majority">STEWART, Judge.

Appellee, Beckham Bates, has title to the minerals in land located on Beaver Dam Branch and Myra’s Branch of Rockhouse Creek in Letcher County. To the north and west of Beckham Bates’ property is an adjoining tract owned by his brother, Ralph Booten Bates, appellant herein. Still farther to the north is the property of the heirs of L. W. Fields.

The O. K. Coal Company, owned and operated by J. D. Banks, hereinafter referred to as Banks, obtained mineral leases from the above landowners and mined coal under these leases from 1955 to 1959. Under the terms of the lease with Beckham Bates, Banks was obligated to pay twenty cents per ton for the coal mined. Appellant, Ralph Booten Bates, and the Fields heirs leased their mineral rights to Banks for a royalty of twenty-five cents per ton for the coal removed. Banks also agreed to pay Beckham Bates five cents per ton for coal mined from the Fields heirs’ property and hauled through underground passageways of Beckham Bates’ property.

Banks conducted mining operations according to an engineering map prepared by one C. D. Lynch, hereinafter referred to as the Lynch Map. In order to calculate the royalties owed the different landowners, the Lynch Map was used to determine from whose property the coal was mined. The books and records of Banks, which the parties have stipulated as correct insofar as the Lynch Map is correct, indicate the following amounts of coal mined and royalties paid during the years 1955 through 1959:

Landowner Tons Mined Royalty Paid

Beckham Bates 39,634 I 7,926.97

Ralph Booten Bates 56,668 14,167.15

Fields Heirs 18,748 4,687.14

115,059 826,781.26

In addition, the books indicate that Beck-ham Bates received $937.40 as haulage fees for 18,748 tons of coal mined from the Fields tract and transported through Bates’ underground passageways.

Banks completed his mining operations in March of 1959, and never resumed them on the properties involved. A short time later, Beckham Bates leased his land to the David Sexton Coal Company. The beginning date of this lease and the amount of coal mined by the latter company do not appear in the record. Before this company took over the mine, however, Beckham Bates employed the Roy Crawford, Jr., engineering firm, hereinafter referred to as Crawford, to determine the amount of coal that had been mined by Banks and by a company which held the lease prior to Banks.

On May 20, 1960, the survey reported by Crawford disclosed an engineering mistake of 37 degrees made in the preparation of the Lynch Map. Thus the mine entry and coal *718workings shown by the Lynch Map on the Beckham Bates and Ralph Booten Bates properties are swung downward, when oriented with the Crawford Map, in an arc 37 degrees to the south of where the coal workings appear. Crawford then made a survey of the land south of the Beckham Bates tract, which is owned by the Collins and Johnson Mining Company, and also of the land owned by the Fields heirs. This survey was completed on December 15, 1960, and a map was prepared which is hereinafter referred to as the Crawford Map.

In July of 1961 Beckham Bates brought suit against Banks, Ralph Booten Bates and the Fields heirs for $400,000. The complaint alleged coal had been wrongfully mined from Beckham Bates’ land, and that the royalties in settlement therefor had been erroneously paid to Ralph Booten Bates and the Fields heirs.

The Fields heirs employed a mining engineer to inspect their property and, upon his recommendation, they entered into an agreed order with Beckham Bates and Ralph Booten Bates. In this order all the parties agreed that no coal had been mined from the property of the Fields heirs; and that of the 18,748 tons of coal for which royalties had been erroneously paid to the Fields heirs, 7,377 tons had actually been mined from the land of Ralph Booten Bates and 11,371 tons from the land of Beckham Bates. The Fields heirs thereupon made restitution to Ralph and Beckham Bates in the amounts of $1,659.20 and $1,705.65, respectively.

Thereafter, Ralph Booten Bates moved that the Lynch Map be stricken from the record as incompetent evidence. This motion was overruled and the parties agreed that the cause be submitted to the trial judge for an opinion and a judgment by the court. After making calculations, which are not questioned on this appeal, the circuit court ordered that Beckham Bates recover from his brother, Ralph Booten Bates, the sum of $6,109.60, and that Banks recover from Beckham Bates and Ralph Booten Bates the sums of $3,000 and $1,527.40, respectively, for erroneous payments made according to the Lynch Map.

Appellant on this appeal contends the judgment should be reversed because the trial court committed reversible error, first, by admitting and considering the Lynch Map as competent evidence and, next, in holding that the Crawford Map was decisive as to the amount of coal taken from the respective properties.

It is argued the Lynch Map should not have been used as a basis for any of the findings of fact of the trial judge, because it was not introduced by its maker, and it had not been signed or certified by him. The trial judge ruled the Lynch Map was admissible.

It was shown that C. D. Lynch, the maker of the map, became sick and incapacitated, that his testimony could not be taken, and that he died shortly after this litigation began. H. H. Smith, a licensed practicing engineer, with thirty years’ experience, testified that he was associated with Lynch in engineering work for many years; and that he recognized the map as the handiwork of Lynch. Smith was employed by Banks during the last year of his operations on the properties and Smith made postings on the map as the mining by Banks progressed. Banks testified he was guided in his mining operations solely in accordance with the Lynch Map.

The engineer who prepared the Crawford Map stated that the Lynch Map was used only as an aid in making tonnage calculations when it was actually impossible to survey due to the bad condition of the mine.

In 20 Am.Jur., Evidence, sec. 930, p. 783, it is stated:

“The proof of authenticity required preliminary to the introduction of an instrument in evidence need not be by direct proof. Authenticity of documentary evidence may be shown, so as to render it admissible in evidence, by *719indirect or circumstantial evidence— that is, by facts and circumstances from which the jury may infer the execution of the document.”

In the light of the facts and the applicable law we believe the trial court properly admitted the Lynch Map into evidence.

The parties by the execution of the agreed order conceded an engineering error of 37 degrees was made in the engineering map of C. D. Lynch, and that the parties were not correctly paid by Banks for the actual tonnage mined from the various properties. The Crawford Survey, insofar as the engineering error is concerned, has gone unchallenged. Ralph Booten Bates offered no evidence to refute the findings of the survey made by Crawford. This survey was properly authenticated by Roy Crawford, Jr., a registered engineer.

It is the contention of Ralph Booten Bates that the witnesses of Beckham Bates were unable to determine by actual survey the total tonnage mined by Banks. However, this is immaterial inasmuch as the parties stipulated 115,050 tons were actually mined and removed from all of the properties. The only question the trial court determined should be resolved is the extent to which Ralph Booten Bates has been unjustly enriched at the expense of Beckham Bates.

It is established by the survey of Crawford that part of the coal thought to have been mined from Ralph Booten Bates’ property, and for which he received payment, was in fact taken from the property of Beckham Bates, except for that portion removed from Ralph Booten Bates’ and Beck-ham Bates’ property for which the Fields heirs received payment. Since the Fields heirs have made restitution to the various parties, there is left for determination only the question of the amount of coal mined from Beckham Bates’ property for which Ralph Booten Bates received payment.

Based upon the actual tonnage figures of the Banks records, the correctness of which is not in dispute, and the survey made by Crawford, which is not under attack, it became a matter of arithmetical computation to determine the extent of unjust enrichment of Ralph Booten Bates at the expense of Beckham Bates and Banks.

The trial court found that only 33,496 tons of coal were mined from Ralph Booten Bates’ property and that, on this basis, he should have been paid only $8,374.00. This was, according to the Crawford Survey, an overpayment to him of $7,452.00. The trial court further found that 30,548 tons of coal owned by Beckham Bates were mined by Banks for which Ralph Booten Bates was paid $6,109.60. This is the amount the judgment decreed Ralph Booten Bates should pay Beckham Bates. The difference of $1,343.40 between $6,109.60 and the total overpayment to Ralph Booten Bates, plus an overpayment of $184 made by the Fields heirs to him, amount to $1,527.40. This is the sum the judgment awarded Banks.

We conclude the factual findings of the trial court, in respect to the payments due Beckham Bates and Banks, should not be disturbed, as we are of the opinion the evidence amply supports these findings.

Wherefore, the judgment is affirmed.

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