opinion: SIMONS, Circuit Judge.
  The cause is here for the second time. In our former decision Rymer v. Anchor Stove & Range Co., 6 Cir., 70 F.2d 386, we adjudged the present appellees guilty of unfair competition in simulating the design of appellant’s heaters, which were sold to the mail order house of Montgomery Ward & Company of Chicago, without sufficient indicia thereon to show their origin, and affirmed a decree granting the plaintiffs injunctive relief and reference to a master to assess damages.
  Upon the first appeal no complaint was made with respect to the remedy decreed below, nor was it contended that the plaintiff was entitled to profits made by the defendant upon the heaters there held to infringe the plaintiff’s rights. Neither was there objection to the accounting and assessment of damages adjudged. In sustaining the decree we said (page 389) : “We recognize equally with the court below the difficulty of submitting to the master the proofs upon which damages may be assessed. The difficulty is not, however, insurmountable. Certainly with respect to the orders actually cancelled and not reinstated upon explanation by the plaintiff to its dealers, there is a sufficiently adequate factual basis for measuring damages, though we do not mean by this to imply that the proofs should be limited to such cancellations.”
  When the cause' was returned to the District Court and by it referred to a master for an ' accounting, the plaintiff offered no proof of damages sustained by reason of cancelled orders, but sought an order requiring the defendants to open their books for inspection, first as to the number of infringing heate'rs sold by them to Montgomery Ward & Company, and second as to the profits which they had made on such heaters. The master granted the plaintiff an order of the scope requested, but upon exception it was amended by the District Judge in so far as it concerned the defendants’ profits, on the ground that such profits were not within the scope of the interlocutory decree' sus--tained in this court and that neither court nor master could enlarge or alter a decree sustained upon review. The plaintiff then contented itself with proof tending to show its damage to be $5.65 lost profit on each of 3,335 heaters which it claimed it would have sold had the defendants not resorted to unlawful simulation and infringement of its proprietary right, and had they not sold an equal number of infringing heaters to' Montgomery Ward & Company. No proof of any kind was adduced to show that either Montgomery Ward & Company or a single .one of its customers would have bought heaters from the plaintiff had the condemned simulation not taken place, or that the plaintiff had lost a single customer thereby.
  The master found the sales of the defendant to Montgomery Ward & Company to be in the number indicated, and the average net profit per heater of those sold by the plaintiff in 1928 to be $5.65. • He thereupon awarded the plaintiff damages in the sum of $18,842.75, on the ground that the presumption in cases of infringément and unfair competition is against the wrongdoer. This award the District Court set aside because of the failure of the proofs to indicate that the sales to Montgomery Ward by the defendants resulted in any loss of sales to the plaintiff, and a decree was entered awarding the plaintiff but nominal damages.
  Upon the present appeal the plaintiff complains that the court should have permitted the master to ascertain the profits made by the. defendants on their sale of heaters to Montgomery Ward & Company and to award it such profits, and that the court should have sustained the master’s - award of damages arrived at by multiplying the plaintiff’s' profit per heater unit by the number of units the defendants sold to Montgomery Ward & Company.
  Since the decision in Hamilton-Brown Shoe Co. v. Wolf Bros. & Co., 240 U.S. 251, 36 S.Ct. 269, 60 L.Ed. 629, and by analogy to the relief granted in patent and trade-mark infringement cases, it is clear that the infringer may be required in > equity to account for and yield up his gains to the true owner upon a principle analogous to that which charges a trustee with the profits acquired by a wrongful use of the property of the cestui que trust. As there pointed out, when equity jurisdiction is rested upon some equitable ground, such as the right to injunction, the court will retain it for the purpose of administering complete relief rather than send the injured party to a court of law for damages, and the infringer’s profits are then allowed as an equitable measure of compensation on the theory of a trust ex maleficio, and it is not fatal that the plaintiff is unable to show what proportion of the profit is due to the trade-mark or the patent and what to the intrinsic value of the commodity, for (page 273) “it is more consonant with reason and justice that the owner of the trademark should have the whole profit than that he should be deprived ofs any part of it by the fraudulent act of the defendant.”
  The difficulty which the appellant encounters here is that in the case as originally made below it sought no recovery of the defendants’ profits upon any trust theory. It asked for injunction and an accounting for damages. When it appealed to this court it complained of the scope of the decree only in so f.ar as it failed to include heaters other than those sold to Montgomery Ward & Company. No complaint was made as to the failure of the court by its decree to hold it entitled to the defendants’ profits. This decree we sustained, and while refusing to enlarge its application, the plaintiff within its limits secured the precise relief sought. The order of reference upon remand followed the terms of the decree. Our décision and mandate have become the law of the case and the court, below was not in error in overruling the order of the master looking toward the ascertainment and award to the plaintiff of the defendants’ profits. Sharpless Co. v. Lawrence, 3 Cir., 213 F. 423.
  As to recovery of lost profits by way of damages, the usual principles apply. As was said by this court in Dickinson v. O. & W. Thum Co., 6 Cir., 8 F.2d 570, 575, “When a plaintiff in a trade-mark or unfair competition case seeks to recover damages, the burden is on him to prove by competent and sufficient evidence his lost sales, or that he was compelled to reduce prices as the result of his competitor’s wrongful conduct. There is no presumption of law or of fact that a plaintiff would have made the sales that the defendant made.” The authorities sustaining this principle are sufficiently cited in the text. Especially is this true when the alleged infringer sells his product at a substantially lower price, for “It does not follow, because a party makes a purchase at a lower price, that he would have bought the same article at a higher price.” Cincinnati Siemans Gas Co. v. Western Siemans Co., 152 U.S. 200, 206, 14 S.Ct. 523, 526, 38 L.Ed. 411.
  The presumption relied upon by the master is undoubtedly derived from those cases in which an award of profits made by the wrongdoer is made to the person injured on the theory that the wrongdoer is not to be permitted to profit by his unlawful act. Liability for damages arises solely from the injury done to the property rights of the adverse party, and is not supported by the fiction which places the infringer in the position of a trustee and requires him to account for profits made as such. Dickinson v. Thum Co., supra; United States v. Bitter Root Development Co., 200 U.S. 451, 26 S.Ct. 318, 50 L.Ed. 550; Tilghman v. Proctor, 125 U.S. 136, 148, 8 S.Ct. 894, 31 L.Ed. 664.
  The decree below is affirmed.