prescription and acquiescence, there remained at that time a creek separating Hog Island from the mainland and it was not until the spoilage had been dumped by avulsive processes that Hog Island became a part of the South Carolina mainland.
“5. Has the Special Master correctly ruled that the area known as Southeastern Denwill, if it presently encroaches on the southern side of the mid-point of the Savannah River as it existed in 1787, now belongs to Georgia?
“6. Has the Special Master correctly ruled that Jones Island, at all pertinent times, was in the State of South Carolina?
“7. Did the Special Master err in diverting from the doctrine of medium filum acquae as established by the 1922 decision of this Court, in proceeding eastwardly *387after leaving the southern tip of Turtle Island?” 1 Rep. 112-113.
Georgia’s exceptions to both reports are directed to the Special Master’s recommendations concerning (a) the Barn-well Islands (other than Rabbit Island, as to which Georgia does not now except), (b) Oyster Bed Island and the mouth of the Savannah River, (c) the “use of a right-angle line to connect the boundary in stream around an island in the Savannah River with the boundary in the mainstream of the river,” see Ga. Exceptions ii, (d) the Master’s ruling that islands of natural formation emerging after the Treaty of Beaufort are not in Georgia if they emerged “on the South Carolina side of the river,” ibid., and (e) the Master’s use of the navigation channel, rather than the geographic middle of the “mouth” of the Savannah River, as the starting point for his delineation of the lateral seaward boundary. Georgia’s exceptions, so far as the First Report is concerned, thus are directed only to the first, second, fourth, and seventh of the issues listed by the Master. Some of the claims Georgia pressed before the Master, e. g., the one relating to Jones Island, are not presented for review here; we treat those claims as now abandoned.
South Carolina takes exception to the Master’s recommendations concerning (a) the lateral seaward boundary, (b) “two narrow strips of land well downstream from the City of Savannah,” (c) the “downstream area known as Horseshoe Shoal,” and (d) “the line which resulted from the placement of Horseshoe Shoal in Georgia.” See S. C. Exceptions 2. So far as the First Report is concerned, these exceptions thus are directed only to the first, fifth, and seventh of the issues listed by the Master.
Before we consider these several exceptions specifically, we note that Georgia’s reaction to the First Report is straightforward. It asserts that under the 1787 Treaty all islands in the Savannah River are in Georgia; that, despite this treaty provision, the Master would place certain islands *388in South Carolina; and that his First Report “reflects his fundamental dissatisfaction with the boundary line as established by the framers of the Treaty of Beaufort and as construed by this Court in 1922.” Ga. Exceptions 7. This has led the Master “to diverge, at virtually every opportunity, from the boundary which has been established since 1787, in order to place his recommended boundary in or near the mainstream or the navigation channel of the river.” Id., at 8. South Carolina, of course, disavows this characterization of the Special Master’s decision.
We turn to the exceptions in an order we select.
III
The Barnwell Islands
These islands were four in number and were named by the Barnwell family, in downstream order, Rabbit Island, Hog Island (referred to as “Barnwell Island” on some older United States Coast Survey maps), Long Island (referred to as Barnwell Island No. 2 on some maps), and Barnwell Island No. 3 (actually the fourth island and not present when the family named the others). As has been noted, Georgia takes no exception to the Special Master’s recommendation that Rabbit Island, although in the Savannah River in 1787, now be adjudged to be in South Carolina. This leaves us with Hog Island, Long Island, and Barnwell Island No. 3.
Georgia states that the Barnwell Islands remained as islands in the Savannah River and discernible as such well into the 20th century, when, because of the activity of the United States Army Corps of Engineers, they became affixed to the South Carolina shore. Ga. Exceptions 13. South Carolina opines that the Barnwell Islands area is the most valuable land in the present dispute. It consists of at least 450 acres of high ground only a short distance downstream from the city of Savannah. It is “clearly capable of future economic development.” Response for South Carolina 1-2.
*389Georgia’s argument is essentially this: Long acquiescence in the practical location of an interstate boundary, and possession in accordance therewith, often has been used as an aid in resolving boundary disputes. See, e. g., Rhode Island v. Massachusetts, 4 How. 591, 638-639 (1846); Louisiana v. Mississippi, 202 U. S. 1, 53 (1906). Possession and dominion are essential elements of a claim of sovereignty by prescription and acquiescence. Virginia v. Tennessee, 148 U. S. 503, 524 (1893). The duration of any purported dominion by South Carolina was judicially terminated by the above-cited Fifth Circuit decision in 1955. In line with that decision, and at all times since, Georgia has exercised dominion, sovereignty, and ownership of the Barnwell Islands. The Corps of Engineers has possessed and occupied Barnwell pursuant to a deed granted by Georgia for a spoilage easement. The doctrine of prescription and acquiescence may not be used aggressively to acquire territory; it may be used only to confirm the current status. In any event, proof adduced by South Carolina falls short of what is required to change the boundary solemnly accepted by the two States in 1787.
Georgia further maintains that the State asserting the claim must make a showing of acquiescence by the neighboring State. New Jersey v. Delaware, 291 U. S. 361, 376, 377 (1934). Inaction, in and of itself, is of no great importance; what is legally significant is silence in the face of circumstances that warrant a response. Here, it is said, there is little evidence either of prescription by South Carolina or of actual or constructive notice to Georgia sufficient to imply acquiescence by Georgia. Except for the activity by the Corps of Engineers, the islands received scant attention from anyone except members of the Barnwell family. And, apart from some rice planting, there is little evidence of activity on the islands other than illegal whiskey production and the rais*390ing of hogs fed with the mash. The fact that moonshining could be carried on successfully shows how little attention was paid to the islands by Georgia authorities and the public generally. Except for the placement of a battery on the islands by Confederate forces during the War Between the States, there never was any resident on the islands and no schools, roads, or other public improvements.
Georgia acknowledges two grants by South Carolina, one in 1795 and the other in 1813. The grants and accompanying plats, however, identify the property only as “islands.” These, says Georgia, were invalid because the 1787 Treaty reserved all islands in the river to Georgia. Thus, South Carolina cannot build its case on those grants. To be sure, there were 1868 deeds describing the property as in South Carolina, but these were intrafamily conveyances by the Barnwells and, in any event, provided no notice to anyone until they were recorded in 1930. There also were a marriage settlement in 1832 and a mortgage in 1871 but these, too, were intrafamily transactions. Anyway, their descriptions were insufficient to constitute notice of claim by South Carolina. The same is true of a deed in 1896 whereby the Barnwell brothers conveyed their interests in the islands and other family property to their sisters. A sheriff’s deed in 1940 was insufficient to convey title, because of inadequate description of the property, and did not constitute notice to Georgia of any South Carolina claim of jurisdiction. The same is true of a 1942 deed from the Forfeited Land Commission of South Carolina to E. B. Pinckney.
There were taxes paid to Beaufort County, S. C., by the Barnwell family and later by Pinckney, but the tax records contain no information identifying the property, and even after 1930 there was no correlation between the acreage reported for taxes and the acreage conveyed by the deeds. The claim of South Carolina prescription and Georgia ac*391quiescence is contradicted “by considerable evidence” that Georgia and United States officials understood the islands to be in Georgia. Ga. Exceptions 34. There was a Georgia grant in 1760. In 1825, 1830, and 1831, taxes were paid to Chatham County, Ga. Many maps show the Barnwell Islands (other than Rabbit) to be on the Georgia side of the boundary line between the two States.
Thus, the short duration of actual possession, the limited South Carolina official Acts, and the paucity of published or recorded documents referring to the islands as in South Carolina fall far short, Georgia claims, of establishing the open and continuous possession required to confirm a boundary by prescription. This is especially so since the islands remained as islands in the river until well into the 20th century, and since South Carolina continued to recognize officially the Treaty of Beaufort with its provision that all islands in the river are in Georgia. This is not a situation where Georgia can be held to have acquiesced.
South Carolina, in its turn, first takes the position that the 1955 Fifth Circuit case has no effect whatsoever, directly or indirectly, on the present litigation. South Carolina was not a party in that case, and the case did not fix the boundary between the States. It further argues that Georgia asserted no act of dominion or control over the Barnwell Islands from 1787 until the 1950’s, and acquiesced in South Carolina’s jurisdiction through long inaction in the face of the latter’s continuing and obvious exercise of dominion since 1795.
With all this before us, and recognizing that each side advances some facts favorable to its position, we decide this issue in favor of South Carolina. We agree that the 1955 case in the Fifth Circuit cannot be regarded as fixing the boundary between the States. Although some South Caro-linians were served with process, they were local officials and a person whose name appeared in the chain of title. South *392Carolina itself was never served and made no appearance. See Martin v. Wilks, 490 U. S. 755, 761-762 (1989). In any event, this Court, not a Court of Appeals, is the place where an interstate boundary dispute usually is to be resolved. See Durfee v. Duke, 375 U. S. 106, 115-116 (1963). The judgment in the 1955 case, therefore, does not control the issue of South Carolina’s sovereignty. Nor do the incidental effects of that case transform the judgment into one that binds South Carolina. This conclusion needs no additional fortification, but, if it did, we would note that South Carolina twice, in 1955 and again in 1957, asked this Court to have the Barnwell area boundary question resolved. Georgia opposed those applications, and leave to file was denied each time by this Court. South Carolina attempted to get the issue here, but until the present litigation was instituted and allowed to proceed, this aspect of the boundary issue was not before this Court.4
We need not here repeat in detail the extensive record evidence and the tax and conveyancing documents relied upon by the Special Master in reaching his conclusion. It suffices to say that the entire area in the late 18th and early 19th centuries was low marshy ground. The islands were separated from Georgia by the wide and deep waters of the Savannah River, but were separated from South Carolina only by streams so shallow that they were described as “sometimes dry.” Record, S. C. Exh. B-8. See Handly’s Lessee v. Anthony, 5 Wheat. 374, 381 (1820). The South Carolina grant in 1813, the almost-uniform taxation of the property, the South Carolina seizure and subsequent sale for unpaid taxes, policing and prosecutorial activities by South Carolina au*393thorities, patrolling by South Carolina wildlife officers, and other factors, all support the Special Master’s conclusion that, in any event, South Carolina established sovereignty by prescription and acquiescence.
Georgia seeks to avoid the effect of this evidence on the ground that it had no reasonable notice of South Carolina’s actions and therefore cannot be said to have acquiesced in them. But inaction alone may constitute acquiescence when it continues for a sufficiently long period. See Rhode Island v. Massachusetts, 15 Pet. 233, 274 (1841); Vermont v. New Hampshire, 289 U. S. 593, 616 (1933). And there is more than mere inaction on the part of Georgia. The record contains substantial evidence of events that put Georgia on notice of South Carolina’s exercise of sovereignty. Parts of the islands were cultivated, as the Master found, for more than 30 years prior to 1880. This was readily discernible, for rice cultivation requires dikes, and the presence of dikes on the islands appeared on maps of the area as early as 1855. Ga. Exh. 156, App. B to 1 Rep. Georgia was chargeable with knowledge that the Treaty of Beaufort placed all the Savannah River islands in Georgia. Yet Georgia authorities could have discovered there was no record of taxation or other sovereign action over these lands by Georgia except, possibly, for three isolated instances in the early part of the 19th century. Some documents recorded in Georgia, because they also involved Georgia property, describe the islands as in South Carolina. There is evidence, too, that Savannah residents were aware of cultivation on the islands. “It is conclusively settled in England, that open and notorious adverse possession is evidence of notice; not of the adverse holding only, but of the title under which the possession is held .... And in the United States we deem it to be equally settled.” Landes v. Brant, 10 How. 348, 375 (1851).
South Carolina must prevail as to the Barnwell Islands issue, and we overrule Georgia’s exception with respect thereto.
*394<5
Islands Emerging After the Treaty of Beaufort
The unnamed island west of Pennyworth, the island east of Pennyworth called “Tidegate,” and Oyster Bed Island all emerged after the Treaty of Beaufort was signed in 1787.5 Georgia claims these islands and argues that, by the terms of the Treaty, the boundary in the vicinity of each island runs between that island and the South Carolina shore. The first Article of the Treaty, see n. 1, supra, provides:
“The most northern branch or stream of the river Savannah from the sea or mouth of such stream to the fork or confluence of the rivers now called Tugoloo and Keowee, . . . reserving all the islands in the said rivers Savannah and Tugoloo to Georgia . . . shall forever hereafter form the separation limit and boundary between the States of South Carolina and Georgia.”
This Court considered this provision in 1922 in Georgia v. South Carolina, 257 U. S. 516. Both States agreed that the presence of an island on the South Carolina side of the river altered the boundary so as to bring the island within the jurisdiction of Georgia. In its decision on the merits, the Court resolved two contested issues relevant here.
First it held, ruling in Georgia’s favor, that “where, in any of the boundary rivers here involved, there are no islands the location of the boundary line between the two States is the thread of the river — the middle line of the stream — regardless of the channel of navigation . . . .” Id., at 521. It rejected South Carolina’s alternative position, which would have placed the boundary at the low water mark on the Georgia side of the river: “The express reservation of the islands to Georgia and the placing of the boundary line in the most northerly branch of the Savannah and then of the Tugaloo *395river up to the ‘northern boundary of South Carolina,’ makes it clear that where there are islands in the river the line must be between them and the South Carolina shore, for otherwise the Georgia islands would be within the State of South Carolina.” Id., at 520-521. Because the “northern branch or stream” clause by definition would bring the boundary north of the low water mark on the Georgia side, the Court thought it unlikely that the parties intended the low water mark to be the benchmark where no islands were present. The more logical reading of the Treaty was that each State would take to “the middle of the stream.” Id., at 521.
Second, the Court held that, where there was an island in the river, the boundary would be midway between the island and the South Carolina shore. This conclusion followed from the determination that the “northern branch or stream” of the river, where an island was present in the northern half of the river, would be the “branch or stream” that ran between the island and the northern shore, and from the Court’s first holding that the midpoint of the relevant body of water was the appropriate place to draw the boundary.
Two principles established by the 1922 decision are pertinent here. First, although it is by no means self-evident on the face of the Treaty that the “northern branch or stream” refers to the “stream” that each island — however small and however close to the northern shore — creates between itself and the shore to the north of it, that was the construction of the Treaty agreed upon by the parties in 1922 and adopted by this Court. Apparently it was thought that a contrary rule, whereby the “northern branch or stream” referred only to a “branch or stream” that made a major departure from the main body of the river, would create an unmanageable boundary, because then the Treaty’s additional reservation of the islands to Georgia would create pockets of Georgia territory within South Carolina wherever islands existed on the South Carolina side of the “northern branch or stream” defined in this larger sense. Second, under the principle that *396each island in the river created a new “northern branch or stream,” each island was not only reserved to Georgia under the reservation clause of Article I, but also formed a point of reference, by which the boundary would be drawn.
The Court, in its 1922 decision, did not expressly determine the treatment to be given islands that emerged after the Treaty of Beaufort was signed, so that decision is not controlling on this is she. The Special Master found, and South Carolina agrees, that the better reading of the Treaty in light of the 1922 decision is that the clause “reserving all islands ... to Georgia” refers only to islands in existence in 1787 and that the “most northern branch or stream,” as applied to a “branch or stream” going to the north of an island, similarly refers only to islands in existence when the Treaty was signed. The Treaty’s establishment of the boundary “forever hereafter” would thus be unaffected by after-emerging islands. Georgia argues that the provision of Article I “reserving all islands ... to Georgia” includes such after-emerging islands and that, accordingly, the reference in the Treaty to the “most northern branch or stream of the river Savannah” means the stream flowing to the north of any island currently in the river. We think South Carolina and the Special Master have the better argument.
Georgia’s solution, whereby each emerging island not only is newly “reserv[ed] ... to Georgia” but also creates a new “northern branch or stream” by which the boundary between the States must be drawn, would create a regime of continually shifting jurisdiction. Even the smallest emerging island, no matter how near the South Carolina shore, would cause the entire boundary between the States to shift northward, depriving South Carolina not only of the land that constitutes the island but also any riverbed between the island and the center line that previously formed the boundary. We doubt that the parties, in drafting the Treaty, meant to create a boundary that shifted so radically each time a new island emerged in the river. To the contrary, Article I of the *397Treaty purports to fix the boundary “forever hereafter,” a goal that would be frustrated were the boundary to jump northward each time a new island appeared on the South Carolina side of the river. A construction of the Treaty that avoids sudden changes in the boundary would be more consistent with this language, and also comports with the principles of simplicity and finality that animated the Court’s reading of the Treaty in 1922, and with the respect for settled expectations that generally attends the drawing of interstate boundaries. Cf. Virginia v. Tennessee, 148 U. S. 503, 522-525 (1893).
We recognize, of course, that the normal rules relating to accretion and erosion may cause the boundary line between the States to shift over time, so that the line will not necessarily be fixed as of any particular point. But it is one thing to say that the parties meant that gradual shifts in the path of the river would shift the boundary gradually, to the extent of the accretion; this rule is consistent with settled expectations and with the parties’ interest in maintaining their riparian rights. See Nebraska v. Iowa, 143 U. S. 359 (1892). It is quite another thing to infer that the parties meant that each new island, however formed, would alter the boundary line to a degree that could be dramatically out of proportion to the physical change brought about by the formation of the island itself.
Finally, Georgia points to the statement in the 1922 decree that all islands “formed by nature” in the Chattooga River, like the islands in the Savannah and the Tugaloo, were reserved by the Treaty to Georgia. Georgia v. South Carolina, 259 U. S., at 572. This reference, Georgia contends, necessarily implies that the reservation clause in the Treaty includes after-emerging islands, since man-made islands did not exist in the river in 1787. There is no indication, however, that the Court knew of this fact in 1922. No issue of after-emerging islands was even before the Court, and the decree simply described the river as it then was.
*398In light of the foregoing, we agree with the Special Master that islands that emerged after 1787 do not affect the boundary line between the two States. Georgia’s exception with respect to that issue is overruled.
V
Oyster Bed Island and the Mouth of the River
Oyster Bed Island, which was not in existence in 1787 and which emerged in the 1870’s or 1880’s, is one of the most easterly or downstream islands in the Savannah River. It lies north of Cockspur Island and southeast of Turtle Island. Both Turtle Island and its westerly neighbor, Jones Island, are now conceded by the parties to be in South Carolina. Georgia accepts the Special Master’s location of the boundary between the two States immediately upstream and west of Oyster Bed as midway between Jones Island and certain Georgia islands in the river. Ga. Exceptions 38-39.
Georgia complains, however, that west of Oyster Bed, opposite the southern point of Turtle Island, the Special Master’s recommended boundary departs from the middle of the stream and, going east, makes an “abrupt jog [to the southeast] to reach the navigation channel of the river.” Id., at 38. The result is that Oyster Bed Island is placed in South Carolina, a consequence, Georgia says, that is contrary to this Court’s 1922 ruling in Georgia v. South Carolina, supra.
Georgia fortifies this argument by asserting that in the 1870’s a major navigation channel of the river flowed north of Oyster Bed, but that the Corps of Engineers blocked this northern channel by a training wall and later by deposit of hydraulic fill in order to force the water into the channel south of Oyster Bed. It stresses that only Georgia has exercised dominion and control over Oyster Bed and, indeed, ceded it to the United States in 1820.
It seems to us that this portion of the controversy between the two States centers on the determination of the “mouth” of *399the Savannah River and encounters no inconsistency with what this Court said in Georgia v. South Carolina. The Savannah River’s “mouth” was not defined in the Treaty of Beaufort. Georgia argues that the mouth, as referred to in the Treaty, must be located in the vicinity of Tybee Island, rather than somewhat upstream. Tybee lies south and east of Cockspur. We accept that submission and regard Tybee as forming the south side of the river’s mouth. Usually, there are two opposing “headlands” marking and constituting the mouth of a river. See Knight v. United States Land Assn., 142 U. S. 161, 207 (1891) (Field, J., concurring). This is the “headland-to-headland” principle used in defining the limits of bays and rivers. 2 A. Shalowitz, Shore and Sea Boundaries § 141, p. 367 (1964). It is not always that simple, however. Sometimes the mouth of a river is difficult to delineate. See S. Jones, Boundary-Making: A Handbook 130 (1945). Because of the absence of a reasonably close headland to the north, Georgia is driven to argue that the boundary at the mouth of the Savannah River must be the geographical middle between Tybee and the closest points of land in South Carolina, that is, Daufuskie Island, lying north and northeastward of Turtle Island, and Hilton Head Island, almost six miles north of Tybee.
We conclude that this is not a realistic determination of the Savannah River’s mouth, and we agree with the Special Master in rejecting the argument.
The difficulty lies in the fact that Tybee Island, the most seaward point of land on the southern side of the river, has no counterpart of high land on the northern side. The geographical feature taking the place of the customarily present opposing headland is, instead, a shoal, long recognized as confining the river. It is true, of course, that the Corps of Engineers affected the flow by its training wall and hydraulic fill. But the shoal which directed that flow has been recognized for many years. Furthermore, Hilton Head Island and *400Daufuskie Island are so far distant that it is impossible to say that they even touch the Savannah River.
Given this somewhat uncommon type of river mouth, the Special Master’s conclusion that the northern side of the Savannah’s mouth is the underwater shoal is not unreasonable. To accept Georgia’s proposition here would result in having Georgia waters lie directly seaward of South Carolina’s coast and waters.
Georgia’s exception with respect to Oyster Bed Island and the mouth of the Savannah River is overruled.
>
The “Right-Angle” Principle
This Court in its 1922 decision in Georgia v. South Carolina ruled that (1) at any point where there is no island in the Savannah River, the boundary “is on the water midway between the main banks of the river when the water is at ordinary stage,” and (2) where there is an island the boundary “is midway between the island bank and the South Carolina shore when the water is at ordinary stage.” 257 U. S., at 523. This seemingly simple and routine resolution, however, results in a problem, not decided in the 1922 case, when the midline of the stream encounters an island and must move northward to qualify as the line midway between the island bank and the South Carolina shore. Where and how does this boundary movement to the north take place? Is it when the midline touches the island, if it does touch it at all, and does it then move at right angles until it reaches a point midway between the island bank and the South Carolina shore? Does it then proceed accordingly until the island is bypassed and the midline of the stream is to be met and followed, and is a right angle to be applied there as well?
A line midway between the banks of a river, known as the medium filum acquae, Shalowitz, supra, at 374, is easily es*401tablished, for every point of the midline is equidistant from the nearest points on the opposite shores. See New Hampshire v. Maine, 426 U. S. 363, 371 (1976) (White, J., dissenting). But, as noted, the ease of ascertainment disappears when an island and the Treaty of Beaufort are encountered. Such is the case here, particularly with respect to the Special Master’s treatment of the line around Pennyworth Island north of the city of Savannah.
This issue clearly was not determined, and perhaps was not even contemplated, by the framers of the Treaty. What the Special Master did in the absence of authority — and we have found none — was to use the line midway between an island and the South Carolina shore (as the parties agree is proper) until the island ended and ceased to lie opposite the shore. There the boundary was to revert to the middle of the river. The Master then used a right-angle line connecting the island-to-bank center line with the bank-to-bank center line by the shortest distance. South Carolina urges that this is the most reasonable approach to this unique problem and that the Master’s recommended device should be adopted.
Georgia’s position, also apparently unsupported by deci-sional authority, but see S. Boggs, International Boundaries: A Study of Boundary Functions and Problems 183 (1966), is that the use of the right angle is simply wrong. Instead, Georgia argues, that, with an island’s presence, the boundary is to be marked by the use of a point which is “tri-equidistant” from the South Carolina shore, the island shore, and the Georgia shore. The boundary then would pass through this point and otherwise be equidistant from the South Carolina shore and the Georgia shore, or island, as the case may be. See Ga. Exceptions 50-51.
We think that Georgia has the better of this argument. Its submission, it seems to us, is sensible, is less artificial than other lines, is fair to both States, and is generally in line with what was said in Georgia v. South Carolina.
*402Georgia’s exception to the right-angle principle used by the Special Master is therefore sustained, and Georgia’s approach, not that of the right angle, is to be utilized wherever this fact situation is encountered in the stretch of the Savannah River under consideration.
VII
Southeastern Denwill and Horseshoe Shoal
Elba Island is downstream from the city of Savannah and upstream from Jones and Oyster Bed Islands. Denwill is a plantation on the South Carolina side of the river; it is opposite Elba but extends eastward beyond that island. Horseshoe Shoal is slightly downstream from there. See App. D of 2 Rep.
Prior to the performance of work in the area by the Army Corps of Engineers, the navigation channel north of Elba was a broad expanse which, in the Corps’ estimation, was excessively wide. In the 1880’s, the Corps undertook to improve the navigation channel by restricting the river’s width. This was effected by the construction of a training wall north of Elba Island during 1891-1895, by sedimentation that took place, and by deposits of dredge material behind the wall. Land in the area of southeastern Denwill formed initially as marsh islands adjacent to the wall and then grew to be connected to the South Carolina shore.
Similar changes took place at Horseshoe Shoal, an area that now connects Jones Island and Oyster Bed Island.
The Special Master recommended that the additions to Denwill and Horseshoe Shoal be awarded to Georgia. South Carolina takes exception to this. Referring to App. D of 2 Rep., South Carolina asserts: “Approximately 1 mile of riverfront land on the South Carolina side of the river would be placed in Georgia.” S. C. Exceptions 6. It emphasizes that the additions to Denwill took more than 40 years to form, that is, between the time the first diversion wing-dam *403structures were built, and 1924 when the old bed appeared above water. Id., at 7. The training wall, two miles long, was permeable, and permitted sedimentation behind it before the dredging and filling occurred. South Carolina observes that the Special Master nowhere specifically states that the process in fact was avulsive, but it asserts, pointing to several references by the Master to avulsive procedures, that “it is clear that he considered the process to be avulsive.” Id., at 9. South Carolina also notes that all those activities worked to the benefit of the city of Savannah, and that “Georgia’s port was the only beneficiary of the dredging.” Brief in Rebuttal for South Carolina 5.
Georgia, in its turn, notes the Corps’ relocation of the northern bank of the river at southeastern Denwill over a half mile south of its original location. See App. C of 1 Rep. It asserts that the land in dispute did not form as gradual accretion from the South Carolina shore toward the river but, instead, rose in the river immediately behind the training wall and was the result of the construction of the wall and the deposit of dredge spoil behind it.
South Carolina’s exception as to Horseshoe Shoal is like its Denwill exception. It asserts that, as was the case with Denwill, training works and dredging by the Corps led to sedimentation and filling. As a result, the Shoal is now a long isthmus of high ground connecting Jones Island and Oyster Bed Island. It was formed “in the same way, and over a comparable period, as the additional land on Denwill.” S. C. Exceptions 13-14. The major training work in this area, too, was between 1890 and 1894. Wing dams were placed and then hydraulic fill. But “even before large-scale dredging and filling began, the area was close to becoming a dry elevation solely as a result of the 30 years of sedimentation caused by training works.” Id., at 14-15.
General rules concerning the formation of riparian land are well developed and are simply expressed and well accepted. *404When the bed is changed by the natural and gradual processes known as erosion and accretion, the boundary follows the varying course of the stream. But if the stream leaves its old bed and forms a new one by the process known as avulsion, the result works no change of boundary. Arkansas v. Tennessee, 246 U. S. 158, 173 (1918). Sometimes, the problem is to distinguish between the two.
Here we have a situation where interference in the river’s flow was not caused by either of the adjoining States, but by the United States Army Corps of Engineers. It is generally held, of course, that one cannot extend one’s own property into the water by landfilling or purposefully causing accretion. See, e. g., Seacoast Real Estate Co. v. American Timber Co., 92 N. J. Eq. 219, 221, 113 A. 489, 490 (1920).
We conclude, not without some difficulty, that Georgia has the better of the argument as to these two areas. It is true, of course, that avulsive action ordinarily calls to mind something somewhat sudden or, at least, of short duration, whereas accretion has as its essence the gradual deposit of material over a period by action of water flow. This is so even though it may have been caused partly or wholly by placed obstructions. See County of St. Clair v. Lovingston, 23 Wall. 46 (1874).
Some of the changes here were caused gradually by the deposit of sediment by river waters. Others were caused by the deposit of fill through the use of a hydraulic-pipeline dredge employed by the Corps pursuant to the paramount right of the United States Government to improve navigation. See South Carolina v. Georgia, 93 U. S. 4 (1876). The rapidity of some aspects of the dredging and other processes led the Special Master to conclude that the changes in the Savannah River were primarily avulsive in nature. Although the question is close, on balance, we think this particular record as to this particular river supports the recommendation made by the Master. We therefore overrule *405South Carolina’s exceptions as to southeastern Denwill and Horseshoe Shoal.
VIII
Addition to Bird Island
Bird Island, as described by South Carolina, “is now part of an elongated island several miles long, in the middle of the river across from Jones Island.” S. C. Exceptions 16. It has merged with Long Island. See Apps. C and D of 2 Rep. South Carolina initially took exception to the Special Master’s conclusion that a sliver of land on Bird Island was in Georgia rather than in South Carolina. The latter State’s position was that, in line with its accretion argument with respect to Denwill and Horseshoe Shoal, the boundary for like reasons should run through part of Bird Island. S. C. Exceptions 17.
The Special Master’s Second Report, on Georgia’s motion, clarified any confusion that may have existed with respect to Bird Island. His recommended boundary line is now carefully described as passing north of the island, so that Bird Island in its entirety would be in Georgia. See App. D of 2 Rep., modifying App. F of 1 Rep. And South Carolina “responded by essentially agreeing.” 2 Rep. 19. This serves to eliminate the dispute over the island, and South Carolina’s exception, initially made, is overruled.
IX
The Lateral Seaward Boundary
Each side has noted an exception to the Special Master’s recommendation concerning the lateral seaward boundary between the States. What the Master has done here begins with his resolution of the issue concerning the river’s mouth, a recommendation we have approved in Part V hereof. He accepted, as do we, that Tybee Island is to be regarded as the “headland” for the south side of the mouth of the Savannah River, and that the long-existing shoal forms the north side of the mouth.
*406A seemingly complicating factor is that the Georgia coast and the South Carolina coast, where they meet at the river, do not run at exactly the same angle from due north. While each extends southwest-northeast, Georgia’s coast is roughly 20 degrees from north-south and South Carolina’s roughly 47 degrees. Thus, lines drawn perpendicularly from each coast overlap off the coast, and overlap more as the distance from the shoreline increases. This wedge-shaped overlap is the primary focus of the two States’ respective exceptions.
The Master’s recommended line continues down the river’s mouth until it intersects a line, from Tybee Island’s most northern point to Hilton Head Island’s most southern point, where it then proceeds out to sea perpendicularly to that line.
South Carolina claims that the described overlap is the only area reasonably in dispute, but that the Master’s line runs at an angle about six degrees north of the most favorable line Georgia could expect to receive, i. e., a line perpendicular to Georgia’s coast. Thus, says South Carolina, the Master’s line is wholly outside the area of overlap. South Carolina urges that the area of overlap be split “more or less equally.” S. C. Exceptions 22.
Georgia’s exception relates “only to the starting point of the proposed lateral seaward boundary.” Reply Brief for Georgia 17. It submits that “the geographic middle of the mouth of the Savannah River should be used as the starting point of the maritime boundary,” ibid., but that if this argument fails, the boundary as recommended by the Master should be upheld.
The Master observed that neither Georgia’s Charter of 1732 nor the 1787 Treaty of Beaufort made any reference to the lateral seaward boundary between the States. 2 Rep. 1. He noted that in 1969 the States reached a tentative agreement upon a boundary projecting due east from the mouth of the river, but that this agreement was not ratified by Congress and never was effective. Id., at 2. The two States have entered into a stipulation, approved by the Solicitor *407General of the United States, whereby they agree that no interest of the United States is affected by this Court’s ultimate determination as to the location of the lateral seaward boundary between the States. The Master accordingly concluded that the Federal Government was not a necessary party. Id., at 3. He then proceeded to apply principles of international law, citing Wisconsin v. Michigan, 295 U. S. 455 (1935), and Texas v. Louisiana, 426 U. S. 465 (1976).
The Master reviewed the States’ respective contentions. He noted that Georgia cited the 1958 Geneva Convention on the Territorial Sea and the Contiguous Zone, April 29, 1958 [1964] 15 U. S. T. 1607, T. I. A. S. No. 5639, and particularly the first paragraph of Article 12 thereof, id., at 1610, which recites that neither of two adjacent States is entitled “to extend its territorial sea beyond the median line every point of which is equidistant from the nearest points on the baselines.” The Baseline Committee, operating in the 1970s’, drew its line between Hilton Head Island and Tybee Island. The Master noted that he had determined the mouth of the river to be only approximately a mile north of the southern end of the baseline at Tybee Island. Nevertheless, in drawing the lateral seaward boundary the Master felt controlled by international law. “[Therefore, it does not follow that the starting point of the lateral seaward boundary must merely be an extension of the land boundary between the states, although such a factor must be considered as highly persuasive.” 2 Rep. 5. Georgia’s claimed starting point for the lateral seaward boundary was at a point halfway between Hilton Head Island and Tybee Island, and thus about two miles north of where the land boundary met the baseline.
The Special Master noted that South Carolina contended that the boundary line must start at the point where the inland boundary, if extended, intersected the baseline. This would result in the boundary’s being delimited seaward in a southeasterly direction running substantially parallel to the channel providing the entrance to the river. The Master *408then turned to the “equidistant principle” referred to in Texas v. Louisiana, supra. He observed, however, that while the equidistant principle “may be a slightly preferred method of delimitation, it does not reach the stature of a rule of law.” 2 Rep. 16. Instead, “it is the principles of equity which should guide the conclusion in each particular case.” Ibid.
The Special Master recommended that the lateral seaward boundary between the two States be along a line drawn at right angles to the baseline beginning at a point marked “X” on App. A to 2 Rep. until that line reached the outer limit of the territorial sea as that outer limit existed on December 27, 1988.6 He felt that this was a proper utilization of equitable principles. 2 Rep. 18. He further recommended that Georgia and South Carolina “be required to suitably mark the lateral seaward boundary in the water area at the joint expense of the two states.” Ibid.
We adopt the recommendation of the Special Master as to the lateral seaward boundary between South Carolina and Georgia. We conclude that it gives equitable balance and recognition to the so-called equidistant principle and to the inland boundary between the two States, and does so with the least possible offense to any claimed parallel between offshore territory and the coast itself. The States’ respective exceptions as to the lateral seaward boundary are overruled.
*409X
In summary:
1. Each exception advanced by South Carolina is overruled.
2. Georgia’s exception to the Special Master’s use of the right-angle principle, discussed in Part VI hereof, is sustained.
3. Each other exception advanced by Georgia is overruled.
4. Each recommendation made by the Special Master in his two reports, and as to which no exception has been taken, is adopted (subject to the reservation expressed in n. 7, infra).
5. Each recommendation made by the Special Master, and as to which an exception has been advanced but overruled, is adopted.7
The parties are directed promptly to prepare an appropriate proposed decree in line with these conclusions. Because the Special Master has been discharged, see 493 U. S. 1053 (1990), the proposed decree shall be submitted directly to this Court for its review and consideration. The Court assumes that the parties will be able to agree upon the form *410of the decree. If they are unable to agree, each State shall submit to the Court its own formulation with any supportive comment deemed necessary. The Court will then draft the decree and enter it.
No costs are allowed.
The Court retains jurisdiction to entertain such further proceedings as from time to time may be necessary or advisable to effectuate the forthcoming decree and the rights of the respective parties.
It is so ordered.
All Members of the Court join in Parts I, II, III, and VIII of the opinion. Part IV is joined by all except The Chief Justice and Justice Kennedy. Part V is joined by all, except that The Chief Justice and Justice Kennedy do not join a portion of that Part. Part VI is joined by all except Justice White and Justice Marshall. Part VII is joined by all except Justice Scalia and Justice Kennedy. Part IX is joined by all except Justice Stevens and Justice Scalia.
The first two Articles of the Treaty read:
“Article the first.
“The most northern branch or stream of the river Savannah from the sea or mouth of such stream to the fork or confluence of the rivers now called Tugoloo and Keowee, and from thence the most northern branch or stream of the said river Tugoloo till it intersects the northern boundary line of South Carolina if the said branch or stream of Tugoloo extends so far north, reserving all the islands in the said rivers Savannah and Tugoloo to Georgia; but if the head spring or source of any branch or stream of the said river Tugoloo does not extend to the north boundary line of South Carolina, then a west line to the Mississippi, to be drawn from the head spring or source of the said branch or stream of Tugoloo river which extends to the highest northern latitude — shall forever hereafter form the separation limit and boundary between the States of South Carolina and Georgia.
“Article the second.
“The navigation of the river Savannah at and from the bar, and mouth, along the north east side of Cockspur Island and up the direct course of the main northern channel, along the northern side of Hutchinson’s Island, opposite the town of Savannah to the upper end of the said island, and from thence up the bed, or principal stream of the said river, to the confluence of the rivers Tugoloo and Keowee, and from the confluence up the channel of the most northern stream of Tugoloo river to its source and back again by the same channel to the Atlantic ocean: Is hereby declared to be henceforth equally free to the citizens of both States, and exempt from all duties, tolls, hindrance, interruption or molestation whatsoever, attempted to be enforced by one State on the citizens of the other, and all the rest of the river Savannah to the southward of the foregoing description is acknowledged to be the exclusive right of the State of Georgia.” Reprinted in App. A to Ga. Exceptions.
It is to be noted that the Treaty did not state whether the boundary was the middle of the northern branch or stream of the Savannah River, or whether it was on the South Carolina bank, or whether the bed was held jointly.
The 1798 Constitution of Georgia reflected the same theme. It provided:
“The limits, boundaries, jurisdictions, and authority of the State of Georgia do, and did, and of right ought to, extend from the sea or mouth of the *382river Savannah, along the northern branch or stream thereof, to the fork or confluence of the rivers now called Túgalo and Keowee, . . . reserving all the islands in said rivers Savannah and Túgalo to Georgia . . . Art. I, §23.
See H. R. Doc. No. 357, The Federal and State Constitutions, Colonial Charters, and Other Organic Laws, 59th Cong., 2d Sess., vol. 2, p. 794 (1909).
Georgia’s present Constitution of 1983, as amended, contains no provision relating to the State’s boundaries. Georgia statutes, however, provide:
“The boundaries of Georgia, as deduced from the Constitution of Georgia, the Convention of Beaufort, the Articles of Cession and Agreement with the United States of America entered into on April 24, 1802, the Resolution of the General Assembly dated December 8, 1826, and the adjudications and compromises affecting Alabama and Florida, are as follows:
“From the sea, or the mouth of the River Savannah, along the stream thereof to the fork or confluence made by the Rivers Keowee and Túgalo, and thence along said River Túgalo until the fork or confluence made by said Túgalo and the River Chattooga, and up and along the same to the point where it touches the northern boundary line of South Carolina, and the southern boundary line of North Carolina, which is at a point on the thirty-fifth parallel of north latitude, reserving all the islands in said Rivers Savannah, Túgalo, and Chattooga, to Georgia . . . .” Ga. Code Ann. § 50-2-1 (1986).
“The boundary between Georgia and South Carolina shall be the line described as running from the mouth of the River Savannah, up said river and the Rivers Túgalo and Chattooga, to the point where the last-named river intersects with the thirty-fifth parallel of north latitude, conforming as much as possible to the line agreed on by the commissioners of said states at Beaufort on April 28, 1787.” § 50-2-2.
Similarly, South Carolina’s present Constitution of 1895, as amended, has no provision as to that State’s boundaries. The State has a statute which reads:
“From the State of Georgia, this State is divided by the Savannah River, from its entrance into the ocean to the confluence of the Toogaloo and Seneca Rivers; thence up the Toogaloo River to the confluence of the Tallulah and the Chattooga Rivers; thence up the Chattooga River to the 35th parallel of north latitude, which is the boundary of North Carolina, the line *383being midway between the banks of said respective rivers when the water is at ordinary stage. And when the rivers are broken by islands of natural formation which, under the treaty of Beaufort, are reserved to the state of Georgia, the line is midway between the island banks and the South Carolina banks when the water is at ordinary stage.” S. C. Code Ann. § 1-1-10 (1986).
The relevant provisions of the 1922 decree read:
“1st. Where there are no islands in the boundary rivers the location of the line between the two States is on the water midway between the main banks of the river when water is at ordinary stage;
“2nd. Where there are islands, the line is midway between the island bank and the South Carolina shore when the water is at ordinary stage;
“3rd. That all islands formed by nature in the Chattooga river are reserved to Georgia as completely as are those in the Savannah and Tugaloo rivers.”
It also seems to us, for what it may be worth, that there is no qualitative difference in the type of proof offered by South Carolina for Rabbit Island and the rest of the Barnwell cluster. The islands were granted together, often conveyed together, and taxed in the same manner. Rabbit and Hog were both diked and cultivated for rice. Yet Georgia has not pursued its claim to Rabbit Island.
Some of the Barnwell Islands also may have emerged after the Treaty, but our conclusion that they belong to South Carolina by prescription, see Part III, supra, makes the time of their emergence immaterial.
This date is utilized because on December 27, 1988, the President issued a Proclamation that the territorial sea of the United States thenceforth extended to 12 nautical miles. See Proclamation 5928, 54 Fed. Reg. 777 (filed Jan. 6, 1989). The Special Master specifically concluded his determination of the lateral seaward boundary at the outer limit of the theretofore existing 3-mile territorial sea. He felt that there were legal problems confronting the coastal States with respect to the extended portion of the territorial sea and, further, that consideration of an extended boundary line would exceed this Court’s reference to him. 2 Rep. 27-28.
One might suggest, perhaps, that the Special Master in his Second Report assumed that the United States had utilized “straight baselines” in constructing the coast near the mouth of the Savannah River. See 2 Rep. 12-14. Such baseline use would have been authorized by Article 4 of the Geneva Convention on the Territorial Sea and the Contiguous Zone, April 29, 1958 [1964] 15 U. S. T. 1606, 1608 T. I. A. S. No. 5639. Article 4, however, provides this only as an option. We are not aware of any instance where that provision has been employed in the determination of the United States coastline. See, e. g., United States v. California, 381 U. S. 139, 167-169 (1965); United States v. Louisiana (Louisiana Boundary Case), 394 U. S. 11, 68-73 (1969); United States v. Louisiana (Alabama and Mississippi Boundary Case), 470 U. S. 93, 99 (1985). If the Special Master in fact made the assumption, we refrain from adopting that portion of his discussion. The assumption is not necessary for a decision in the present litigation, and we leave the question of its propriety for another day.