delivered the opinion of the Court.
This suit was instituted by petitioner, the state of Texas, in behalf of itself, Yoakum County, and political subdivisions of the county, against respondents, J. A. Whittenburg, Jr., and others, for the collection of ad valorem taxes for the years 1942 to 1949 inclusive, alleged to be due and unpaid on account of respondents’ ownership of mineral interests, referred to herein as oil payments, in three sections of land in Yoakum County. The trial court granted petitioner’s motion for instructed verdict and rendered judgment for petitioner against respondents, J. A. Whittenburg, Jr., and Roy R. Whittenburg, as trustees of the J. A. Whittenburg Estate, for $20,229.70, against a number of respondents described as Geo. A. Whittenburg Heirs for $10,-038.72, and against several respondents described as beneficiaries of the Mattie Hedgecoke Estate for $1,428.80. A substantial part of the judgment is for penalties and interest.
The Court of Civil Appeals, holding that the evidence raises an issue or issues of fact as to the validity of the valuation and assessment of the oil payments, reversed the judgment of the trial court and remanded the cause. 259 S.W. 2d 270.
On July 20, 1937, J. A. Whittenburg, Jr., and Roy R. Whittenburg, executors of the estate of J. A. Whittenburg, and others of the respondents executed to Denver Producing and Refining Company as lessee two oil and gas leases, one of Surveys Nos. 831 and 863, and the other of Survey No. 830, Block D, John H. Gibson ,grantee, in Yoakum County. Each of the leases reserved to the lessors as free royalty the equal one-eighth part of all *208oil produced and saved from the leased premises, and a one-eighth gas royalty; and each of the leases reserved also to the lessors an additional one-fourth of the minerals to be produced by the lessee, free of cost or expense to the lessors, and delivered to the credit of the lessors in the same manner as provided for delivery of the one-eighth royalty, “until lessors, their heirs, representatives and assigns shall have received from the net proceeds derived from the sale of said additional one-fourth interest reserved a sum of money equal to $1,250.00 per acre for each and every acre in the above described lease.” Survey 830 being a school land section sold by the State with reservation of the minerals, the lease of that survey provided that the lessee should pay to the State of Texas its share of the consideration and make other payments in accordance with the requirements of the Relinquishment Act.
The valuation for taxation of the oil payment of $1,250.00 per acre, payable out of the one-fourth interest in the minerals, admittedly an interest in land and taxable as such, is the subject matter of the controversy herein. Oil was soon produced under the leases. The payments from production were regularly made and full payment of the $2,400,000 measuring and limiting the reservation of the one-fourth interest was completed early in 1949.
Of the $2,400,000 payable under the reservation, $2,000,000 was payable to the respondents. During the years 1938, 1939, 1940 and 1941, the respondents received the sum of $284,093.56, leaving unpaid and remaining due thereon the sum of $1,715,-906.44. The remaining unpaid portion of the oil payment, the percentage this portion bore to the whole payment, rounded to even figures, and the assessed valuation for each of the years on the oil payment and the reversion is shown in the following table:
*209The State made a prima facie case of the validity of the assessed valuations by introduction in evidence of the official records. Article 7326, Vernon’s Annotated Civil Statutes; State v. Republic Natural Gas Co., Tex. Civ. App., 181 S.W. 2d 592, writ ref. w.m. The burden then rested on the respondents, if they expected to prevail, to go forward with proof which would meet the requirements of law for avoiding the valuation. In discharge of this burden, respondents contented themselves with introduction of certain records highlighting comparative values placed on the unlimited 1/8 royalty owned by them and on the reversionary interest owned by the lessee in the % of production out of which the oil payment was to be made. They offered no testimony whatever as to the market value in the years involved of any of the three property interests — the oil payment, the reversionary interest in the *4 of production, or the unlimited 1/8 royalty. Neither did they offer any testimony of the market value of, or the value assessed by the Boards of Equalization on any other like property in the county.
Article VIII, Section 1 of the Constitution provides that “Taxation shall be equal and uniform” and that all property “shall be taxed in proportion to its value, which shall be ascertained as may be provided by law.” By Article 7174, Revised Civil Statutes, 1925, the Legislature has directed that “real property shall be valued at its true and full value in money,” and by Article 7212 has directed boards of equalization to hear evidence touching the “market value or true value” thereof. Our courts have interpreted these provisions to mean that assessed valuations shall be based on “the reasonable cash market value” of property. Rowland v. City of Tyler, Tex. Com. App., 5 S.W. 2d 756.
Since the courts of this state, in common with the courts of other jurisdictions, early recognized that exact uniformity and equality of taxation was unattainable, Rosenburg v. Weeks, 67 Texas 578, 4 S.W. 899, 901; Cooley on Taxation, 4th Edition, Vol. 1, § 259, they have sought through the years to lay down certain rules by which the force of an attack on assessed valuations, duly fixed by boards of equalization, may be measured.
It is now well settled that the assessment of property for tax purposes is a quasi-judicial function of boards of equalization and that no attack on valuations fixed by such boards can or will be sustained in the absence of proof or fraud, want of jurisdiction, illegality, or the adoption of an arbitrary and fundamentally erroneous plan or scheme of valuation. State v. Houser, 138 *210Texas 28, 156 S.W. 2d 968, 970-971; Druesdow v. Baker, Tex. Com. App., 229 S.W. 493, 495. Moreover, when their official action is attacked it will be presumed that such boards discharged their duties as public agencies according to law and acted in good faith. Zachry v. City of Uvalde, Tex. Com. App., 42 S.W. 2d 417; Lubbock Hotel Co. v. Lubbock Ind. Sch. Dist., Tex. Civ. App., 85 S.W. 2d 776, no writ; Hinkson v. Lorenzo Ind. Sch. Dist., Tex. Civ. App., 109 S.W. 2d 1008, writ dism.
While it has been held that a grossly excessive valuation may, in law, be sufficient to establish such fraud or illegality as to render a valuation void, Johnson v. Holland, 17 Texas Civ. App., 210, 43 S.W. 71, writ denied; City of Sweetwater v. Baird Development Co., Tex. Civ. App., 203 S.W. 801, no writ; Simkins v. City of Corsicana, Tex. Civ. App., 86 S.W. 2d 792, no writ; Howth v. French Ind. Sch. Dist., Tex. Civ. App., 115 S.W. 2d 1036; French Ind. Sch. Dist. v. Howth, 134 Texas 211, 134 S.W. 2d 1036, it is held with equal emphasis that mere errors in judgment or the fact that a trial judge of jury differs with the valuation fixed will not suffice as a basis for avoiding the board’s action. Simkins v. City of Corsicana, supra; Druesdow v. Baker, supra; State v. Houser, supra.
If a valuation fixed by a board of equalization is attacked on the ground of unlawful or arbitrary discrimination, it is not sufficient to show, comparatively, that in other isolated instances, property of equal or greater value than that in suit, was valued at less, Dallas County v. Dallas Nat. Bank, 142 Texas 439, 179 S.W. 2d 288, or even that other property was omitted from the tax rolls altogether, Sam Bassett Lbr. Co. v. City of Houston, 145 Texas 492, 198 S.W. 2d 879; City of Wichita Falls v. J. J. & M. Taxman Ref. Co., Tex. Civ. App., 74 S.W. 2d 524, writ refused ; Howth v. City of Beaumont, Tex. Civ. App., 118 S.W. 2d 350, no writ, except where the omission was the result of a deliberate and arbitrary plan or scheme to permit certain classes of property to escape their fair share of the tax burden, City of Houston v. Baker, Tex. Civ. App., 178 S.W. 820, writ refused. To prevail on the basis of unlawful discrimination it is not necessary that the taxpayer make a comparative showing with all other property in the county, Dallas County v. Dallas Nat. Bank, supra, but he must make at least a reasonable showing in that respect. Ibid.
When the attack is made because the board followed an arbitrary plan or scheme of fixing values, the taxpayer, to prevail, must show not only that the plan was an arbitrary and illegal *211one but also that the use of the plan worked to his substantial injury. Druesdow v. Baker, supra; Rowland v. City of Tyler, Tex. Com. App., supra; Lubbock Hotel Co. v. Lubbock Ind. Sch. Dist., supra, page 778, where it is said: “A mere theory may not be litigated * * *. There must be more than the mere adoption of a fundamentally wrong principle or method of taxation. The courts grant relief upon ‘the adoption of a fundamentally wrong principle or method, the application of which substantially injures the complainant.’ ”
The respondents have not contended on appeal that the valuation's fixed by the Boards of Equalization on the oil payment were grossly in excess of the reasonable cash market value thereof in any year, as indeed they cannot, since there is in the record no evidence of such value. What they do contend is that (1) the Boards adopted and followed an arbitrary and fundamentally wrong plan or scheme of valuing their oil payment at substantially the same value as was placed on their unlimited royalty, failing and refusing to take into consideration the factor of the diminishing value of the oil payment, and (2) the Boards unlawfully discriminated against them by failing, from year to year, to lower the value on the oil payment and raise the value on the reversion.
Basic to both of the foregoing contentions is respondents’ assertion that the Board failed and refused to follow this Court’s opinion in State of Texas v. Quintana Petroleum Co., 134 Texas 179, 133 S.W. 2d 112, 117, 128 A.L.R. 843, interpreting that opinion to require, in cases like the instant one, that the valuation on the oil payment must be decreased and the valuation on the reversion increased each year as payments are made. The holding in the Quintana case was made in response to an expressed fear by the State that if such oil payments were held to be taxable the State would lose its right to taxes on the reversionary interest of the lessee during the years when the oil payment was paying out, a loss it could never recoup. The Court simply set this fear at rest. It was not said in that case that, regardless of other factors and considerations affecting reasonable cash market value, boards of equalization would be required each year to place a diminishing value on the oil payment and an increasing value on the reversionary interest. It was said only that, assuming continued production, the oil payment would become less valuable and the reversion more valuable as payments were made and that “these facts must be taken into consideration” in valuing such interests.
*212Apart from the single circumstance that the assessed valuation of the oil payment was not decreased and the assessed valuation of the reversion was not increased each year, a circumstance which, standing alone, would not raise a fact issue that the Board failed and refused to consider the factor mentioned in the Quintana case, there is no evidence in the record that the Board failed to consider it. On the contrary, the testimony of Bert Bartlett, a deputy tax assessor-collector during the years 1942, 1943, and 1944 and at the time of the trial is positive that the factor was considered along with a number of other factors such as amount of reserves, allowables, the price of oil and the length of time required for the oil payment to pay out. These factors were equally as important as the factor mentioned in the Quintana case in determining the reasonable cash market value of the oil payment and of the reversion, and under this record, which is devoid of proof, we have no way of now knowing whether the ultimate valuations fixed by the Board were illegal, arbitrary or discriminatory.
Irrespective of the absence of evidence to show failure by the Boards to consider the factor mentioned in the Quintana case, respondents nevertheless contend that the Board acted arbitrarily and illegally by assigning to the oil payment substantially the same value as was assigned to their commensurate unlimited royalty. They themselves admit that this was not true for some of the years involved, as, for instance, they say in their brief that in 1948 “the one-fourth oil payment was valued nearly 20% more than if it had been an unlimited royalty.” It would be indeed a strange rule, the application of which would result in striking down the assessed valuations for the years 1942 to 1946, inclusive, when the value placed on the oil payment was substantially the same as the value placed on the unlimited royalty and would leave standing as valid the assessed valuation for 1948 when such value was fixed at 20% more than the unlimited royalty. But dealing alone with the years 1942-1946, a period during which the record does show that the oil payment was assessed at substantially the same figure as a commensurate unlimited royalty, the record is devoid of any proof of prejudice or injury to respondents.
Under the late decisions of the courts of this state, some of which are cited above, it is recognized that to obtain relief from a valuation fixed according to some arbitrary rule the taxpayer must show substantial injury. One of the latest cases on the subject is Montgomery County v. Humble Oil & Ref’g. Co., Tex. Civ. App., 245 S.W. 2d 326, 335. In that case proof on the trial *213showed and the trial court found, that whereas the Board of Equalization had assessed all non-mineral property in Montgomery County at 10% of value it had arbitrarily assessed Humble’s mineral properties at 33-1/3% of their value, as fixed by the Board’s own witnesses at the hearing conducted by the Board. Humble sought and obtained from the trial court an injunction against collection of its taxes on the ground that the admittedly arbitrary nature of the assessment voided the same without the necessity of proof of injury. The trial court upheld this contention, declining to require that Humble make proof on the trial that the assessed valuation was in fact in excess of 10% of value and declining to permit the State to offer evidence that the valuation was not, in fact, in excess of 10% of the reasonable cash market value of the properties. The Court of Civil Appeals reversed the judgment and dissolved the injunction, holding that there could be no proof of injury in the absence of evidence that Humble’s property was, in fact, valued at more than 10% of its market value, and saying: “We think the fact that in the hearing before the Board of Equalization there was no issue or contest over the proposed valuations of the mineral properties as being about one-third of the actual market value of the properties cannot be any reason for holding that in a suit for injunction Humble did not have the burden of showing that it had been injured by the acts of the Board complained of, and that such proposed valuation in fact was about one-third of the actual market value of its mineral property.” While we stamped Humble’s application for writ of error “Refused, no reversible error,” the record reflects that the foregoing question was the only one presented in the application and we could hot have refused it if we had not agreed that the burden rested on Humble to make proof of injury by offering evidence of market value and thereby showing that the value assessed on its properties was in excess of 10%. It is not perceived how any sound basis could exist for applying a different rule in a suit by the State for the collection of taxes.
Respondents offered no evidence in this case showing the respective market values of the oil payment and the unlimited royalty. It may well be that the unlimited royalty was grossly undervalued, in which event the arbitrary placing of the same value on the oil payment benefited rather than injured respondents.
Even if it were conceded that the assessment on the unlimited royalty was based on its market value and that the limited oil payment was, as a matter of law, substantially less valuable, *214there would yet be lacking any proof of injury. While assessments are made against property and not against persons and boards of equalization are directed by Article 7174 to assess each property interest separately, judicial relief is granted only to persons to relieve them of unjust and disproportionate tax burdens that grow out of illegal and discriminatory assessments. A taxpayer cannot show that he has been subjected to discrimination by an arbitrary and illegal assessment, or that by virtue thereof he is being required to bear an unjust or disproportionate share of the tax burden, by proof that separate property interests of different market values owned by him are assessed at substantially the same value, or that separate property interests of equal market values owned by him are assessed at substantially different values. He can only make the necessary showing by proof that his property interests are assessed substantially higher than property interests of equal or greater market value owned by others. This is clearly the rule laid down in Missouri, K. & T. Ry. Co. of Texas v. Hassell, 57 Tex. Civ. App., 522, 12S.W. 190, writ denied, cited with approval by the Supreme Court of the United States in Baker v. Druesedow, 263 U.S. 137, 44 Sup. Ct. 40, 68 L. Ed. 212.
Much of what has been said applies with equal force to the contention that the high valuation placed on the oil payment and the failure to lower it from year to year compared with the low valuation placed on the reversion and the failure to raise it from year to year establishes unlawful discrimination. Here, again, no testimony of the respective market values of the two property interests was offered. From the table set out above it will be noted that in January 1942, only 14% of the oil payment had been paid in the preceding four years. At that rate of payment it would have appeared to the Board, assuming continued production, that it would require 28% years to discharge the full obligation, or 24% years to discharge- the balance then remaining unpaid. Reduced allowables or a drop in the price of oil would have lengthened the pay-out period. The estimated reserves may not have been such as to support a belief that the oil remaining at the end of the pay-out period would be of substantial value. Moreover, the owner of the reversionary interest had an investment on which it could expect no return of any character during the long pay-out period. In addition, the oil payment was to be delivered free of production costs and before the lessee could realize any return from the % interest after it vested, it was first necessary that it recoup the cost of producing the oil payment. All of these were important factors in determining the market value of the reversionary interest in 1942, and for aught *215we know all of them were considered by the Board of Equalization. All of them also existed, albeit in somewhat lesser degree, in 1943, 1944, 1945, and 1946. The testimony of Mr. Bartlett is that the Boards tried to ascertain the market value of the reversion and to place on it an assessed valuation at the same percentage used in assessing other property. There is no testimony that they did not do so.
Neither is there any proof of injury to respondents from the disparity in these values. The reversion may have been grossly undervalued. If it was, this fact alone would not entitle the respondents to have the assessed valuations placed on their oil payment declared void.
We think the Court of Civil Appeals was in error in holding on this record that respondents were entitled to go.to the jury on the foregoing issues. We are also convinced that the Court erred in reversing the trial court’s judgment on the other ground discussed in its opinion.
Petitioner sued a number of respondents as the heirs of George A. Whittenburg for the taxes levied against the interest in the oil payment owned by those heirs or by the George A. Whittenburg Estate, and sued several of the respondents as beneficiaries of the Mattie Hedgecoke Estate for the taxes, levied against the interest in the oil payment owned by that estate, and personal judgment was rendered against the respondents, who are the heirs of George A. Whittenburg, jointly and severally, and personal judgment was rendered against the beneficiaries of the Mattie Hedgecoke Estate jointly and severally. Complaint is made that each of the heirs of George A. Whittenburg is or was the owner of only an undivided interest and not of the entire interest owned by all of the George A. Whittenburg heirs, and that each of the beneficiaries of the Mattie Hedgecoke Estate was the beneficiary of only an undivided interest, and that each should have been held responsible only for the tax on his undivided interest.
It seems that Bashara v. Saratoga Independent School District, 139 Texas 532, 163 S.W. 2d 631, would support this contention but for the fact that the assessments were made in the manner in which the property was rendered. The record shows that the interest or property jointly owned by the George A. Whittenburg heirs was rendered and assessed in the name of George A. Whittenburg heirs, and tax receipts show that payments were made by and for the George A. Whittenburg heirs of *216the taxes on the surface and royalty owned by them and assessed is the same way against them as heirs. The same is true with respect to the rendition and assessment of the interest owned by the Mattie Hedgecoke Estate and of the receipt to that estate for the taxes in the year 1948 on its surface and royalty interests. It was stipulated by the parties and found by the trial court that the estate of Mattie Hedgecoke was distributed among the respondents who were sued as beneficiaries of that estate, and that the property so distributed to them had a value in excess of the taxes claimed against them.
In our opinion there was no error in rendering personal judgment jointly against the heirs of George A. Whittenburg for the taxes for the years 1942 to 1949 inclusive, and no error in rendering personal judgment jointly against the beneficiaries of the Mattie Hedgecoke Estate for the taxes for the year 1948. Denman v. State, Tex. Civ. App., 85 S.W. 2d 252; State Mortgage Corporation v. Ludwig, 121 Texas 268, 48 S.W. 2d 950 ; French Independent School District v. Howth, 134 Texas 211, 214, 215, 134 S.W. 2d 1036; Dallas Title & Trust Co. v. City of Oak Cliff, 8 Tex. Civ. App., 217, 27 S.W. 1036.
We have examined the other points of error which the respondents had before the Court of Civil Appeals and find no sufficient reason therein for reversal of the trial court’s judgment. Accordingly the judgment of the Court of Civil Appeals is reversed and the judgment of the trial court is affirmed.
Opinion delivered February 24, 1954.