In this patent infringement suit we face questions of liability and the proper measure of damages. Hughes Tool Company, the plaintiff-appellant, sued to recover damages for infringement of its patent covering a steel and rubber seal which protects the bearings of rotating drill bits used in drilling oil wells. The district court found that G. W. Murphy Industries, Inc., the defendant-cross appellant, had infringed the patent in suit and should compensate Hughes Tool by paying a reasonable royalty. On appeal Murphy challenges the finding of liability; Hughes challenges the adequacy of the award. We affirm on both issues.
I. Facts
The patent in suit, U. S. Patent No. 3,075,781, covers a bearing seal used in rock bits.1
The district court found:
“7. The bearing seal of the patent was designed to function in rock bits having a roller cone construction. Such bits include a head section, which can be threaded onto the lower end of the drill stem, and rotatable conical shaped cutters mounted on bearings at the lower end of the head. In operation the bit is lowered into the hole and the drill stem is rotated causing the conical cutters to roll upon the bottom of the hole with great force, and thus disintegrate the rock formation. Such a bit will continue to drill until either (1) the cutting structure on the surface of the cones has broken down, or (2) the bearings on which the cutters turn have worn out, at which time the effective life of the bit is ended.”
The life of the bearings is to a large degree dependent on lubrication, and as early as 1918 unsuccessful attempts were made to seal the bearings to prevent the escape of lubricant and to retard the entrance of foreign particles. Since the 1920’s Reed Roller Bit Company (Murphy’s predecessor), Hughes, and others competed to find an effective rock bit seal. For years however, this *925goal eluded them.2 Finally, in the late 1950’s Hughes developed the seal—the subject of the patent in suit. The first sealed bearing bits embodying the invention became commercially available in 1960.
The subject of the patent in suit is a seal shaped like the outside rim of a dinner plate, that is, like the frustrum of a shallow cone. It is one piece, steel encased in rubber. The rubber exterior is contoured to form sealing pressure pads at the opposite faces of the inner and outer diameters. To provide a sealing engagement with the bit shaft, over which the seal is mounted, a rubber bead may be provided at the inner diameter of the seal. In operation, a conical cutter, positioned over the bit shaft, is forced upon the seal, partially flattening it. As the seal flattens, its pressure pads are pushed against the opposing circular faces of the bit shaft and the conical cutter. To protect the life of the seal, there is some clearance provided between the inner diameter of the steel interior of the seal and the bit shaft. The rubber bead, which may be provided to fill this space, does not prevent the seal from moving radially and rotating slightly on the shaft. These capabilities are termed “radially floating” and “sliding and sealing engagement” in the patent. The point of least resistance to rotation, and the point where the primary movement occurs, is the interface between the outer diameter of the seal and the conical cutter.
Particularly in hard rock formations, seals covered by the patent in suit have significantly reduced bearing wear, and in so doing have increased up to five times the effective life of bits. The district court found that even “[i]n less dramatic situations, the driller can expect at least a thirty to fifty percent increase in overall effectiveness”.
The Hughes seal proved so successful commercially that in May 1960 Reed’s research department feared that “it is only a matter of time before our worthy competitor perfects their grease seal to a point where we will be virtually out of the insert bit business”.3 Reed began testing a two-piece seal consisting of two metal cores encased in rubber and held in compression by a separate metal *926spring. The two-piece seal is not charged with infringement. Although the two-piece seals were never fully satisfactory and were never put into actual production, Reed sold approximately 40 bits containing two-piece seals made by its research department. The district court found that the two-piece seal was a commercially viable noninfringing alternative to the one-piece seal. In late 1962 Reed began experimenting with the one-piece seal later found by the district court to infringe patent no. 3,075,781. In 1963 Reed put the one-piece seal into production.
The Reed one-piece seal is virtually identical to the Hughes seal.4 Hughes and Reed had differing theories, however, of how to mount the seals on the bit shafts. The Hughes seal was mounted with grease between the seal and the shaft to permit “radial floating” and a “sliding and sealing engagement” with the shaft. In Reed bits, on the other hand, the seal was mounted in a tight rubber-to-metal engagement, called an “interference fit”, in an attempt to eliminate any movement between the seal and the shaft. The dry friction between the rubber of the seal and the steel of the shaft was intended to, and did in fact, inhibit rotation and radial floating. But even with their “interference fits” the Reed seals rotated on their shafts during their effective lives. Robert A. Cunningham, one of the inventors of the patented seal, testified that he had retrieved and examined 33 one-piece seals from Reed bits. Each seal had effectively protected the bearings. Of these seals, 32 showed positive signs of rotation. Charles Robert Frederick, Murphy’s witness, reported that he had found evidence of rotation in 75 to 80 percent of the Reed one-piece seals he had examined.'
Rotation of the Reed seals on their shafts proved highly injurious to the seals; indeed, ultimately rotation destroyed the seals. Reed recognized this fact early and, in order to minimize the damage to the seals, in 1965 Reed began polishing its bit shafts. Although this practice reduced the wear on the seals, it also eased rotation.
Neither Murphy nor Hughes sold seals separately from bits. From 1963 through 1969 Murphy (and its predecessor, Reed) sold 19,463 bits containing one-piece seals for a total sales price of $9,745,998. The great majority of the defendant’s sales during this period, however, were of nonsealed bits, which sold for approximately $110 less than the sealed bits. The total premium that Murphy gained by including the infringing one-piece seals in its bits was $2,143,980.
Approximately 31 percent of the bits Murphy sold containing infringing seals were covered under a Hughes patent on the complete drill bit and cutters. In accordance with a license agreement, the defendant paid Hughes a royalty of six percent of the selling price of the entire drill bit. The total royalty amounted to approximately $266,000.
The district court found that Murphy’s one-piece seal infringed the patent in suit, and awarded Hughes damages representing 1.25 percent of the selling price of the bits containing infringing seals. The total amount of the award was $121,824.98.
II. Liability
Murphy argues that the district court should have held, as a matter of law, that there was no infringement of the patent in suit. Murphy bases this contention on two theories; first, that Hughes is estopped from asserting that Murphy’s seal infringed, and second, that even if literal infringement occurred, Murphy is not liable because any infringement was inadvertent, detrimental, and the result of malfunctioning. Neither of these theories has merit in this case.
*927In 1962, after receiving notice that the patent for its seal had been allowed, Hughes filed to amend the patent. Hughes desired to strike the references to “radially floating” and “sliding” in an effort to assure patent protection of seals “fitted interferingly on the shaft or bearing pin of a rock bit”. The amendment was disallowed for procedural reasons. Hughes thereafter filed for a separate patent. Murphy now contends that in filing for the amendment Hughes made admissions which estop it from asserting that the Murphy seal, which rotates only a small amount on the shaft, is an infringement of the patent in suit. The primary basis for Murphy’s argument is the following statement, made by an attorney for the applicants :
“1) The amendment is needed because Applicants and their assignee-employer have been manufacturing and marketing assemblies and seal rings in accordance with the amended claims, i. e., with the seal ring fitted interferingly on the shaft or bearing pin of a rock bit. As all 10 of the allowed claims presently contain limitations negating such interference fit, they would not protect all structures actually being manufactured.”
We disposed of this estoppel argument five years ago in a case dealing with the same Hughes patent. In Smith Industries International v. Hughes Tool Co., 5 Cir. 1968, 396 F.2d 735, Smith Industries attempted to avoid liability for infringing Hughes patent no. 3,075,781 by contending, as Murphy does here, that admissions made by Hughes’ attorneys when applying for an amendment to the patent in suit estopped it from complaining of infringement. We held in Smith Industries that the Hughes’ admissions established only that its patent did not cover “an ‘interference fit’ so tight as to anchor the seal to the shaft and prevent it from independent rotation”. Id. at 739. Hughes’ admissions did not speak to an “ ‘interference fit,’ where the inner diameter of the seal is smaller than the outer diameter of the shaft, with some independent rotation of the seal possible.” This holding was echoed by the findings of the district court in the instant ease.
There is no question but that Reed’s one-piece seals were not anchored to the shaft in such a manner that rotation was prevented. The evidence conclusively established that rotation of the Murphy seals on the shaft was the rule, not the exception; the two witnesses at trial who had studied the matter agreed that at least 75 percent of the Reed seals examined after use in a drill bit in the field showed signs of rotation. Thus, as in Smith Industries, we hold that Hughes is not estopped from claiming an infringement of its patent.
This Court stated in Smith Industries that the rotation of Smith’s seals on the shaft was “critical” to the question of infringement. 396 F.2d at 740. If the seal had not rotated, it would not have infringed. Like the Smith seal, the Reed one-piece seal is substantially identical to the Hughes seal in appearance and function. Infringement, therefore, is largely a question of rotation. Murphy does not strenuously contest on appeal the district court’s findings that its seals rotated and thus literally infringed the patent in suit. Rather, Murphy maintains that because any rotation of its seal was unintended, yielded no benefit, and in fact was detrimental to the seal and consequently to the bit, literal infringement should not carry with it liability.
We recognize that there may be times where literal infringement should be overlooked. This is not an instance, however, where the allegedly infringing device only occasionally strays across the patent boundary. See Pratt v. United States, 1942, 43 F.Supp. 461, 476, 95 Ct.Cl. 608. Rotation was a fact; it was “typical” of field operation. Nor is this an instance where what is literally wrong is too trifling to justify judicial intervention. See Condenser Corp. *928v. Mieamold Radio Corp., 2 Cir. 1944, 145 F.2d 878, 880. There was, in the early 1960’s, no way to seal bearing bits without some rotation of the seal on the shaft.5 Indeed, Reed discovered that it must accept rotation, and, to reduce seal wear, Reed polished the steel shafts of its commercial sealed bearing bits, thereby reducing friction and actually facilitating rotation. But regardless of Reed’s concession to rotation, the fact that an infringer has attempted to avoid infringement and failed does not alter his basic liability. He has unlawfully deprived the patent holder of the fruits of his invention, and he must make compensation. That the infringer cannot easily accomplish the same ends as the patentee without infringement, of course is a reflection of the value of the patent. Whether or not Reed desired or intended that its seal rotate, therefor, is irrelevant.
Murphy’s argument that because rotation is detrimental to its seal the infringement should be ignored is also without substance. To establish liability for patent infringement it is not necessary to show the benefit to the patented device of each of the points of similarity between it and the infringing device. It is enough that “the two devices do substantially the same work in substantially the same way and accomplish the same result”. Stearns-Roger Manufacturing Co. v. Ruth, 10 Cir. 1932, 62 F.2d 442, 448.
III. Damages
The defendant sold 19,463 bits containing infringing seals. During the period that the defendant was manufacturing and selling these bits, 1963-1969, the defendant continued to sell bits, otherwise the same, without seals for a lower price. The parties stipulated below that the total premium received for the presence of the infringing seals in the bits was $2,143,980. Of the premium, $163,-834 represented profit. The bits sold for a total price of $9,745,998, of which $1,469,903 was profit. The crucial question with regard to damages on appeal concerns the proper measure of sales and profit. Did the plaintiff suffer damages from the loss of the premium or from the loss of the total price of the bits?
Arguing that the total price of the bits is the proper standard, Hughes employs a variation of the “entire market” rule. Under this rule, where the patented feature, although a small part of an article, gives the article its entire commercial value, the value of the entire article may be considered in computing damages. See Garretson v. Clark, 1884, 111 U.S. 120, 121, 4 S.Ct. 291, 28 L.Ed. 371; Electric Pipe Line, Inc. v. Fluid Systems, Inc., 2 Cir. 1957, 250 F.2d 697, 700; National Rejectors, Inc. v. A.B.T. Manufacturing Corp., 7 Cir. 1951, 188 F.2d 706, 709, cert. denied, 342 U.S. 828, 72 S.Ct. 51, 96 L.Ed. 626. Hughes concedes that the seals did not provide the entire commercial value of the bits, but argues that the seals were the “motivating cause” of the purchase, that the seals “induced” the purchase. Thus, Hughes insists, had the purchasers not been able to obtain sealed bits from the defendant, they would have obtained sealed bits from the other manufacturers in the industry, and Hughes would have gotten its share of the sales.
Superficially, Hughes’ argument has appeal. Whether or not the article would have some commercial usefulness without the patented feature is irrelevant where it is clear that the patentee would have made the sale of the article had not the defendant infringed. See Graham v. Jeoffroy Manufacturing, Inc., 5 Cir. 1958, 253 F.2d 72, cert. denied, 358 U.S. 817, 79 S.Ct. 28, 3 L.Ed.2d 59. But where the article has com*929mercial value independent of the patented feature, establishing that the infringer would not otherwise have made the sale of the article becomes particularly difficult. This problem is especially severe where, as here, the defendant sold substantially the same article, minus the patented feature, at a discount. We cannot assume that those purchasers who bought sealed bits from the defendant for a premium would have bought sealed bits from the plaintiff (at a premium) rather than buying unsealed bits at a lower price from the defendant. Certainly, as the district court observed, other factors such as “price reliability, versatility, service after sale, [and] company reputation” might have influenced purchasers. And we must agree with the district court that the evidence is lacking that such factors did not play a role. The question whether the defendant would have made all or some of the sales of bits without the seals is one of fact, and the burden of proof was on the plaintiff to show that it would not have. We do not find that the district court was clearly erroneous in its finding that the plaintiffs failed to meet this burden. Thus, we hold that the district court properly limited damages to the seals.6
We turn to the question of the proper measure of damages. Hughes contends that it should have been awarded lost profits on that percentage of the defendant’s sales which, by market share analysis, the plaintiff could expect to have gained. But for the defendant’s infringement, Hughes argues, the defendant’s sales of sealed bits would have been made by the remaining firms in the sealed-bits industry in the proportion their sales bore to those of their competitors, except the defendant. Based on its share of the sealed-bits market, Hughes share of the defendant’s profits would have been $138,654.7
In order to recover lost profits in a patent infringement action the patentee must prove that “in all reasonable probability, the Patent Owner would have made the sales which the Infringer has made”. Livesay Window Co. v. Livesay Industries, Inc., 5 Cir. 1958, 251 F.2d 469, 471. Although the patentee need not establish lost profits with scientific accuracy, neither may lost profits be arrived at by conjecture. See Electric Pipe Line, Inc. v. Fluid Systems, Inc., 2 Cir. 1957, 250 F.2d 697, 699. The district court here found that the plaintiff “failed to demonstrate with ‘reasonable probability’ what portion of defendant’s infringing sales it would have made”. We do not view this finding as clearly erroneous.
Whether proof of market shares may ever be sufficient to pass the “reasonable probability” test for damages is an interesting question; we reserve it for future consideration. In this instance the market itself is inadequately defined. Hughes assumes, but does not *930prove, that the proper market for consideration is the market for sealed bits. Hughes did not satisfy the district court, however, and does not satisfy us, that had the defendant’s customers not been able to purchase sealed bits from the defendant they would nevertheless have purchased sealed bits from another company. As we have stated, we cannot assume that the purchasers would not have substituted unsealed bits (at a discount) from the same manufacturer for sealed bits (at a premium) from another. Thus, we are left without anchor. Without some firm basis for determining the relevant market, we cannot explore further the merits of the market-share contention. And with no definite market, clearly the variables are too many and the speculative nature of lost profits too great to form a basis for recovery. .
When actual damages are not proved, the plaintiff is entitled to a “reasonable royalty”. See Wallace & Tiernan Co. v. City of Syracuse, 2 Cir. 1930, 45 F.2d 693; 35 U.S.C. § 284.8 In determining a reasonable royalty, the trial court attempted to discover “what a manufacturer desiring to use the patented device would be willing to pay as a royalty for its use”. Randolph Laboratories, Inc. v. Specialties Development Corp., 3 Cir. 1954, 213 F.2d 873, 875, cert. denied, 348 U.S. 861, 75 S.Ct. 91, 99 L.Ed. 678. See also Faulkner v. Gibbs, 9 Cir. 1952, 199 F.2d 635, 639; Reynolds Spring Co. v. L. A. Young Industries, Inc., 6 Cir. 1939, 101 F.2d 257, 261. In effect, the court adopted the fiction that the parties negotiated for a license. The court assumed that there was a “willing seller” and a “willing buyer”. Georgia-Pacific Corp. v. United States Plywood-Champion Papers, Inc., 2 Cir. 1971, 446 F.2d 295, 296, cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114. Employing this standard, the district court found that, had the parties negotiated for a license in 1963 for the patented seal, they would have agreed on a royalty amounting to 1.25 percent of the gross sales price of all bits carrying the seal.
What is a reasonable royalty is a question of fact. Faulkner v. Gibbs, supra, 199 F.2d at 639; United States Frumentum Co. v. Lauhoff, 6 Cir. 1914, 216 F. 610, 625. And the trial court’s determination must be upheld unless clearly erroneous. See F.R.Civ.P. 52(a). We are unable to say that the district court’s award failed to meet this test. Before 1963 the defendant had paid a royalty of less than one percent of the sales price of a drill bit for use of a patent covering a device—a nozzle—to be included in the bit. There is little reason to suspect that to gain use of the one-piece seal Reed would have departed from this practice of paying a minimum royalty for less than a complete drill bit.
Hughes points to evidence adduced at trial that seals may increase the life of drill bits two to five times, and that the search for an effective seal had continued unsuccessfully for 40 years until the development of the Hughes seal. But the district court' found, supported by the evidence, that the non-infringing Reed two-piece seal was available as a viable alternative. To be sure, the two-piece seal was less efficient than the one-piece seal and cost more to manufacture and install. Moreover, the two-piece seal was never put into actual production. Nevertheless, Reed’s two-piece seals were marketable; Reed sold approximately 40 bits containing the two-piece seals made in its research department.9 The existence of a non-*931infringing alternative reduces the value of the patent and thus the damages from infringement. See Union Carbide Corp. v. Graver Tank & Manufacturing Co., 7 Cir. 1960, 282 F.2d 653, 670-671, cert. denied, 365 U.S. 812, 81 S.Ct. 692, 5 L.Ed.2d 691; Columbia Wire Co. v. Kokomo Steel & Wire Co., 7 Cir. 1911, 194 F. 108, 110. We agree with the district court that the availability of the two-piece seal would have enhanced the defendant’s bargaining position in license negotiations with Hughes in 1963.
An examination of the award from the perspective of the premium received for the seals reinforces our belief that the district court’s determination that the award represents a reasonable royalty is not clearly erroneous. The damages awarded by the trial court, $121,824.98, equal 5.68 percent of the premium, $2,143,980, the defendant gained by including the patented seals in its drill bits. The royalty awarded by the district court, therefore, approaches the six percent royalty the defendant paid Hughes from 1960 for use of the design of a complete drill bit. And again, the availability of the noninfringing two-piece seal diminishes damages payable for infringement. Finally, it should be noted that the six percent royalty was on the total selling price of the bits, including the premium. Consequently, the 5.68 percent royalty on the selling price of the seal awarded by the court is in addition to the six percent that Hughes has already received on approximately 31 percent of the defendant’s bits which contained infringing seals. In short, we find that the district court’s award was eminently fair.
Affirmed.
. The patent, issued to Hughes Tool Company on January 29, 1963, was held valid by the district court and by courts in earlier litigation. Hughes Tool Co. v. Smith Industries International, W.D.Tex.1966, 284 F.Supp. 908, aff’d, 5 Cir. 1968, 396 F.2d 735.
. The district court found :
“13. There are special and difficult problems associated with designing an effective rock bit seal. In the first place, the seal must be small in order to be accommodated in the very limited space available in a rock bit, and to avoid sacrificing the bearing capacity and other structures which occupy such space. Secondly, the seal must be capable of withstanding the adverse environment in which the rock bit operates. Drilling at depths of several miles or more, the bit is subjected to an atmosphere of abrasive fluid at temperatures of up to 340 degrees. Fluid pressures of from 3,000 to 20,000 pounds per square inch, average mechanical loading on the bits of from 30,000 to 75,000 pounds, and rotary motion varying between 30 and 300 revolutions per minute are common.
14. Under these conditions, the seal must possess a combination of strength and resiliency suitable to permit it to maintain sealing engagement with surfaces on the rotating cutter and bit leg. In operation, these surfaces only rotate with respect to each other, additional complex and rapid movements occur. Because of the inherent looseness of rock bit bearings, and the extreme stresses produced by running on the rough patterned surfaces at the bottom of the hole, the cones are forced into axial, radial, and compound wobbling movements relative to the shaft. Such movements occur with great rapidity. To be effective, the seal must not only follow this erratic motion, it must endure it.
15. Lastly, the compound movements of the cutters with respect to the shaft cause rapid volumetric changes within the bearing cavities of the bit. These volumetric changes result in abrupt pressure differences between the hot grease inside the bearing cavity and the hot, abrasive drilling fluid on the outside, and produce alternately “pumping” and “suction” forces across the seal. Pressure differences up to 100 psi, occur as rapidly as 1,800 cycles per minute. The seal must continue to function under such hostile conditions.”
. Insert bits contain teeth made of very hard steel inserted into the steel roller cones.
. The only difference is that the Hughes seal has a radially corrugated core, while the Reed seal’s core is plain.
. In 1969, within three months of notice of infringement, the defendant converted all its sealed bits to noninfringing “glued-on” seals, cemented, as the name implies, to the shaft. The defendant does not contend, however, that the process of gluing the seals to the bit shafts was available earlier.
. Judge Clark in his dissent, infra, p. 931, quotes extensively from findings of the district court which chronicle the importance of the invention of effective rock bit seals. We do not dispute the significance of the seals. Indeed, the seals proved their value in the market place; their presence in Murphy’s bits permitted a price hike of $110, more than 25 percent of the selling price of the bits without seals. But the findings quoted by Judge Clark do not show that the market for sealed bits was independent of the market for unsealed bits, and that, if Murphy had not sold sealed bits, its customers would have bought them from other manufacturers. We rely on the clear finding by the trial court, stated in its opinion, that “there is little evidence in the .record which would reveal whether purchasers of ‘sealed bearing bits’ were motivated solely by a desire for the sealed feature or whether other influences were at work”.
.
Year Defendant's Profit Plaintiff's % share of total sealed-bits mkt. (without Defendant) Plaintiff's share of Defendant's Profits
1963 (last half) $ 1,502 X $ 1,502
1964 11,034 93.2 10,284
1965 15,436 98.1 15,143
1966 473 97.4 461
1967 26,407 93.9 24,796
1968 91,515 80.8 73,944
1969 (1st Qtr.) 17,467 71.7 12,524
$138,654
. 35 U.S.C. § 284 provides, in pertinent part:
“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. . . . ”
. Judge Clark quotes in his dissent, infra, at p. 933, findings by the district court indicating that the one-piece seal was superior to the two-piece seal. Of course it was. If it were not, Murphy would have put into production the two-piece seal, instead of the one-piece seal. The critical fact, however, is *931that Murphy sold approximately 40 bits containing two-piece seals. We view this fact as adequate support for the finding of the trial court, stated in its opinion, that the two-piece seal represented a “commercially viable alternative” to the infringing one-piece seal,