*346 MATTHES, Circuit Judge.

For the second time this case is before us on a petition to review the Tax Court’s determination of the income tax liability of petitioners for the years 1955, 1956 and 1957. The key issue in the first appeal was whether the Tax Court erred in failing to apply the Cohan rule 1 to a portion of the expenditures made by petitioners. We decided that issue in favor of petitioners and remanded, “for further proceedings consistent with this decision.” Poletti v. C. I. R., 330 F.2d 818, 824 (1964). The purport and effect of that opinion is one of the issues in this proceeding.

Since the pertinent facts relating to the nature of petitioners’ business, mode of operation, and general type of expenditures, claimed to be deductible as ordinary and necessary business expenses [§ 162(a), Internal Revenue Code, 1954], are adequately detailed in our first opinion, we forego further reference to those facts, except as necessary in connection with the issues now before us. However, the proceedings in the Tax Court on remand are relevant to the present controversy, and will be outlined.

The Tax Court ordered the case placed on the Washington, D. C. Calender of September 9, 1964, and directed the parties to submit recomputations consistent with this court’s opinion, or to move with respect thereto. Both the Commissioner and petitioners complied by submitting proposed recomputations and supporting memoranda. Contemporaneous with the submission of their proposed recomputation, petitioners also filed an “alternative motion for appointment of Commissioner or for trial setting.” In the motion, petitioners alleged that, unless respondent (Commissioner) “stipulates at least to those items so specifically proved heretofore, the trial of this cause wll require many days in Court, and possibly weeks”. On October 14,1964, there was a hearing before the Tax Court (Honorable G. G. Withey), consisting primarily of an explanation by counsel for petitioners of their proposed recomputation. At the conclusion of the hearing, the Court announced that the motion for appointment of a Commissioner to hear evidence and for another trial was denied. 2

In light of our first opinion, which held that the Cohan rule must be applied, the Commissioner proposed, in his re-computation, that the following method be employed to determine the deficiencies for the years in question: subtract from deductions claimed (a) the amounts for which no expenditures had been shown; (b) items expressly disallowed by the Tax Court which petitioners did not question on the first appeal; (c) an amount, for 1957, conceded by petitioners not to have been deductible; and (d) amounts stipulated by both parties to have been properly deducted. The Commissioner proposed that the Cohan rule then be applied to the balance, which would result in allowing fifty per cent of the remainder as deductions. The Tax Court adopted the Commissioner’s proposal and applied the Cohan rule to claimed deductions amounting to $7,798.77, $11,603.55, and $29,-493.47, for the years 1955, 1956 and 1957, respectively. Applying this method of computation, the Tax Court found deficiencies of $4,701.25, $7,229.55, and $19,-345.35, plus additions, for those years; as compared to the Tax Court’s previous findings of deficiencies amounting to $5,977.08, $10,456.40, and $24,537.14, plus additions.

Petitioners’ motion for reconsideration was denied. This review proceeding followed.

Two basic points are presented for our determination: (1) whether petitioners *347 were entitled, as a matter of right, on remand to offer evidence — that is, whether, under our prior opinion and mandate, the Tax Court was required to grant another hearing; and (2) whether, as petitioners contend, the Tax Court erred in failing to fully allow ordinary and necessary business expenditures “that were proved, by the evidence, and in applying, instead, the Cohan Rule * * *»

The question regarding the effect of our first opinion brings into play legal principles which are undisputed. The controversy emanates from disagreement as to meaning of our opinion; particularly, whether the opinion constituted a mandate to the Tax Court to hold another evidentiary hearing.

We start from the premise that an inferior court has no authority to deviate from the mandate issued by an appellate court. Briggs v. Pennsylvania R. Co., 334 U.S. 304, 306, 68 S.Ct. 1039, 92 L.Ed. 1403 (1948); Thornton v. Carter, 109 F.2d 316, 320 (8 Cir. 1940); Gunn v. United States, 283 F.2d 358, 361 (8 Cir. 1960); Paull v. Archer-Daniels-Midland Co., 313 F.2d 612, 617 (8 Cir. 1963).

In the Thornton case, supra, the controlling effect of the opinion and mandate of an appellate court was discussed, at some length, by the late Judge San-born, who stated in part:

“A mandate is completely controlling as to all matters within its compass, but on remand the trial court is free to pass upon any issue which was not expressly or impliedly disposed of on appeal. Since, however, a final judgment upon the merits concludes the parties as to all issues which were or could have been decided (Guettel v. United States, 8 Cir., 95 F.2d 229, 230, 118 A.L.R. 1060 and cases cited), it is obvious that such a judgment of this court on appeal puts all such issues out of the reach of the trial court on the remand of the case. That court is without power to do anything which is contrary to either the letter or spirit of the mandate construed in the light of the opinion of this court deciding the case.” Id., 109 F.2d at 320.

See also, Herzberg’s, Inc. v. Ocean Acc. & Guarantee Corp., 132 F.2d 438, 441 (8 Cir. 1943).

In our Gunn case, supra, in which the central issue was the effect of the opinion in our earlier case of Gunn v. C. I. R., 247 F.2d 359 (8 Cir. 1957), we recognized that legal propositions which an appellate court settles on appeal ordinarily cannot be questioned again, and that “[t]his principle has been applied in tax litigation.” (Citing cases) 283 F.2d, at 361. A corollary to the principle that a mandate is completely controlling as to all matters within its compass is the rule that, upon a reversal and remand for further consistent proceedings, the case goes back to the trial court for a new determination of the issues presented as though they had not been determined before, pursuant to the legal principles enunciated in the appellate court’s opinion, which must be taken as the law of the case. United States v. Iriarte, 166 F.2d 800, 803 (1 Cir. 1948); Roth v. Hyer, 142 F.2d 227, 229 (5 Cir. 1944).

With these principles in mind we now determine just what was decided by this court in our disposition of the prior appeal.

Petitioners, in their first appeal, presented two basic contentions: (1) That the Tax Court erred in failing to allow deductions specifically proved, by their evidence, for the years 1955, 1956 and 1957; and (2) That, for the balance of the deductions held not to be fully proved, the Tax Court erred in failing to make allowances in the nature of approximations, under the rule of the Cohan case, for each of those years.

The Commissioner contended that petitioners failed to show that they were entitled to any deductions in excess of the amounts allowed by the Tax Court and, that there were no expenses with deducti- *348 bility sufficiently shown to justify application of the Cohan rule.

With this background, we examine our prior opinion. After reviewing the facts and the method used by the Tax Court in arriving at the deficiencies, we observed in our first opinion:

“Simply stated, the issue is whether the Tax Court erred in failing to apply the Cohan rule to expenditures over and above those stipulated and allowed as deductible, even though finding that a portion thereof constituted deductible business expenses. We believe the Tax Court fell into error in this regard.” 330 F.2d 818, at 820.

Having so defined the issue, we then considered, at some length, the evidence of expenditures made by petitioners, with the obvious purpose of showing that “the taxpayer had proven some allowable expenditures in excess of the stipulated amounts for 1956.” Id., at 821. It is clear that our review of the evidence of expenditures made by petitioners was intended to and, in fact, did demonstrate that there was no basis for respondent’s (Commissioner’s) contention that the Tax Court had properly declined to apply the Cohan rule “to any of the balance of allowable expenditures for 1956 over and above the stipulated deductions.” Id., at 821. Having demonstrated the applicability of the Cohan rule to the balance of allowable expenditures, we stated in conclusion:

“We find it necessary to remand because the Tax Court did not apply the Cohan rule to that balance of the admittedly allowable expenditures over and above the stipulated amounts for the year 1956. We are not, however, prejudging its future findings in requiring that application of the rule would necessarily, in other years at issue, demand additional deductions other than the amounts already allowed by respondent. The Tax Court is the trier of the facts and could conceivably, depending on the evidence at retrial, find a different amount than allowed initially as deductible for the years 1955 and 1957.” Id., at 823-824. (Emphasis supplied).

Petitioners seize upon the sentence in our prior opinion which we have italicized above, and interpret it to mean that the Tax Court was compelled to grant a retrial. In reaching that conclusion, petitioners have taken the statement out of context. They have ignored the tenor of the opinion as a whole and, specifically, the statement immediately following that relied upon, which reads:

“The burden still remains upon the taxpayer to prove the connectivity of business purpose to establish his right to the claimed, deductible expenditures. The Cohan rule must be applied, however, to expenditures over and above those stipulated as deductible if the court finds, as it did here, that the taxpayer sustained his burden of proof with respect to the deductible nature of some of these expenditures.” Id., at 824.

From a study of our prior opinion, in context, it is clear that the Tax Court was required, on remand, to apply the Cohan rule to expenditures which had been proved to be deductible in some undetermined amount. Our opinion did not compel the Tax Court to grant a rehearing in order to allow the submission of additional evidence. It merely directed the Tax Court to apply the Cohan rule to the expenditures properly deductible, in part. At most, our opinion allowed the Tax Court, if it so chose, in the exercise of its discretion, to receive additional- evidence with regard to expenditures to which the Cohan rule should be applied. In light of the manifest purpose of our prior disposition, we are unable to find any sound basis for granting another trial, apparently for the purpose of enabling petitioners to bolster the evidence bearing upon the deductibility of a larger amount of the expenditures.

It is readily apparent that petitioners’ second point on this appeal is identical to their first contention in the prior appeal, to wit, “the court erred in failing to allow deductions specifically proved by peti *349 tioner’s evidence for the years 1955, 1956 and 1957.”

Petitioners may not, in view of our prior opinion, charge the Tax Court with error in failing to make additional allowances for claimed deductible expenditures before it applied the Cohan rule. Neither are they entitled to another review of that question by this Court. “When a case has been decided by this court on appeal and remanded to the District Court, every question which was before this court and disposed of by its decree is finally settled and determined.” Thornton v. Carter, supra, 109 F.2d at 319. Our consideration of the evidence, the Tax Court’s decision, and the contentions of the parties, caused us to conclude, in our first opinion, that the only meritorious question for determination was whether the Tax Court had erred in failing to apply the Cohan rule to a portion of the expenditures. We resolved that issue in favor of petitioners and remanded. The Tax Court followed our mandate.

We realize that perhaps our opinion would have been capable of more meaningful understanding if we had expressly held that there was no substance in petitioners’ first contention. However, a rational consideration of our prior opinion, in its entirety, convincingly demonstrates that the issue was necessarily disposed of by implication. Petitioners are not entitled to secure another adjudication upon any issue which was “expressly or impliedly disposed of” on the first appeal. Thornton v. Carter, supra, at 320; Paull v. Archer-Daniels-Midland Co., supra, 313 F.2d at 617.

Nevertheless, we have again examined petitioners’ evidence which allegedly proved the deductibility of expenditures other than those to which the parties stipulated. The evidence unqualifiedly shows that the expenditures were made. However, we agree with the Tax Court that the evidence “does not enable us to determine with certainty that numerous of the expenditures in controversy bore a proximate relationship to the carrying on of petitioners’ employment agency business”. Since an unidentifiable part of the expenditures was of a deductible nature, on remand the Tax Court properly applied the Cohan rule and allowed fifty per cent of the expenditures to be deducted.

Finding no error, we affirm.

Notes

. Cohan v. Commissioner, 39 F.2d 540 (2 Cir. 1930).

. In announcing his decision, Judge Withey stated: “Now very obviously the petitioner reads the mandate of the Court of Appeals considerably different than I do. I don’t find that there is any provision in the mandate specifically requiring the taking of additional testimony unless there is some showing made to the effect that there is now newly discovered evidence available which I don’t find there is.”