
    TRIO PROCESS CORPORATION, Appellant in 75-1556, and Franklin Smelting & Refining Co., a partnership v. L. GOLDSTEIN’S SONS, INC. and Metal Bank, Inc. TRIO PROCESS CORPORATION and Franklin Smelting & Refining Co., a partnership v. L. GOLDSTEIN’S SONS, INC. and Metal Bank, Inc., Appellants in 75-1557.
    Nos. 75-1556, 75-1557.
    United States Court of Appeals, Third Circuit.
    Argued Nov. 17, 1975.
    Petition for Rehearing Before the Panel Granted Feb. 12, 1976.
    Reargued March 24, 1976.
    Decided April 23, 1976.
    
      Thomas M. Ferrill, Jr., Blue Bell, Pa., for appellant; Roger Norman Coe, Allen V. Hazeltine, Blue Bell, Pa., of counsel.
    John M. Calimafde, Arthur M. Lieberman, Robert A. Schroeder, Hopgood, Calimafde, Kalil, Blaustein & Lieberman, New York City, for cross-appellants.
    Before VAN DUSEN, ADAMS and R0-SENN, Circuit Judges.
   OPINION OF THE COURT

ADAMS, Circuit Judge.

In May 1972, this Court determined that United States Patent No. 3,076,421, owned by Trio Process Corporation (Trio), is a valid patent, that it had been willfully infringed by L. Goldstein’s Sons, Incorporated (Goldstein), and that the case should be remanded to the district court for a determination of damages. The question posed by the present appeal is whether the district court on the remand erred in assessing the damages.

I.

The patented process which undergirds this controversy is a technique for salvaging copper from scrap wire by the use of a special furnace in which the heat removes the insulation from the wire.

Although a patent was not issued until 1963, the owner, Trio, had instituted a program of licensing almost immediately after completion of the development of the removal method in the late 1950’s. In fact, licensure was the only use Trio made of the patent; it never utilized the process itself.

The licenses sold by Trio were for five-year periods. Minkin Metal Company bought the first license. The purchase price of $20,000 covered both the license itself and the furnace needed to use the process; $13,000, or $2,600 per furnace year, was allocated for the license, and $7,000 for the furnace. Goldstein was the next purchaser, buying two sets of licenses and furnaces in 1960, one set for $20,000 and the other for $15,000. Agreements were subsequently entered into by Trio with four other buyers between 1962 and 1969 at the $20,000 rate. One company bought the package in 1967, with a modified but more expensive furnace, for $25,000. Another purchased the package later in the same year for $19,500. After a decision by Trio to raise the price, two more were sold in-1972 for $25,000. No licenses have been granted since this Court’s decision holding that the patent is valid.

Despite our determination in 1972 that the patented method had been willfully infringed by Goldstein, the infringement continued through 1973. In January of that year, Trio sought, and was granted, an injunction against Goldstein’s continuing use of the technique. Following the ensuing violation of the strictures of the injunction, the district court entered an order holding Goldstein in contempt. This Court affirmed that order in March 1974.

While the contempt motion was being adjudicated, proceedings were taking place before a master in order to determine damages due Trio for Goldstein’s infringement of the patent. The district court appointed the master in January 1973 and his report was filed, after the taking of extensive testimony, in June 1974. The master approached the damage issue by comparing Goldstein’s costs of operating the patented process with the costs of a similar, unpatented process. He found that use of the Trio process saved Goldstein $52,791 per furnace year in labor costs alone, and that other, smaller, savings accrued to Goldstein from use of the patented method as well.

In order to reach a “reasonable royalty” for use of the patent by the infringer, the master halved Goldstein’s savings in labor costs, and concluded that $26,390 was a reasonable royalty for each furnace year. Multiplying this figure by the number of furnace years of infringement and making slight modifications, the master found damages of $1,564,804. The master recommended trebling this amount, as allowed by 35 U.S.C. § 284 (1970). After trebling and the addition of interest, the total damage figure proposed by the master was $5,062,-954.

The district court viewed the damage computation not with regard to the money saved by the defendant as a result of its infringement, as the master had, but in terms of what Trio had lost. It looked first to the initial sum of $2,600 per furnace year — the amount actually charged by Trio for licenses in the 1960-1970 era. The district court then increased the $2,600 figure on the assumption that the open infringement had reduced the market price of the license, and proceeded to set damages at $7,800 per furnace year for the years prior to the decision by this Court on validity, a figure three times the rate charged by Trio during the 1960’s. Damages were set at $15,000 per furnace year for the period following the 1972 adjudication. The employment of these two figures resulted in total primary damages of $653,839. The trial judge then proceeded to use a double multiplier — in contrast to the master’s trebling figure — and denied attorneys’ fees. With interest, the total damages computed by the district court were $1,726,525.

Both parties appealed the award of damages. Trio contends that the master’s determination was correct and should not have been disturbed by the district court. It argues that the reduction was contrary to economic fact and that the district judge should have based its calculations upon the reasonable royalty set by the master. Trio further asserts that the damage multiplier should not have been reduced from three to two by the district judge since Goldstein allegedly exhibited a substantial degree of bad faith in its infringement of the patent and there are, Trio declares, no mitigating circumstances sufficient to justify the reduction of the multiplier.

Goldstein maintains that the license fee generally charged by Trio during the 1960’s —$2,600 per year for a five-year period, or $13,000 — is the proper basis for measuring damages, and that there is no reason to depart from this rate which was established by Trio itself. Goldstein further claims that there was no evidentiary basis whatever for the district court’s decision to increase the established rate to $7,800 and $15,000 per furnace year, respectively, in order to assess damages. The final challenge by Goldstein to the damage award concerns the multiplier. Since it allegedly followed the advice of counsel in using the Trio method, Goldstein argues that it was improper for the court to multiply the primary damages at all.

II.

In assessing damages, the district court chose, as the rate of a reasonable royalty for the periods preceding and following this Court’s May 1972 decision on validity, figures approximately three and six times as large as the $2,600 price usually charged by Trio per furnace year for licenses during the 1960’s.

We find no error in the first step of the district court’s damage calculation, namely, focusing upon the losses suffered by the patent holder rather than upon the profits illegally made by the patent infringer. The approach utilized by the district court has been mandated since the decision in Aro Manufacturing Co. v. Convertible Top Replacement Co., 377 U.S. 476, 84 S.Ct. 1526, 12 L.Ed.2d 457 (1964). The Supreme Court there ruled that “to determine the damages that may be recovered from [the infringer] here, we must ask how much [the patent holder] suffered by [the] infringement— how much [the patent holder] would have made if [the infringer] had not infringed.” Id. at 507, 84 S.Ct. at 1543, 12 L.Ed.2d at 480. Because Trio is not itself engaged in the metal reclaiming business, the trial court correctly held that the only damage Trio had suffered was the loss of the royalties it would have received if Goldstein’s use of the process had been made under an appropriate licensure agreement.

The district court did not act improperly in ascertaining that the license rate established by Trio in the 1960’s may have been artificially depressed by Goldstein’s ongoing infringement, and that the reasonable royalty should therefore be set at a level above the actual license rate. As one court has accurately observed, “[i]t is a fact of economic life that an open infringement tends to reduce a patentee’s fees from its subsequent licensees who must meet the infringer’s competition, and such infringement deters potential licensees from taking a license.”

However, the trial judge erred in ruling that the amount of a reasonable royalty for the Trio process increased after the decision by this Court ascertaining the patent’s validity. If a patent is adjudged valid, the single reasonable royalty to be paid for its infringement is determined with reference to the judicial approval of the patent. “The reasonable royalty must ... be determined . . . upon the hypothesis that the patent was valid and would be respected.” The reasonable royalty thus established is applied to the full period of infringement, because “determination of an assumed reasonable royalty is in essence a device for retroactively reaching a just result . . .

In addition, we cannot discern any basis for the district court’s choice of a particular royalty. The district court merely, as he put it, “considered the depressing effect that defendant’s infringement may have had on the royalties” and “considered the many factors suggested by the Georgia-Pacific case,” and then fixed the royalty. There was no description of the manner in which the royalty rate was affected by the evidence proffered by the parties: the existing licensure rate and the testimony of expert witnesses expressing views of the appropriate level of a reasonable royalty. In the absence of such an articulation, we cannot know the specific method of the district court’s determination of the reasonable royalty. For this reason, we must remand.

On remand, the district court should give proper regard to the rule that the extent of the deviation of existing license fees from a reasonable royalty must be determined solely on the basis of the submitted evidence and upon an evaluation of the factors that could affect the reasonable royalty rate, not upon mere conjecture. That rule is derived from a line of several Supreme Court decisions that instruct the federal courts to allow damages in a patent action only to the extent indicated by appropriate evidence.

As long ago as 1860, the Supreme Court ruled in Mayor of New York v. Ransom that “[wjhere a plaintiff is allowed to recover only ‘actual damages,’ he is bound to furnish evidence by which the [trier of fact] may assess them. . . . Actual damages must be calculated, not imagined, and an arithmetical calculation cannot be made without certain data ott which to make it.” This doctrine has been developed over the years in several cases. Rude v. Westcott and Boesch v. Graff followed the original Ransom holding precisely. In an early twentieth century decision on the question, the Court reiterated the rule that “ ‘in order to get at a fair measure of damages, or even an approximation of it, general evidence must necessarily be resorted to.’ ” And the holding in Sinclair Refining Co. v. Jenkins Petroleum Process Co., 289 U.S. 689, 53 S.Ct. 736, 77 L.Ed. 1449 (1933), that a bill of discovery may be made available to enable the plaintiff in a patent case to prove his damages, was necessarily erected upon the foundation that such proof is a prerequisite to recovery.

It was thus improper for the district court to fix the reasonable royalty without an explanation of how the particular level chosen was related to the evidence proffered by the parties. The cause thus must be remanded for reconsideration.

III.

Following the guidance given by 35 U.S.C. § 284 that “the court may increase damages up to three times the amount found or assessed,” the district court doubled the damages it had calculated. The factor by which damages are multiplied is within the sound discretion of the district court. There has been no demonstration, in view of the facts of this case, that the doubling of the damages constituted an abuse of that discretion.

IY.

That portion of the district court’s judgment dealing with damages will be vacated, and the cause will be remanded for further proceedings consistent with this opinion. 
      
      . The original defendant, L. Goldstein’s Sons, Inc., was succeeded in interest by Metal Bank of America, Inc. Both these parties will be referred to in this opinion as Goldstein.
     
      
      . Trio Process Corp. v. L. Goldstein’s Sons, Inc., 461 F.2d 66 (3d Cir.), cert. denied, 409 U.S. 997, 93 S.Ct. 319, 34 L.Ed.2d 262 (1972).
     
      
      . A detailed description of the process can be found in the opinion concerning the validity and infringement of the patent. Trio Process Corp. v. L. Goldstein’s Sons, Inc., 461 F.2d 66 (3d Cir.), cert. denied, 409 U.S. 997, 93 S.Ct. 319, 34 L.Ed.2d 262 (1972).
     
      
      . The price thus did not change upon issuance of the patent in 1963.
     
      
      . Although the last two transactions were finalized after this Court’s May 1972 decision, the parties to the contracts had committed themselves to the price of $25,000 prior to that decision.
     
      
      . Trio Process Corp. v. L. Goldstein’s Sons, Inc., 493 F.2d 1401 (3d Cir. 1974).
     
      
      . Goldstein’s violation of the district court’s January 1973 injunction was also referred to the master for an evaluation of the damages it had caused Trio.
     
      
      . The concept of a reasonable royalty represents the minimum measure of damages provided by 35 U.S.C. § 284 (1970).
     
      
      . The statute provides:
      Upon finding for the claimant the court shall award the claimant damages adequate to compensate for the infringement, but in no event less than a reasonable royalty for the use made of the invention by the infringer, together with interest and costs as fixed by the court.
      When the damages are not found by a jury, the court shall assess them. In either event the court may increase the damages up to three times the amount found or assessed.
     
      
      . Additionally, the district court awarded $5,000 to Trio for Goldstein’s contempt of the injunctive order.
     
      
      . In its notice of appeal, Trio preserved its right to appeal both the district court’s order that Goldstein pay Trio a contempt penalty of only $5,000 and the district court’s refusal to award Trio attorneys’ fees; Trio has not pursued these points in its appeal, however, and accordingly we do not address them.
     
      
      . This approach was taken in order to comply with the provisions of 35 U.S.C. § 284. See note 9 supra.
      
     
      
      . Hartford Nat’l Bank & Trust Co. v. E. F. Drew & Co., 188 F.Supp. 353, 362 n.50 (D.Del.), modified, 188 F.Supp. 347 (D.Del.1960), aff’d per curiam, 290 F.2d 589 (3d Cir.), cert. denied, 368 U.S. 825, 82 S.Ct. 45, 7 L.Ed.2d 29 (1961).
     
      
      . General Motors Corp. v. Blackmore, 53 F.2d 725, 729 (6th Cir. 1931).
     
      
      . Georgia-Pacific Corp. v. U. S. Plywood-Champion Papers, Inc., 446 F.2d 295, 300 (2nd Cir.), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971). Accord, Hartford Nat’l Bank & Trust Co. v. E. F. Drew & Co., supra at 362-63.
     
      
      . He was referring to Georgia-Pacific Corp. v. United States Plywood Corp., 318 F.Supp. 1116, 1120 (S.D.N.Y.1970), modified, 446 F.2d 295 (2d Cir.), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971).
     
      
      . An exhaustive list of the factors to be considered can be found in Georgia-Pacific Corp. v. United States Plywood Corp., 318 F.Supp. 1116, 1120 (S.D.N.Y.1970), modified, 446 F.2d 295 (2d Cir.), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971).
     
      
      . 64 U.S. (23 How.) 487, 16 L.Ed. 515 (1860).
     
      
      . Id. at 488.
     
      
      . 130 U.S. 152, 167, 9 S.Ct. 463, 32 L.Ed. 888 (1889) .
     
      
      . 133 U.S. 697, 706, 10 S.Ct. 378, 33 L.Ed. 787 (1890) .
     
      
      . Dowagiac Mfg. Co. v. Minnesota Moline Plow Co., 235 U.S. 641, 35 S.Ct. 221, 59 L.Ed. 398, 649 (1915), quoting Suffolk Co. v. Hayden, 70 U.S. (3 Wall.) 315, 320, 18 L.Ed. 76 (1866).
     
      
      . The rule was recognized again more recently in United States v. National Lead Co., 332 U.S. 319, 352 n. 8, 67 S.Ct. 1634, 91 L.Ed. 2077 (1947). See also Molinaro v. Lafayette Radio Electronics, 62 F.R.D. 464, 466 (E.D.Pa.1973).
      The statutory language in force when these earlier Supreme Court decisions were made differs from the language of the current statute, but only in immaterial ways. See Act of August 1, 1946, ch. 726, § 1, 60 Stat. 778; Act of Feb. 18, 1922, ch. 58, § 8, 42 Stat. 392; Act of Mar. 3, 1897, ch. 391, § 6, 29 Stat. 694; Act of July 8, 1870, ch. 230, § 59, 16 Stat. 207; Act of July 4, 1836, ch. 357, § 14, 5 Stat. 123; Act of April 17, 1800, ch. 25, § 3, 2 Stat. 38. The relevant decisions of the Supreme Court would thus appear to have full effect today.
     
      
      . We do not decide whether the presentation of additional evidence will be necessary to the decision of the district court; rather, we leave that decision to the district court. However, counsel for both parties stated at reargument, in writing and orally, that, in their view, additional evidence was not necessary for the assessment of damages.
     
      
      . Hartford-Empire Co. v. Shawkee Mfg. Co., 163 F.2d 474, 480 (3d Cir. 1947).
     
      
      . The questions whether and to what extent to multiply the reassessed damages may also be reconsidered by the district court.
     