J. CURTISS BROWN, Chief Justice.

This is an appeal from the judgment of the trial court in a trespass to try title suit in which William V. and Manilla Swank McBride (appellees or the McBrides) were awarded title to and possession of two five-acre tracts of land in Galveston County. The McBrides claimed the land by adverse possession from Lois Dobbin Auchterlonie and Iona Marie Marsh Dobbin, who are the sole surviving heirs of the record owners, Thomas M. and R. Alma Dobbin (appellants or the Dobbins). In three points of error the appellants contend there is insufficient evidence to support the trial court's finding of a peaceful and adverse possession by the appellees, and the trial court erred in quieting title in the appellees. We find no error and affirm.

The tracts of land in question are lots 1 and 1-A in block 72 of the San Leon Farm Home Tracts in Galveston County. The five-acre lots are contiguous and are located in the middle of a 300-acre pasture. The 300-acre pasture is enclosed on three sides by a barbed-wire fence with wooden posts. The pasture is enclosed on the fourth side by a natural bayou. The fence was built around 1956 by Manilla Swank McBride and her first husband, Mr. Swank. After building the fence the Swanks began grazing approximately 70 head of cattle in the pasture, including the lots in question, until Mr. Swank's death in 1963. After Mr. Swank's death Manilla began leasing the entire pasture to third parties for the grazing of cattle. This leasing continued after her marriage to William McBride in 1966 and until the time the McBrides brought a trespass to try title suit against the appellants claiming the land by adverse possession based upon fencing the land and the grazing of cattle. Although not specified in the appellees' petition, both sides concede the action was brought under the ten year statute of limitations. Tex.Rev.Civ.Stat.Ann. art. 5510 (Vernon 1958).

In their first two points of error the appellants contend there was insufficient evidence of a peaceful and adverse possession. In particular appellants argue that the use of the land exclusively for grazing will not support the trial court's finding of adverse possession by the appellees.

One who seeks to establish title to land by virtue of the statute of limitations assumes the burden of proof upon the issue, and the proof must be clear and satisfactory. Orsborn v. Deep Rock Oil Corp., 153 Tex. 281, 267 S.W.2d 781 (1954). One of the elements of adverse possession on which appellees bore the burden of proof was the claim of right. Since there is no evidence in the record that appellees gave actual notice of their claim to the heirs of Thomas and Alma Dobbin, appellees' adverse possession must be based on open and visible acts which are so clear and unambiguous that knowledge on the part of the record owner must be presumed. Stafford v. Jackson, 687 S.W.2d 784, 788 (Tex.App. — Houston [14th Dist.] 1985, no writ).

It is well settled that the mere grazing of land incidentally enclosed as a result of the construction of fences built for another purpose does not constitute possession that will ripen into title by limitations; the claimant who relies upon grazing only as evidence of his adverse use and enjoyment must show as part of his case that the land in dispute was designedly enclosed. Osborn v. Deep Rock Oil Corp., 267 S.W.2d at 785; Jamail v. Gene Naumann Real Estate, 680 S.W.2d 621, 626 (Tex.App.-Austin 1984, writ ref'd n.r.e.). Thus, where land has been designedly enclosed and used continuously for grazing purposes for the statutory period, such use is sufficient notice of hostile claim to support a claim of adverse possession. Mixon v. Clark, 518 S.W.2d 402, 406 (Tex.Civ.App.-Tyler 1974, writ ref'd n.r.e.). In determining whether the land was incidentally or designedly enclosed, we must look to the whole fencing pattern and its use as well as other facts and circumstances. Id.

The evidence shows that the fence enclosing the land claimed by appellees was constructed in 1956 by Mrs. McBride and her first husband for the purpose of grazing cattle, and it has been so used ever since. The fence, which is composed of four strands of barbed-wire attached to wooden posts, has been replaced completely by the appellees twice following major hurricanes. One of the appellees' lessees testified that the fence has been in place since 1956, is highly visible and has always been used as an enclosure for grazing cattle.

The appellees have shown that the land claimed was designedly enclosed for the purpose of grazing cattle and as such have met their burden of proving an open and hostile use required to establish title by adverse possession. Stafford v. Jackson, 687 S.W.2d at 787; Mixon v. Clark, 518 S.W.2d at 406. Cf. Orsborn v. Deep Rock Oil Corp., 267 S.W.2d at 786, in which the evidence was held insufficient to establish title by adverse possession where the claimants had no part in the construction of the fences enclosing the land claimed nor did the record disclose for what purpose the fences were built, and the land was used only occasionally for grazing. Appellants' first two points of error are overruled.

In their third point of error appellants allege the trial court erred in quieting title in the appellees. Appellants first argue that Tex.Rev.Civ.Stat.Ann. art. 5511 (Vernon 1958) precludes appellees' claim of adverse possession. This statute provides that a tract of land owned by one person and entirely surrounded by a tract owned, claimed or fenced by another shall not be considered adversely possessed by the claimant unless the interior land is separated from the circumscribing land by a fence.

Article 5511 was enacted in 1891 to protect owners of small tracts when their tracts are entirely surrounded by a tract or tracts owned or claimed by another. Richey v. Miller, 142 Tex. 274, 177 S.W.2d 255, 258 (1944). Since its enactment there have been very few court decisions construing article 5511. However, the record shows that no single owner "owned" all the property surrounding the lots in issue as contemplated by the statute since lots 2 and 2-A lying immediately to the east of lot 1-A were not purchased by the appellees until 1978, which was after title by limitations matured. The testimony of Mr. McBride makes clear that prior to his purchase of lots 2 and 2-A he recognized Mr. Cullinan to be the owner; thus at least these two lots preclude the applicability of article 5511 as they were not "owned" within the meaning of the statute. In addition, appellee did not seek a finding by the court that appellant owned or claimed all surrounding lands, thus this is an implied fact issue made to support the judgment of the trial court. Tieuel v. Southern Pacific Transportation Co., 654 S.W.2d 771 (Tex.App.-Houston [14th Dist.] 1983, no writ). We therefore hold that article 5511 does not apply since the land in question is not entirely surrounded by land owned by the appellees. See Nagel v. Hopingardner, 464 S.W.2d 472 (Tex.Civ.App.-Houston [14th Dist.] 1971, no writ). Having little case law guidance on this issue, we recognize that other applications of article 5511 are not foreclosed by our interpretation.

Appellants also contend that Mr. McBride's testimony that he offered to purchase the lots in 1978 or 1979 is an acknowledgment of title in another which defeats any limitation claim the appellees may have had as a matter of law. Appellants rely on Wolgamot v. Corley, 523 S.W.2d 491 (Tex.Civ.App.-Waco 1975, writ ref'd n.r.e.), to support this contention. However, the court in Wolgamot further refines this rule of law by stating that the possessor's acknowledgment of title in another when made before the completion of the bar by the statute of limitations will defeat the limitation. Id. at 495. The record shows that appellees' adverse possession began in 1956 with the fencing of the land for grazing cattle, thus limitation title matured under the ten year statute prior to appellees' offer in 1978 or 1979; therefore the recognition or acknowledgment of appellants' title would not destroy the limitation title which had previously matured. See Collins v. Ivey, 531 S.W.2d 357 (Tex.Civ.App.-El Paso 1975, writ ref'd n.r.e.). Appellants' third point of error is overruled and the judgment is affirmed.