
338 F.Supp. 984 (1972)
UNITED STATES of America, Plaintiff,
v.
Harold Wesley ZAGER et al., Defendants.
Civ. A. No. 67-C-384.
United States District Court, E. D. Wisconsin.
February 29, 1972.
*985 David J. Cannon, U. S. Atty., by Joseph P. Stadtmueller and Richard P. Broder, Asst. U. S. Attys., Milwaukee, Wis., for plaintiff.
Robert J. Kay, Madison, Wis., for defendants.

OPINION AND ORDER
REYNOLDS, District Judge:
This is a quiet title action involving 74.56 acres of land in Forest County, Wisconsin, brought by the United States pursuant to Title 28 U.S.C. § 1345.
The crux of the dispute is that in 1938 when the Government resurveyed Section 7, Township 38 North, Range 12 East, 4th Principal Meridian, in Forest County, it found that the meander line made of Lake Julia in the Government's original survey of 1859 was erroneous, and that 112.11 acres of land (74.56 of which are in dispute today) lay between the meander line of 1859 and the meander line of 1938. The Government claims that none of the disputed land was ever transferred from Government ownership. The defendants, who are owners of the lots abutting the 1859 meander line, claim the contrary.
On February 6, 1968, I ruled that a prior default judgment against the Secretary of the Interior in a quiet title action involving this land, Zager v. Udall, C.A. No. 65-C-171 (E.D.Wis.1966), was not res judicata against the United States. United States v. Zager, 280 F. Supp. 877 (E.D.Wis.1968). Subsequently this case was tried before me on the merits. In this opinion, which represents my findings of fact and conclusions of law in accordance with Rule 52 *986 of the Federal Rules of Civil Procedure, I find for the defendants.

I. THE FACTS
The Surveys and the Land. In 1859 William E. Daugherty, a deputy surveyor under Government contract, subdivided Township 38 and meandered the several lakes within it.[1] On the basis of Mr. Daugherty's notes an official Government plat was drawn up indicating the various bodies of water and dividing the land into lots. The plat of 1859 indicates that Lake Julia comprised roughly one-third of Section 7 of Township 38. Another third of the section was subdivided into four lots designated 1, 2, 3, and 4, each shown to abut a portion of Lake Julia's shore line.

It was further indicated that Lot 1 consisted of 40.60 acres, Lot 2 of 46.80 acres, Lot 3 of 56.60 acres, and Lot 4 of 63.05 acres, for a total of 207.05 acres.
In 1938 Section 7 was resurveyed by the Government and a new plat was drawn up and accepted in 1942. The new plat indicated that Lake Julia took up substantially less than a third of the section and that a substantial amount of land lay between the 1859 meander line and the 1938 meander line. This omitted land was in turn divided into five lots designated 5, 6, 7, 8, and 9. Lot 5 consists of 29.77 acres, Lot 6 of 22.96 acres, Lot 7 of 3.69 acres, Lot 8 of 4.09 acres, and Lot 9 of 51.60 acres, for a total of 112.11 acres. The total acreage of Lots 1 through 9 then is 319.16 acres, 112.11 of which were omitted from the 1859 survey. Stated in terms of percentages, the land omitted from the 1859 survey is 35.13 per cent of the total acreage of Lots 1 through 9. Alternatively, stated in terms of a ratio, the ratio of surveyed land to omitted land is roughly 2:1.
Defendants have not contested the accuracy of the 1938 survey, and photographs of Section 7 taken from the air attest to the fact that the 1938 meander line comports to reality. It is equally clear from the testimony that the shoreline of Lake Julia today is substantially *987 the same as it was in the mid nineteenth century. Thus, the discrepancy between the 1859 and 1938 surveys must be attributed to Mr. Daugherty. But if the error lay at Daugherty's feet, the Government produced little evidence as to the cause of the error. Thus, there is no evidence of fraud or of a "paper survey"; rather it is clear that a meander of Lake Julia was actually made by Daugherty. Nor can this be termed a simple case of incompetence, for as the Government stated in its closing argument, "there is no question but what the great percentage of his [Daugherty's] work was in fact accurate." On the other hand, error in a nineteenth century Government survey is anything but unusual. Indeed, one of the Government's expert witnesses from the Bureau of Land Management agreed on cross-examination with the statement that "there were just a fantastically large number of errors of different sizes and proportions in surveying of the meanders of lakes and streams at this time [1859]."
While it would be but conjecture to single out the cause for error in the 1859 survey, the land surveyed and the history of Government surveys in Wisconsin do offer some suggestions as to what might have happened.
"There are several reasons why meandering was loosely done. In the first place surveys were rushed to completion to prevent timber trespass. The report of the Surveyor General for the Wisconsin district to the Commissioner of the General Land Office states that in many places the timber was the most valuable consideration, and that the government would be unable to dispose of those lands which had been logged before the survey. The surveying crews were rushed to keep ahead of timber trespassers who operated along driveable rivers.
"Wisconsin surveys were supervised by a Surveyor General located at Dubuque, Iowa. It is a long distance from Dubuque to the northern part of our state. Tote roads were the thoroughfares for the greater part of the distance. Inspection was naturally more lax than it would have been if the district office had been located within the state.
"The shorelines of many lakes were overfallen with trees and brush making traversing difficult. Hence the surveyors kept their line back some distance from the shore to insure good going. If they encountered a marshy strip or bay they ran the meander line around such areas also, because they were of the opinion that timber was the only valuable consideration in the sale and purchase of the land. Since marshes were devoid of timber, they were shown as water.
"Peninsulas and points frequently escaped the attention of the surveyors because at the price of land at that time they were not worth much consideration.
"Then, too, there is evidence of `paper' surveying, where a surveyor, knowing the difference in latitude and departure between two adjacent meander posts, computed a traverse between them. As a result, a poor approximation of the actual feature was plotted on the government plat.
"It is also true that many of the surveys in our northern counties were completed at a loss to the contractors. Contracts let in 1860 and 1861 were fulfilled in 1863 and 1865 when money had depreciated fully fifty per cent.
"The surveyors are not to be held for these irregularities in general. It was the policy of the government to run meander lines in an approximate way. The land had little value, and the surveys were made as accurately as the price of the land warranted. It little mattered if a tract lay outside the meander line; the cost of running a traverse around the area might have exceeded its value. Leaving swamps outside was of little consequence, since they were usually devoid of merchantable timber, and timber was presumed to be the only asset. (Surveyor General's *988 Report to the Commissioner of the General Land Office, 1860.) The government was satisfied that the surveys were adequate enough for the purpose of conveying all of the land along the water courses, and the lands were patented without reservation.[2]
In the instant case the omitted land is to a large extent marsh land. Daugherty described the entire township as follows:
"Over one half of this Township is swamp, which is wholly unfit for cultivation. The soil on the dry land is very thin and poor, worth but little for purposes of agriculture. A large majority of the timber (except in the swamp) is * * * [?]  look [?] of a heavy growth."
In 1938, of the 417.74 acres resurveyed it was estimated that over half  227.50 acres  was swampland, and of the 112 acres of omitted land lying between the 1859 and 1938 meander lines in Section 7, it is stipulated that 43½ acres are swampland.
Chain of Title. Lots 1, 2, 3, and 4 of Section 7 were selected by Wisconsin along with other parcels under the Swamp Land Act of 1850, Title 43 U.S. C. § 981 et seq., and accordingly conveyed to the state by the federal government. In 1886, Wisconsin deeded Lot 1 to Tom Wall, and through mesne conveyances the title to Lot 1 today vests in Jean Otto and Donald E. Koten. In 1898, Lots 2, 3, and 4 were deeded by the state to William J. Neu and John Dohm. Title to Lots 2 and 3 now vest in Jean Otto and Donald E. Koten. In 1924, Lot 4, then owned by W. E. Wiedner, was subdivided and lakefront lots were sold. Title to these lots now vests in Kurt J. Reif, Ernest Bradford, and Florence Bradford. The title to the remainder of Lot 4 through mesne conveyance now vests in Harold Wesley Zager and Carol Jean Zager.
In 1933 certain portions of Northern Wisconsin became the Nicolet National Forest, and in conjunction with this the 1938 survey was undertaken. That survey, as has been noted, discovered that due to erroneous meandering in 1859, 112.11 acres of land in Section 7 were omitted in the original government plat. This omitted land was divided into Lots 5, 6, 7, 8, and 9 and claimed by the Government. In that over half of Lot 5 was swamp, title to that lot was reconveyed to Wisconsin under the Swamp Land Act. Kurt J. Reif obtained a patent to Lot 7 under the Color of Title Act, Title 43 U.S.C. § 1068. Ernest Bradford and Florence Bradford obtained a similar patent to Lot 8.
The United States now claims Lots 6 and 9 of Section 7 as public land not disposed of through any conveyance. The defendants claim that title to Lots 6 and 7 vested in the State of Wisconsin in the nineteenth century when Lots 1, 2, 3, and 4 were originally given to the state under the Swamp Land Act, and that accordingly title now vests in them through mesne conveyances.

II. THE LAW
As a general rule when the United States patents land "according to an official plat of survey, showing meander lines along or near the margin of a body of water, the plat is to be treated as part of the conveyance and the water itself [as opposed to the meander line in the survey] constitutes the boundary."[3] Further, a "resurvey by the United States after the issuance of a patent does not affect the rights of the patentee * * *."[4]
It is conceded by the Government that if this general rule is applicable to the instant case, then judgment must be given to defendants. This follows in that if the general rule is applicable when the United States conveyed Lots 1 *989 through 4 in Section 7 to Wisconsin, the lots it conveyed were bounded by Lake Julia as opposed to the meander line on the 1859 plat. The Government, however, maintains that when Lots 1 through 4 were conveyed, title was given for the land up to the meander line because the instant case represents an exception to the general rule.
An exception to the rule is recognized "where * * * the facts conclusively show that no body of water existed or exists at or near the place indicated on the plat or where * * * there never was, in fact, an attempt to survey the land in controversy."[5] The facts in the instant case, however, demonstrate just the opposite. Rather the Government relies on a related exception recognized in cases of "such gross and palpable error as to constitute in effect a fraud upon the Government."[6]
In dealing with the exception based on gross error, it is important that the adjective "gross" not be overlooked, for as indicated earlier when dealing with the Government surveys of the last century, error is to be expected. Indeed, the general rule is founded upon this expectation for the rule "evolved because of the difficulty surveyors had in following the edge or margin of projections of land and all the various sinuosities of the water line."[7] And because when these surveys were undertaken, often "the lands were of such little value, the locality so wild and remote, and the attendant difficulties so great that the expenditure of energy and money necessary to run the lines with minute regard to the sinuosities of the lake would have been quite out of proportion to the gain."[8] Thus, in deciding a question of gross error, attention must be paid to "the amount and proportion of acreage between the meander line and the shore,"[9] and this must be balanced with "the circumstances surrounding the original survey, and the type and comparative value of the land at that time."[10]
In 1960, Justice Fairchild[11] reviewed the various state and federal decisions on gross error and concluded:
"We have examined a number of decisions, including those herein cited, involving early surveys of wild land. In all those where a court has decided that the error in the meander line was sufficient so that the meander line would constitute the boundary, the error has involved a larger acreage than the 73.44 acres in this case. As noted in the Lakelands decision [Lakelands, Inc. v. Chippewa & Flambeau Imp. Co., 237 Wis. 326, 295 N.W. 919 (1931)], the 103.28 acres considered in the Brothertown case [Brothertown Realty Corp. v. Reedal, 200 Wis. 465, 227 N.W. 390 (1930)] appears to be the smallest area where constructive fraud has been found. In all such cases the acreage shown on the plat would have been an understatement of the true area by substantially more than one-third if the land conveyed had been held to run to the shore as the true boundary. Again, the 42 per cent understatement in the Brothertown case appears to be one of the smallest."[12]
*990 Aside from Brothertown, I am aware of no case involving an omitted area of less than 158 acres[13] in which gross error has been found, nor am I aware of any case involving less than 500 acres in which gross error has been found wherein the omitted land was not at least equal in size to the original plat acreage. Thus, in Walton v. United States, a case finding gross error and involving 323 acres of omitted land, United States v. Lane[14] was distinguished as follows:
"In United States v. Lane, the Supreme Court considered the substantial area test [and found no gross error] in an instance where the ratio of surveyed land to omitted land was between 2:1 and 11:1. In this case the ratio is almost 1:3."[15]
The Government, then, in the instant case is on tenuous ground, for the omitted land amounts to only 112.11 acres, involves an understatement of only 35.13 per cent,[16] and the approximate ratio of surveyed land to omitted land is only 2:1.[17] Looking at the land itself, while the Government has offered testimony to the effect that probably it would not have been difficult for Mr. Daugherty to have better meandered Lake Julia, it has offered nothing to refute Daugherty's conclusion that Township 38 was a remote, wild and wet land which in large part was practically worthless at that time. Balancing the amount of omitted land involved and comparing its size to the size of the surveyed lots and weighing this against the nature of the land and survey in 1859, I conclude that the Government has failed to bring forth a preponderance[18] of evidence demonstrating gross error.
NOTES
[1]  "Most of the government surveying in northern Wisconsin was done between 1830 and 1866 under the contract system. The land was first laid out in townships six miles square, which were later subdivided as nearly as possible into sections of 640 acres. When running the section lines, quarter corners were placed at each half mile mark. The quarter lines connecting opposite quarter corners were not run by the surveyors, however. After the section lines were run, lakes and rivers were meandered to furnish information for plotting them on the plat and computing the area of the upland to be charged for. Meanders consist of a course and distance traverse along the water course.

"After the surveyors had subdivided a given township and meandered the waters, they drafted a field plat of their work. They then turned their notes and the field plat in to the Surveyor General for acceptance. If the plat compared with the notes and there were no reason to believe that the work was incorrectly done, the survey was accepted.
"Quarter lines were then projected on the plat by draftsmen in the office. Where lands were made fractional by a meandered water course, the area abutting the lake or stream was subdivided into government lots. The draftsmen were required to use their judgment in arranging the lots in the most convenient and equitable form for both the purchaser and the government. After the lots were arranged, the areas were computed from the plat and the survey notes."
H. S. Tuttle, Title to Wisconsin Lakelands Not Shown on the Government Plat; paper presented before the Wisconsin Society of Engineers, Feb. 16, 1928, p. 3.
[2]  Id. at 4.
[3]  Jeems Bayou Fishing & Hunting Club v. United States, 260 U.S. 561, 564, 43 S.Ct. 205, 67 L.Ed. 402 (1923).
[4]  United States v. State Investment Co., 264 U.S. 206, 212, 44 S.Ct. 289, 68 L.Ed. 639 (1924).
[5]  Jeems Bayou Fishing & Hunting Club v. United States, 260 U.S. 561, 564, 43 S.Ct. 205, 67 L.Ed. 402 (1923).
[6]  Id.
[7]  Internal Improvement Fund of State of Florida v. Nowak, 401 F.2d 708, 716 (5th Cir. 1968).
[8]  United States v. Lane, 260 U.S. 662, 665, 43 S.Ct. 236, 67 L.Ed. 448 (1923).
[9]  Schultz v. Winther, 10 Wis.2d 1, 12, 101 N.W.2d 631 (1960). See also Walton v. United States, 415 F.2d 121, 129 (10th Cir. 1969), and Internal Improvement Fund of State of Florida v. Nowak, 401 F.2d 708, 718 (5th Cir. 1968).
[10]  Id.
[11]  Now Judge Fairchild of the United States Court of Appeals for the Seventh Circuit.
[12]  Schultz v. Winther, 10 Wis.2d 1, 13, 101 N.W.2d 631, 639 (1960).
[13]  French-Glenn Live Stock Co. v. Springer, 185 U.S. 47, 22 S.Ct. 563, 46 L.Ed. 800 (1902).
[14]  260 U.S. 662, 43 S.Ct. 236, 67 L.Ed. 448 (1923).
[15]  Walton v. United States, 415 F.2d 121, 124 (10th Cir. 1969).
[16]  Several different methods of calculating a percentage have been advanced by the parties. The method I use  dividing the sum of the omitted land acreage and the acreage as shown on the original plat into the omitted land acreage  is that which is used in Schultz.
[17]  I use the original plat acreage of Lots 1 through 4 for the surveyed land acreage. It should be noted, however, that some use for comparison the total acres surveyed, i. e., Daugherty surveyed all of Township 38, or the total acreage conveyed in the Government patent. Use of these figures would, of course, give defendants an even stronger case.
[18]  The parties are in disagreement as to the Government's burden of proof in this case, defendants asserting it to be "clear and convincing," the Government arguing it is only a "preponderance." As the Government has failed to meet the lesser burden, I do not decide the issue.
