
172 Mich. App. 354 (1988)
431 N.W.2d 511
GREGORY
v.
LaFAIVE
Docket No. 100517.
Michigan Court of Appeals.
Decided October 17, 1988.
Osstyn, Bays, Ferns & Spray (by Randolph B. Osstyn), for plaintiffs.
Clancey, Hansen, Chilman, Graybill & Greenlee, P.C. (by Walter L. Hansen), for defendants.
Before: BEASLEY, P.J., and SAWYER and WEAVER, JJ.
SAWYER, J.
Plaintiffs brought an action to quiet title to certain property located on the shores of Big Chief Lake (formerly known as Trout Lake) located in Republic Township, Marquette County. Following a bench trial, the trial court entered a *356 judgment of no cause of action. Plaintiffs now appeal and we reverse.
The difficulties in this case arise from two complicating factors. First, there appears to be an error in the original plat of the township as recorded by the United States Surveyor General on March 8, 1849, following the original government survey of the area. Second, the shoreline of Big Chief Lake has shifted somewhat since that original 1849 survey to the extent that a portion of the property in dispute, which was under water according to the 1849 plat, is now dry land. Thus, the instant dispute involves two separate, though interrelated, questions: (1) what is the original boundary line as deeded by the United States government to the purchasers of the land; and (2) how must the originally platted boundary line be reformed today to adjust for the changing shoreline.
The heart of this dispute involves the original boundary line between what was platted as Government Lot 2 and Government Lot 3 in Section 8 of Township 45 North, Range 30 West (Republic Township). Government Lot 2 lies along the westerly shore of what is now known as Big Chief Lake while Government Lot 3, to the south of lot 2, lies along the southwest corner of the lake and included a peninsula which jutted to the north into the lake. The two lots share a small portion of a common boundary line. Specifically, a portion of the southern boundary line of Government Lot 2 on the east side of that lot is also a portion of the northern boundary line of Government Lot 3 on the west side of that lot. This common boundary line roughly falls upon the dividing line between the northwest 1/4 and the southwest 1/4 of Section 8. Indeed, the resolution of the dispute at bar centers on the question whether that common *357 boundary line should exactly conform to the boundary line, as determined by modern survey, between the quarter-sections or whether it deviates somewhat from the quarter-section boundary line. For the reasons to be discussed below, we conclude that the proper boundary line is the one as established in the original plat and which deviates from the "true" quarter-section line as determined by current surveys.[1]
The essence of the trial court's findings is that the east-west quarter-section line determined by modern survey more accurately represents the true quarter-section line than the boundary line between Government Lots 2 and 3 as depicted in the original plat. In so concluding, the trial court referred to 43 USC 752 for the proper method in determining the location of section, half-section and quarter-section boundary lines. The trial court then concluded that the property lying north of the actual quarter-section line belonged to Government Lot 2 and the land lying south of the quarter-section line belonged to Government Lot 3. Since defendants' title to the disputed property follows a chain of title from Government Lot 2[2] while plaintiffs' claim derives from title to Government *358 Lot 3, the trial court ruled in favor of defendants.[3]
We would have no difficulty in agreeing with the trial court's conclusion had the property been deeded from the United States government by use of a metes and bounds description, rather than by "lot" designation. That is, the trial court would be correct had the deeds to Government Lot 3 referred not to "lot 3" but described the lot in metes and bounds, such as "the northeast 1/4 of the southwest 1/4 of section 8," the approximate legal description of lot 3 if the quarter-section line is taken as the northern boundary.[4] Not only does the original government deed convey the property at issue by reference to their lot numbers, "According to the Official Plat of the Survey of the said Land returned to the General Land Office by the Surveyor General," the deeds to the parties at bar also conveyed with reference to lot numbers. Plaintiff Louis Gregory took title to the property by a deed dated May 21, 1945, from his predecessor in title, the Jas. B. Goodman Company, to certain property including "Lot Number Three" of Section 8. Furthermore, the deed received by defendants from their predecessor in title conveys an interest in a "parcel of land being part of Government Lot 2," followed by a metes and bounds description of the parcel being conveyed inasmuch as lot 2 was not conveyed to defendants in its entirety. Indeed, it appears that metes and bounds descriptions were not used in the conveyance of *359 the disputed property until Government Lot 2 first became subdivided and it was necessary to describe the conveyance of less than the whole lot.
As our Supreme Court noted in Poch v Urlaub, 357 Mich 261, 275; 98 NW2d 509 (1959), where land is disposed of by reference to an official plat, the boundary lines shown on the plat control:
In 5A Thompson on Real Property, § 2721, p 1132, it is said:
"When government lands have been disposed of in conformity to a line appearing on an official plat of the government survey, approved by the surveyor general, the location of the line shown on the official plat is controlling."
See also Cragin v Powell, 128 US 691, 696; 9 S Ct 203; 32 L Ed 566 (1888); Woodbury v Venia, 114 Mich 251, 257; 72 NW 189 (1897).
In the case at bar, the original official plat clearly shows the boundary line between Government Lot 2 and Government Lot 3 intersecting the lake at a point on the southwest side of the lake on an inlet or bay of the lake. The quarter-section line as determined by modern survey is to the south of the platted boundary line and does not intersect where that bay is represented on the original plat by the meander line. Since the original plat controls, we cannot accept the quarter-section line as determined by the current survey as the true boundary line between Government Lots 2 and 3; rather, we must employ the originally platted boundary line which is shown as running from the quarter-section monument to a point on the meander line which depicts a bay or inlet on the southwest side of Big Chief Lake immediately to the west of a small peninsula which was platted as part of lot 3. Thus, the true boundary between Government Lot 2 and Government *360 Lot 3 would correspond with the line shown on our illustration as the platted boundary line between the two lots from the 1849 plat.[5]
Having concluded that the originally platted boundary is the appropriate boundary between Government Lot 2 and Government Lot 3, we may make some initial observations. Referring to our illustration at the end of this opinion, accepting without deciding that the meander lines depicted on that illustration for both the original shoreline and the boundary between the two lots are reasonably accurate, we can make some initial determinations of the title of the property at issue. First, all of the property lying south of the platted boundary line, and south of the original shoreline east of where the shoreline meets the boundary line, is a part of Government Lot 3 and, therefore, belongs to plaintiffs since they are now the owners of Government Lot 3. Second, all land lying north of the platted boundary line, and to the west of the original shoreline north of the point where the original shoreline meets the platted boundary line, belongs to Government Lot 2.
Thus, with respect to the lot designated in our illustration as A, the land lying in lot A north and west of the original shoreline meander line (on the northwest side of the bay as platted in 1849) belongs to defendants under their deed from their *361 predecessor in title who owned Government Lot 2. That portion of lot A and lot B lying south and east of the original shoreline meander line (the southern and southeastern shore of the bay depicted by the 1849 plat) belongs to plaintiffs under their deed to Government Lot 3. Similarly, all of lot c belongs to plaintiffs under their deed to Government Lot 3 since it lies either entirely within the original peninsula as depicted on the plat as belonging to Government Lot 3 or because a small amount of accreted land is involved which was entirely an outgrowth from the original shoreline of Government Lot 3.
There remains to be determined the ownership of the central portion of lot A and northern portion of lot B which, although now dry land, was apparently under water at the time of the preparation of the 1849 plat. To determine ownership to this land, we must turn to the rules of dividing accreted land along lakeshores. Since the property in question originated with a grant by the federal government, we must begin with examining the nature and extent of that grant. As noted above, the official government plat is part and parcel of the grant of land by the federal government. Where that plat shows, as it does in the case at bar, a lot being bounded by the meander line of a lake, the grant of land was to the water's edge. Furthermore, the federal government did not retain any rights to the land lying beneath the surface of the water. Rather, the disposition of the lake bed is made with reference to the applicable local state law. Hardin v Jordan, 140 US 371, 380-381; 11 S Ct 808; 35 L Ed 428 (1891). See also United States v Lane, 260 US 662; 43 S Ct 236; 67 L Ed 448 (1923).
It is well-settled in Michigan law that the title of a riparian land owner extends to the middle *362 line of the lake or stream of inland waters. Cutliff v Densmore, 354 Mich 586, 590; 93 NW2d 307 (1958); The Grand Rapids Ice & Coal Co v The South Grand Rapids Ice & Coal Co, 102 Mich 227, 236; 60 NW 681 (1894); Booker v Wever, 42 Mich App 368; 202 NW2d 439 (1972). The method to be employed in determining the ownership of lands formed by accretion.[6] varies somewhat depending on the shape of the body of water involved. In Weisenburger v Kirkwood, 7 Mich App 283, 291; 151 NW2d 889 (1967), this Court outlined the three methods to be utilized in the appropriate cases:
6 Thompson on Real Property (1962 Replacement), § 3078, 1965 Supp, p 18, states:
"Various methods of division of lake beds have been used. If the lake is circular the shoreline is the base and the center line is the vertex of a triangle. If the lake is oblong the lines are drawn perpendicular to a median center. If neither of these methods are possible, the lake bed is divided in proportion to the shoreline owned. The theory on all events is that the shore owners take ratably."
Thus, it is necessary to determine which of the three shape categories Big Chief Lake falls within: circular, oblong, or irregular. While it would appear to us that Big Chief Lake is of irregular shape, we leave it to the trial court on remand to make the initial determination of which category Big Chief Lake falls within and to apply the *363 applicable rules based upon that determination. We do, however, offer some brief comments on the methods of dividing accreted land for guidance to the trial court and the parties. This Court described the method for dividing a circular lake in Aalsburg v Cashion, 14 Mich App 91, 100; 165 NW2d 309 (1968), which in essence is drawing a line from the point where the boundary line met the original lakeshore to the center of the lake. With respect to an oblong lake, the method to be employed is similar to that used in dividing a stream or river. That is, a line is drawn from the point where the boundary line met the original shoreline to the center line of the lake (or stream) as nearly perpendicular as possible. See Weisenburger, supra; A M Campau Realty Co v Detroit, 162 Mich 243, 245; 127 NW 365 (1910).
Finally, turning to the division of accreted land on an irregular lake, the method becomes somewhat more complex. In dividing the new land, the trial court must apportion the accretion between the two adjoining landowners so that their relative portions of new shoreline correspond to the relative portions of their old shoreline. See Cutliff, supra at 590; Booker, supra at 375; Weisenburger, supra at 291. Thus, if two adjoining property owners originally owned a shoreline, the first owner owning two-thirds of the total and the second owning one-third of the total, the new shoreline developed through accretion would be divided between those two property owners by running a line from the point where their common boundary line originally met the shoreline to a point on the new shoreline such that the first property owner still retains two-thirds of the shoreline and the second property owner retains one-third of the shoreline. Of course, the trial court must take into account the individual variances *364 of the shoreline to be divided and draw it the best it can so as to equitably divide the accreted land proportionately between the parties.
In sum, in the case at bar, plaintiffs are entitled to that property which was originally platted as Government Lot 3 in the original, official plat filed by the Surveyor General's office. See Poch, supra. Defendants are entitled to that property deeded to them by the owner of Government Lot 2 which falls within what was originally platted as Government Lot 2. With respect to the lands created by accretion lying in what we have depicted as lot A and lot B in our illustration, the trial court must apportion that land by drawing a line from the point where the originally platted boundary line meets the original shoreline as represented by the meander lines on the original plat to a point on the currently existing shoreline consistent with one of the above-outlined methods. That is, the extended boundary line must either lie along a line drawn from a point the platted boundary line met the original shoreline to the center of the lake if Big Chief Lake is determined to be circular, along a line drawn from the point the original boundary line met the original shoreline perpendicularly to the center line of Big Chief Lake if it is an oblong lake, or, if it is an irregular lake, to a point along the new shoreline which the trial court has determined proportionately divides the new shoreline in the same proportion to the amount of shoreline the parties originally owned under the government plat. Finally, we would note that the best scenario would be for the parties to be able to agree upon the boundary line themselves to be drawn from the point in which the original platted boundary line met the original shoreline to an agreeable point on the currently existing shoreline.
*365 Since we have determined that the trial court erred in its original determination of the boundary line between the parties, we believe it unnecessary to address the parties' argument relative to adverse possession and the doctrine of acquiescence.
Reversed and remanded for further proceedings consistent with this opinion. We do not retain jurisdiction. Plaintiffs may tax costs.
*366 
NOTES
[1]  For the reader's convenience, we have appended to this opinion a drawing of the disputed property. The long dashed line depicts the boundary line between Government Lots 2 and 3 as platted. The short dashed line depicts the shoreline as platted, while the thick solid line depicts the current shoreline. We have divided the disputed area into the areas labelled A, B, and C, each of which runs from the quarter-section line to the current shoreline. This quiet-title action only concerns areas A and B. Furthermore, while our illustration is based upon the exhibits contained in the lower court record, the drawing was prepared by a member of this Court's staff and, accordingly, is only an approximate indication of where boundary lines lie or are claimed to lie. The illustration is intended only to assist the reader in understanding the dispute and this illustration is not necessarily a precise depiction of where the indicated lines actually lie.
[2]  Defendants apparently received deeds to what we have referred to as lots A and B in our illustration from the owner of Government Lot 2. Lot C has never been separately deeded; plaintiffs claim it through their deed to Government Lot 3.
[3]  We would note that title to what we have referred to as lot C in our illustration would, under the trial court's reasoning, lie with the current owner of the remainder of Government Lot 2 since that parcel has never been deeded off and plaintiffs' claim to lot C would be invalid. However, the validity of title to lot C is not at issue in this case.
[4]  That description would be approximate because a portion of the boundary line would be uneven due to it bordering Big Chief Lake.
[5]  We again caution, however, that our representation in the illustration is not a final finding of fact binding as law of the case. Rather, the diagram is included for illustration purposes only. The trial court is free on remand to make such further findings of fact or take such additional evidence as it may deem appropriate and necessary to determine the exact placement of that original meander line shown on the 1849 plat as the boundary between the two lots. We do stress, however, that that meander line is not the quarter-section line determined by modern survey. Furthermore, that meander line which forms the boundary between the two lots must intersect with the meander line which depicts the original shoreline of Big Chief Lake as platted in 1849. That intersection also occurs to the west of the peninsula depicted by that plat.
[6]  In this opinion, we use the term "accretion" in a generic sense rather than using the more precise terms of alluvion and reliction. See Cutliff, supra at 588. It would appear, however, that the shore line in the case at bar changed and added new land by the process of reliction due to a general lowering of the level of Big Chief Lake. See "reliction," Black's Law Dictionary (5th ed). Nevertheless, since the precise method is not material to the resolution of this case, we will use the term "accretion" in a generic sense.
