This Land Court registration case was commenced by four petitions to amend certificates of title and to approve a plan of land described as Plan 314-20. A sketch reproducing the salient features of Plan 314-20 (Figure 4) may be found at the end of this opinion. The petitions allege the plaintiffs’ ownership of certain littoral land (land bordering sea, lake, or pond) as a result of accretion to their registered land. The defendant Acapesket Improvement Association, Inc. (Acapesket), answered by claiming that it, and not the plaintiffs, owns the land in question as a consequence of accretion to its own registered property. Acapesket also claimed a prescriptive easement over the land. The defendant interveners, too, asserted claims of prescriptive easement. The Commonwealth asserted no claims to the disputed land and now urges affirmance of the Land Court judgment.
After a lengthy trial, a judge of the Land Court concluded that the plaintiffs own the land claimed by them and that none of the defendants has rights in that land. The judge ordered the approval of Plan 314-20 if and when it is updated to reflect any changes occurring subsequent to the plan’s filing. He declined to issue an order concerning the amendment of the plaintiffs’ certificates of title until such a plan has been approved. In addition, the judge ordered that the words, “including the sand bar,” the significance of which we shall discuss below, struck from Acapesket’s certificate of title, and that the prescriptive easement claims of the several defendants be denied. Acapesket has appealed, expressly excluding from its appeal, however, the denial of its prescriptive easement claims. The interveners have not appealed. We allowed Acapesket’s application for direct appellate review, and we now affirm the judgment below.
The judge issued a comprehensive twenty-six page decision in which he set forth detailed findings, which were necessarily complex, as well as his rulings and reasons therefor. Our *774description of the facts throughout this opinion is based on the judge’s findings. The land in controversy is, in geological terms, a movable barrier beach, which separates Green Pond in Falmouth from the open ocean waters of Vineyard Sound. The barrier beach is referred to in the relevant certificates of title as a sand bar or sand bars.
The plaintiffs own land described in their title certificates as lots E-7, E-8, E-9, and E-10 shown on Land Court Plan 314H. The accompanying Figure 1 reproduces the salient features of Plan 314H. Acapesket owns five parcels of land described in Certificate of Title 78735. Parcels two and three are shown on Land Court Plan 314H as lots E-3 and E-4. Parcel four as described in Acapesket’s certificate 78735 is of primary importance in this litigation. Parcel four is described in certificate 78735 as “including the sand bar” and certain other land described in Certificate of Title No. 702.
The judge found as follows: “The Certificate of Title which immediately precedes Certificate of Title 78735 in Acapesket’s chain of title is No. 9356, and includes no reference to ‘including the sand bar.’ The deed which conveyed certain property out of Certificate No. 9356 and into Acapesket was prepared by one of Acapesket’s previous counsel. That deed contained the reference to ‘including the sand bar.’ The reference to the sand bar was also included on Certificate No. 78735, subsequent to its original issuance, at the request of Acapesket’s counsel. Land Court approval was not obtained to amend or correct the Certificate but rather Acapesket’s counsel instructed the Registrar by letter to make the change to the Certificate in July of 1979.”
The sand bar (barrier beach) referred to in certificate 78735 is shown on Plan 314-20 as a land mass bounding on the easterly side of lots E-5 through E-10. Lots E-5 through E-10 are also shown on Land Court Plan 314H, but on that plan the land mass is not shown. The plaintiffs are claiming ownership by accretion of so much of the land mass shown *776on Plan 314-20 as lots 478*, 479*, 480*, and 481*.4 Acapesket claims ownership of lots 478*, 479*, 480*, 481*, 479, 478, and 484. Acapesket claims that the entire land mass belongs to it as a result of accretions to a registered sand bar which was described in certificate of title 702.
*776Parcel four in Acapesket’s certificate of title 78735 derives from certificate of title 702, which was issued in 1902. Certificate 702 referred to “Lot A” as depicted on Land Court Plan 314B and described Lot A as including the plaintiffs’ lots along with “the sand bar and lands adjoining Green Pond outlet on the west.” The accompanying Figure 2 reproduces the salient features of Land Court Plan 314B, sheet 2,-dated August 24, 1901.
Plan 314B, sheet 2, shows a barrier beach separating Green Pond from Vineyard Sound divided by an outlet. As the plan shows, the land to the west of the outlet in 1902 included a hook-shaped 200 foot wide peninsula extending approximately 750 feet from the westerly shore of Green Pond (the west-side sand bar). The other sand bar shown on Plan 314B extended westerly from the easterly shore of Green Pond to the outlet (east-side sand bar).
The original location of the two 1902 sand bars is shown by a broken line on the bottom half of Plan 314-20. By 1979, the original location of those sand bars had become almost completely covered by the open waters of Vineyard Sound. In 1902, what was to become lot E-10 had no boundaries on either Vineyard Sound or Green Pond. The land that was to become lots E-5 through E-9 was bounded on the east by Green Pond. In 1925, when Plan 314H was filed, lots E-5 through E-9 were still bounded on the east by Green Pond. In 1926, Land Court Plan 3141, showing the further subdivi-
*778sion of lot E-10, was filed. Figure 3 reproduces the salient features of Plan 3141. At that time, lot E-10 was completely bounded on the east by the west-side sand bar.
*778In 1925, the northerly side of the west-side sand bar had migrated north approximately 150 feet from its 1902 position. In 1926, the southerly shore of this west-side sand bar was approximately 200 feet south of the southerly boundary of lot E-9. The southerly shore of the 1902 west-side sand bar had been approximately 350 feet south of that boundary. In 1926, as shown on Plan 3141 and described in Certificate of Title 702, the west-side sand bar was owned by Thomas Malchman.
From 1926 until 1947 the west-side and east-side sand bars were slowly migrating northward due to erosion on their southerly boundaries and accretion on their northerly boundaries. In 1943, the west-side sand bar was bounding in whole or in part on what had been the 1926 easterly boundary of lots E-7 through E-10. By 1947, the west-side sand bar abutted lots E-7 through E-9 entirely. Lot E-10 was bounding on Vineyard Sound.
Immediately prior to 1950 the west-side sand bar was still bounding on lots E-7 through E-9. There were three or four large storms in 1950, one or more of which caused a breach in the west-side sand bar that resulted in a new inlet for Green Pond in the approximate location of the 1926 boundaries of lots E-7 through E-9. After the formation of that inlet (1951 inlet), but before October, 1951, the old inlet was filled in by accretions to one or both of the two sand bars. The 1951 inlet was approximately 800 feet west of the old inlet.
In 1952, the Department of Public Works (DPW) cut a new inlet for Green Pond supported by two jetties. With reference to the west-side and east-side sand bars, the DPW inlet was and still is located substantially where the original, pre-1951, inlet was. Of course, the inlet, along with the sand bars, was north of its original location. See Plan 314-20 (Figure 4). As the DPW dredged the new inlet, it dumped the excavated material off of what had been the west-side sand bar (by 1951 the west-side and east-side sand bars had be-
*780come one long sand bar). The DPW began dumping the spoil off of the eastern end of the old west-side sand bar’s southerly boundary and continued dumping in a westerly direction. When the DPW had dumped spoil up to the boundary of lot E-10, it then dumped in a northerly direction until the 1951 outlet was filled in. This dumping or filling resulted in the substantial formation of the disputed land mass. The judge specifically found that the dumping of spoil was not a necessary aid to navigation, but instead was only incidental to the new jetties and inlet. We discuss below the legal significance of that finding.
*780The only question on appeal, and therefore the only question we address, is whether Acapesket has any ownership or equitable interest in the land that the plaintiffs assert belongs to them. We begin our legal analysis by setting forth some well-established relevant principles having to do with the rights of littoral landowners. One of these is that, when the boundary between the water and the land changes by the gradual deposit of sand and clay and the like, then the line of ownership ordinarily follows the changing water line. Michaelson v. Silver Beach Improvement Ass’n, 342 Mass. 251, 253-254 (1961). A littoral owner can acquire ownership of such accretions caused by either natural processes or human intervention if they were not caused by the owner himself. Id. at 254. If the accretions are created by government as a necessary aid to navigation, the accretions belong to the government rather than the littoral land owner, id., but, as we have noted, the judge found that the accretions which substantially formed the disputed land mass here resulted from a dumping of spoil that was not in aid of navigation. The dumping was merely incidental to the construction of the new inlet and jetties. Therefore, none of the accretions in this case belongs to the government.
The rule that the owner of littoral land gains ownership of accretions to his land is subject to, and modified by, the further rule that, when two or more littoral owners have rights to simultaneously formed accretions, the rights of the owners in the accretions are to be determined by the doctrine of eq*781uitable division. See Burke v. Commonwealth, 283 Mass. 63, 69 (1933); Allen v. Wood, 256 Mass. 343, 350 (1926). We said in Allen v. Wood, supra: “The object of apportioning accretions is. that they shall be so apportioned as to do justice to each owner, in the absence of a positive prescribed rule and of direct judicial decision to guide, and their division on a non-navigable river frontage is so made as to give each relatively the same proportion in his ownership of the new river line that he had in the old.” Stated in another way, the object of apportioning simultaneous accretions among lots of littoral land is to give each owner the same proportion of the new waterfront that he would have had if the accretions had never occurred. This is critical to our decision.
The judge concluded that the plaintiffs own the land they claim is theirs, namely lots 478*, 479*, 480*, and 481* as shown on Plan 314-20, and that Acapesket has no interest in it, and he approved the division of the land as shown on that plan with one exception not material to the present controversy. Acapesket does not argue on appeal that the judge was wrong in concluding that the plaintiffs have interests in the contested lots, but does contend that it, too, has an interest. Acapesket argues that the judge erred in not equitably dividing the property between the plaintiffs and Acapesket rather than just among the plaintiffs. Acapesket petitions this court to reverse the Land Court judgment and remand the case for equitable division between Acapesket and the other inter-__ ested parties.
The judge reasoned that, as a result of the continuing erosion of its southerly boundary, the original sand bar or sand bars shown on Plan 314B, sheet 2, and Plan 3141 had entirely eroded by 1947 — that the sand bar or bars were no longer in existence by that time. He concluded that the words in Acapesket’s certificate of title 78735, “including the sand bar,” which were added to that certificate in 1979 without Land Court approval, should be struck. The judge also reasoned that when a parcel of land erodes on one side and forms accretions on another, and the process continues until the original parcel ceases to exist and only the accretions re*782main, as occurred with respect to the sand bar in this case, the lot owner’s proprietary interest in the accreted land mass dissolves. “To follow another rule,” the judge said, “would permit someone to maintain a property interest in land which could conceivably migrate hundreds of yards, or more, from its original location. This rule would obviously be inconsistent with conventional concepts of property law which set boundaries for real property at fixed points on the ground.” The judge concluded that Acapesket was not entitled to an equitable division of the land in dispute.
The principal thrust of Acapesket’s argument is that its predecessors in title were the registered owners of the sand bar by virtue of certificates of title issued in 1902 and 1923, and that the settled law of the Commonwealth is that title to accretions is identical to the title to the land to which the accretions are attached. There is no suggestion in the law, says Acapesket, that title to the accretions is subject to divestment upon erosion, complete or otherwise, of the land to which the accretions were attached, and to hold that such divestment takes place threatens the integrity of the land registration system with respect to waterfront property. Acapesket’s contentions are not unreasonable, but they ignore the principle that, when there are simultaneous accretions to several littoral parcels, the rights of the owners are to be determined by equitable division, the object of which is to give each parcel the same proportion of waterfront as it would have had if the accretions had not occurred. Here, if the accretions had not occurred, and Acapesket and its predecessors had owned only the original sand bar, which has entirely eroded away, there would be no waterfront to be proportionally matched or reproduced by a new waterfront. If a judge were now to award Acapesket some portion of the waterfront of the contested land, Acapesket would end up with a percentage of the waterfront despite the fact that, without the accretions, it would have had no land and therefore no waterfront. This would disserve the established objective of equita*783ble division of accretions to littoral land. We conclude that the result reached by the Land Court judge was correct.
Judgment affirmed.
[Figure 4 appears on page 784, infra.]
*784POND VINEYARD