
361 So.2d 1248 (1978)
Daniel A. OLIVER
v.
MILLIKEN & FARWELL, INC., et al.
No. 12017.
Court of Appeal of Louisiana, First Circuit.
June 12, 1978.
Rehearing Denied August 31, 1978.
Writ Refused September 1, 1978.
Ashton L. Stewart, Baton Rouge, counsel for plaintiff-appellant.
Victor Sachse, III, R. Gordon Kean, Jr., Baton Rouge, Paul G. Borron, Plaquemine, Joseph W. Cole, Jr., Philip N. Pecquet, Port Allen, Gordon M. White, Gerald L. Walter, Jr., Baton Rouge, Felicien Y. Lozes, Nathaniel Phillips, Jr., New Orleans, Donald L. Peltier, Thibodaux, Stephen P. Dart, St. Francisville, counsel for defendants-appellees.
Before BLANCHE, COVINGTON and CHIASSON, JJ.
COVINGTON, Judge.
Plaintiff, Daniel A. Oliver, filed this suit on May 26,1969 against defendant, Milliken & Farwell, Inc., to determine the rights of the parties to the alluvion which had formed on the Mississippi River in front of their adjacent properties, which fronted on the river. Thereafter, Oliver joined as defendants all other property owners in front of whose properties this alluvion had formed, Davis (Willie, Ronald and Gerald), Devall Planting Company, Inc. (which is now Harry L. Laws and Company, Inc.), Joan Seidenbach, et al, Mrs. Ina Mae Morris, et al, and Ashland Plantation, Inc. This alluvion is known as Solitude Point, and as of the time suit was instituted, contained 4,293.74 acres. The real value of ownership in Solitude Point stems from the frontage on the Mississippi River, although many mineral leases have been granted by the several parties, and it has a present value also for mineral purposes. The evidence is that the lands of the riparian owners were confirmed in 1805 by the United States to the ancestors in title to the parties, and that this alluvion began to form in front of certain of these lands in 1805.
The trial court held that it was required to divide the alluvion equitably and rendered an interlocutory judgment on May 31, 1973. Oliver appealed the interlocutory judgment on the grounds that it constituted instructions to the surveyor to fix the boundary lines in the division of the alluvion, and that this would cause Oliver irreparable injury in a final judgment when rendered.
This Court affirmed the interlocutory decree on February 11, 1974, reported at 290 So.2d 738 (La.App. 1 Cir. 1974), writ denied, 294 So.2d 549 (La.1974), holding that:
"Viewed as a whole, the frontage to frontage method would produce the fairest results for all the riparian owners in this case."
*1249 The trial court, after affirmation of its interlocutory judgment, and denial of writs by the state Supreme Court, proceeded by ex parte order dated September 4, 1974, to appoint Brown & Butler, engineers, to survey the alluvion in order that a division of this alluvion could be made among the several riparian owners.
This aspect of the instant case commences with this order directing the court-appointed engineers to allocate the alluvion among the several riparian owners on the following basis:
"(a) Frontage to Frontage as defined in Hogue, 241 La. 407, 129 So.2d 194 (1960).
(b) The original frontage line to be determined as the bank lines of maximum westward recession of the Mississippi River reached by the River from 1836 to the present date as recorded with the 1836 land survey and subsequent river surveys. This original frontage line follows with the meanders recorded in the 1836 land survey field notes from section 5 through section 16; thence with the bank line of maximum westward recession as recorded with the official Mississippi River Surveys to the lower end of the lands involved in this suit.
(c) Each owner's proportionate amount of that original frontage shall be his or its pro-rata share of the present frontage; the present frontage shall be determined by an actual survey of the frontage as it now exists."
After lapse of a period of time, the surveyor carried out the order of the trial court. The surveyor's map, dated November 30, 1976, and the surveyor's report, dated December 10, 1976, were annexed to and made part of the final judgment of the district court, viz:
"It is therefore the judgment of this Court that the division of accretion (alluvion) be made in accordance with the map and report herewith attached."
The judgment also ordered that costs be assessed as proportionately computed, and taxed the surveyor's fee as part of the court costs.
A new trial was applied for by motion of defendant Davis and plaintiff Oliver; it was granted, but limited to the method of division used by the surveyor to arrive at the allocation of the alluvion, and the computation and assessment of the costs.
On the hearing for a new trial, the district court determined that the engineers had followed the orders of the Court, except for the allocation of court costs, and signed a judgment to that effect dated November 29, 1977, from which judgment defendant Davis and plaintiff Oliver have appealed.
The primary contention of both appellants is that the surveyor failed to follow the trial court's order, which we have set out above, in allocating the alluvion to the respective riparian owners.
The legislature has early established by law an aleatory relationship between the State and owners of the soil situated on the edge of a river or stream, so that by chance either may gain or lose. LSA-C.C. arts. 509, 510. If alluvion is formed in front of the property of more than one riparian owner, it is to be divided between or among them as the case may be. LSA-C.C. art. 516. In the event additional alluvion is formed by accretion in front of another riparian property, of course, a different allocation may be made. The rule in Jones v. Hogue, 241 La. 407, 129 So.2d 194 (1960), is not a fixed formula applicable to all situations. The Supreme Court made this clear when it stated:
"In sum, when alluvion formed in front of the estates of riparian owners is to be divided, two objects, insofar as possible, are to be attained: (1) Each owner should receive a fair proportion of the area of the alluvion, and (2) each should receive a fair proportion of the new frontage on the water. Because of the varying conditions which obtain in different cases, no one method of effecting a division can be prescribed which will not in some instances result in substantial inequities. The courts can therefore do no more than take each case as it is presented and order an apportionment by the method which will most nearly attain these two objects and do justice between the parties to the particular case."
While when this case was first before the trial court, intermediate appellate court and state supreme court, they were in a position to argue for their favorite formula: frontage-to-frontage, frontage-to-acreage, a combination of those two formulas, or some entirely new formula, for the allocation of Solitude Point, the parties are no longer in such a position. The law of this case is that *1250 the appropriate formula to apply is "frontage-to-frontage."
The frontage-to-frontage formula, although discussed in the Hogue case, was ultimately found not to be applicable to those particular facts. The formula is clearly stated in the old case of Newell v. Leathers, 50 La.Ann. 162, 23 So. 243 (1897):
"What is of consequence is the extent of the old frontage of the tracts on the water course, and from this is to be determined the extent of the new frontage on the water course. This excludes the idea of a proportionate area or acreage system of division between the several tracts fronting on the alluvion to be divided. Each proprietor of the original tracts takes the quantity of alluvion that may be between the lines of his old frontage on the water course, measured forward to the new frontage. The lines by which the new frontage is reached may be parallel, or convergent or divergent, according as the extent of the newly-formed water line may be the same in the one case, or less in the other, or greater in the third, than the ancient water line of the tracts."
As stated before, the district court in the earlier stages of this litigation used the "frontage-to-frontage" formula; this court affirmed; and our Supreme Court denied writs. Messina v. Michael, 324 So.2d 837 (La.App. 1 Cir. 1975), writ denied 326 So.2d 381 (La.1976), held that a division of alluvion allocating the new frontage on the basis of the old frontage was equitable and harmonious with the Hogue principles.
Consequently, the argument of the appellants that the division by the frontage-to-frontage formula gives each substantially less acreage is only an attempt to reargue the equities in an effort to persuade this Court that the division of Solitude Point should have been with regard to some other formula.
As the various maps filed in evidence indicate, at the time of the institution of this suit, the alluvial deposit known as Solitude Point was attached to the southerly portion of Section 5 and to Sections 6 through 20, Township 6 South, Range 12 East, West Baton Rouge Parish, Louisiana. In preparing the map showing the division of the alluvion, the engineering firm appointed by the district court to perform such work was required by the court to determine the "original frontage line" of the riparian properties. Insofar as the properties located in the northerly portion of Solitude Point are concerned, the "original frontage line" was decreed by the court to correspond to the 1836 governmental bank line survey. The map of survey, which was approved by the district court, discloses that the surveyor determined the subject line to be that frontage to which alluvion was presently attached. Properly, he did not include in the original frontage line the northerly portion of Sections 5 or 4, to which alluvion had been attached in 1836, but both of which had completely eroded away at the time this suit was instituted. It seems to us to be quite clear from the Hogue case, as well as the previous opinion rendered by this Court in the present matter, that the division of alluvion among the several riparian owners is to be made as the alluvion existed at the time the division was sought, and not as it may have existed at some earlier time. Only that portion of a riparian owner's frontage to which alluvion was attached when the allocation of alluvion is sought is to be considered in determining the extent of the owners' frontage lines pursuant to Article 516 of the Civil Code.
Article 516 is applicable where alluvion is formed in front of the property of several owners. The Article provides:
"If an alluvion be formed in front of the property of several riparian proprietors, the division is to be made according to the extent of the front line of each at the time of the formation of the alluvion."
This article must be construed consistently with LSA-C.C. art. 509:

*1251 "The alluvion belongs to the owner of the soil situated on the edge of the water. . . ."
The alluvion to be divided can only be that which has been formed by accretion to the existing frontage at the time division is sought. Frontage which has disappeared, such as in Section 4 and the northerly portion of Section 5, can not be considered in allocating alluvion in the instant case. The district court, in reaching its decision embodied in the May 31, 1973, judgment, and this court in affirming said judgment, followed this interpretation. Paragraph (b) of said judgment refers to Section 5, part of which remains, but does not refer to Section 4, which no longer exists.
From a reading of the testimony of Harvey Theriot, who actually surveyed the property in question and allocated the alluvion as an employee of the engineering firm appointed by the district court to perform such tasks, and a comparison of his report with the district court's order of May 31, 1973, we find, as did the trial judge, that the surveyor complied with his order in allocating the alluvion. Each riparian owner's alluvion frontage on Solitude Point was computed using the same percentage, determined by dividing his 1836 survey frontage length by the total length of the 1836 survey and maximum westward recession of the subject properties.
Accordingly, we find that the 4,293.74 acres in the alluvion known as Solitude Point shall be divided in accordance with the annexed "Map Showing Division of Accretion on Solitude Point in Accordance with Judgment of the 18th Judicial District Court, Dated May 31, 1973, prepared by Brown & Butler, Consulting Engineers, Baton Rouge, Louisiana, dated November 30, 1976," which division by acreage is as follows:


Daniel A. Oliver                   -  768.48 acres
Milliken & Farwell, Inc.           - 2314.26 acres
Ashland Plantation, Inc.           -  446.06 acres
Mrs. Ina Mae Morris, et al         -  218.54 acres
Devall Planting Company, Inc.      -  380.80 acres
 (Harry L. Laws & Co., Inc.)
Joan Seidenbach, et al             -  112.01 acres
Willie Hugh Davis, et al           -   53.59 acres
                                     _______
                                     4293.74

The division by frontage is as follows:


                             Original
                          Frontage, 1836      New Frontage
Daniel A. Oliver           6,776.28'             9,521.76'
Milliken & Farwell,
 Inc.                      6,430.81'             9,036.43'
Ashland Plantation,
 Inc.                      1,855.86'             2,607.81'
Mrs. Ina Mae Morris,
 et al,                    1,196.28'             1,680.99'
Devall Planting Company,
 Inc.                      3,066.42'             4,308.86'
Joan Seidenbach,
 et al,                    1,831.26'             2,573.24'
Willie Hugh Davis,
 et al                     2,329.47'             3,273.32'
                          _________             _________
         TOTALS:          23,486.38'            33,002.52'

The trial court in its judgment after new trial decreed that the fee of Brown & Butler, Consulting Engineers, which amounted to $53,200.00, be taxed as court costs, and be assessed and paid by apportioning one-half thereof among the parties in proportion to the acreage allotted to them by the division of the alluvion, and one-half thereof among them in proportion to their new river frontage, and that other court costs be taxed in accordance with the interlocutory judgment rendered May 31, 1973, among the parties in proportion to their new river frontage. We agree with this assessment of the costs. Appellant Oliver does not assign as error the allocation of costs. The appellees do not discuss the allocation of costs in their briefs. Only appellant Davis relates his argument back to a re-argument of the formula to be used in allocating the alluvion and is without merit.
For the foregoing reasons, we affirm the trial court's judgment. The costs of this appeal are to be paid by the appellants Oliver and Davis, each to pay one-half of such costs.
AFFIRMED.
Appendix to follow.
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