opinion: TONE, Circuit Judge.
  This is the second appeal in this patent-infringement case. In the earlier appeal, this court affirmed the District Court’s judgment holding claims 14, 15 and 17 of U.S. Patent No. 2,800,252 valid and infringed and enjoining further infringement. Wahl v. Carrier Mfg. Co., 358 F.2d 1 (7th Cir. 1966). The present appeal presents issues relating to damages for infringement, attorney fees, interest, and, by reason of a cross-appeal, infringement by certain modified devices manufactured and sold by defendant and the allowance of costs.
  Plaintiffs are Eugene A. Wahl, the inventor and owner, and Vibra Screw Feeders, Inc., the exclusive licensee in the United States. The patent, which is described in our earlier opinion (358 F.2d at 2), relates to an auger-type feeder for use in introducing the desired amount of dry materials into a product being compounded. Defendant, Carrier Manufacturing Company, Inc., is a manufacturer of machines that embody auger-type feeders held to infringe the patent.
  Some time after the original complaint was filed, defendant modified its accused device and manufactured and sold modified versions of several different types. Only the original version was involved in the first trial, and therefore the judgment of infringement affirmed by this court covered only that version. While the appeal from that judgment was pending, defendant filed in the District Court a petition for clarification of the judgment, or, in the alternative, for a declaration that the modified versions did not infringe the patent. After this court’s affirmance of the original judgment, the District Court held a second trial on the issues raised by the petition and on October 16, 1968, entered a supplemental judgment determining that all of defendant’s modified versions infringed claim 14.
  Following the entry of the supplemental judgment, from which defendant did not appeal within 30 days, the District Court referred the case to a master for an accounting to determine plaintiffs’ damages and costs. After trial before him, the master, in a report consisting of findings of fact and conclusions of law, to which both sides objected, recommended allowance of damages of $37,-743.03 and costs of $20,240.00. The District Court adopted the master’s findings and conclusions, allowed interest on the damages commencing with the date the master’s report was filed, denied treble damages and attorney fees, and entered judgment accordingly.
  Plaintiffs appeal, urging that the damages allowed are inadequate, that attorney fees should have been awarded, and that interest should have been allowed from the end of each year in which damages were incurred. Defendant cross-appeals, urging that the modified devices do not infringe and that certain costs should not have been allowed. We affirm the judgment of the District Court in all respects except costs.
  Appealability of the Supplemental Judgment of Infringement
  Plaintiffs’ motion to dismiss the cross-appeal as untimely, denied by Judge Stevens as motion judge, is renewed. We adhere to Judge Stevens’s ruling. The time to appeal from the supplemental judgment began to run with the entry of final judgment in this case. Victor Talking Machine Co. v. George, 105 F.2d 697, 699 (3d Cir. 1939), cert. denied, 308 U.S. 611, 60 S.Ct. 176, 84 L.Ed. 511 (1939); Bingham Pump Co. v. Edwards, 118 F.2d 338, 339 (9th Cir. 1941), cert. denied, 314 U.S. 656, 62 S.Ct. 107, 86 L.Ed. 525 (1941).
  Merits of Supplemental Judgment
  Claim 14, held infringed by defendant’s revised structures, requires that the auger be deliberately and controllably vibrated during rotation. This was held to occur in defendant’s original accused device because, although the trough and tube were vibrated independently of the auger, and the auger was secured to the base, the rubber mounts on which the base rested permitted the base and thus the auger to vibrate. (358 F.2d at 5.) Defendant argues that its redesigned feeders do not infringe because they are bolted down, rather than being mounted on rubber feet, and therefore vibration of the auger is not permitted, and claim 14 is not infringed.
  The District Court found, however, that in each of the revised structures the auger was deliberately and controllably vibrated, because the vibrator mounted on the feeder vibrated the entire structure even though it was bolted down. Thus the court found that the modified structures perform substantially the same function in substantially the same way, and the doctrine of equivalents applies. The finding of equivalence is a determination of fact (Hazel-tine Research v. Admiral Corp., 183 F.2d 953, 955 (7th Cir. 1950), cert. denied, 340 U.S. 896, 71 S.Ct. 239, 95 L.Ed. 650 (1950)) and is supported by sufficient evidence, which we need not detail. That finding is not clearly erroneous and therefore cannot be disturbed.
  Damages for Infringement
  The District Court confirmed the master’s finding that the damages proved to have resulted from defendant’s infringement, which occurred during the period 1963 to April 1969, were $37,-743.03. ' Plaintiffs argue that this amount is grossly inadequate.
  First, it is contended that Vibra Screw could have increased its prices on the feeders it sold by 10 per cent if it had not been for defendant’s unlawful competition. Plaintiffs did not offer testimony of customers or other evidence, except testimony of Wahl himself, that customers would have been willing to pay more than they did for Vibra Screw’s feeders. In accepting the master’s finding on this point, the District Court stated:
  “The master found that in spite of the defendant’s infringing efforts, Vibra Screw always maintained a dominant share of the sales of the patented feeders, and based on Vibra Screw’s pricings before, during and after infringement ended, defendant’s sales had little or no effect on Vibra Screw’s pricing of its feeders.”
  The court held that these findings were supported by sufficient evidence and not clearly erroneous. (See Rule 53(e)(2), Fed.R.Civ.P.) We agree.
  Next it is argued that if it had not been for defendant’s unlawful competition Vibra Screw would have reduced its advertising expense by $300,000. This argument is based upon evidence that the “industry norm” of expenditures for advertising in relation to total sales, as reported in the December 29, 1969 issue of Advertising Age, was about half that spent by Vibra Screw, and the testimony of plaintiff Wahl, the company’s president, that it spent twice the industry norm to combat defendant’s illicit feeder competition. There was, however, no effort to show how much of Vibra Screw’s advertising related to feeders and how much related to its products other than feeders. Moreover, during the years 1969 and 1970, when Vibra Screw had no competition from defendant, its advertising expenditures were greater in relation to sales than they were during the years defendant was a competitor. The master and the District Court could reasonably have concluded, as they did, that damages based on excessive advertising expenditures would be speculative.
  Plaintiffs also argue that during the damage period Vibra Screw could have made and sold 212 additional feeders, which was the number of infringing feeders sold by defendant, if it had not been for defendant’s illicit competition, and that its profit on these additional feeders and on related goods and parts would have been 50 per cent. This argument rests upon the assumption that fixed costs would have remained the same and that there would have been no additional labor costs but only incremental costs of material and commissions in making and selling the 212 additional machines. The soundness of this assumption is undermined by the failure of plaintiffs’ accounting experts to make the detailed analysis of all the operations and costs of the company on a daily or weekly basis which would have been necessary to a determination of incremental costs. It is true that the master found that Vibra Screw could have assembled one extra feeder per week without hiring extra workers. But the performance of additional assembly work would presumably mean that other work would not be done, which would somehow be reflected in added costs. Also, if these 212 additional feeders had been built there would have been additional costs for inventory power, and maintenance and wear of equipment used in assembly. The significance of all these costs could only have been determined by making a cost study in depth. The rejection by the master and the District Court of plaintiffs’ incremental cost analysis is further supported by the operating figures for all of Vibra Screw’s operations from 1965 to 1969, which show that its sales nearly doubled while additional operating profits were only about 8 per cent of the increase in sales, and that in the years 1967, 1968, and 1970 Vibra Screw’s operating profits declined while its sales increased. We cannot say that the findings on this subject were clearly erroneous.
  Plaintiffs also attack the finding that defendant’s profits on the infringing feeders it manufactured and sold were 1 per cent, arguing that on an incremental cost theory its profits were much greater and that its eagerness to get the business belied so small a profit. Again plaintiffs did not introduce the kind of evidence that would have been necessary to support an incremental cost approach. And we cannot say that defendant’s eagerness to remain in the market conclusively shows highly profitable operations during the damage period as opposed to hope for profits in the future.
  It is also argued that the finding as to defendant’s profits is inconsistent with the finding that a reasonable royalty would be 10 per cent. That this does not follow is recognized by the patent statute, 35 U.S.C. § 284, which in providing that in no event shall damages be less than a reasonable royalty, recognizes that there can be a reasonable royalty even though the proof shows small actual damages or no actual damages at all. The statute makes a finding of a reasonable royalty necessary in all cases in which damages are to be allowed. It is not necessarily incongruous that damages based on lost profits and damages calculated by applying a reasonable royalty were about the same.
  The findings of the Disctrict Court on the amount of plaintiffs’ damages are not clearly erroneous and therefore must be sustained.
  Treble Damages and Attorney Fees
  Plaintiffs also complain of the District Court’s refusal to treble the damages or allow attorney fees. They argue that defendant’s manufacture and sale, after entry of the original injunction, of the modified feeder ultimately held to infringe claim 14 was contemptuous and therefore, the District Court erred both in not “increasing the damages” under 35 U.S.C. § 284 and in not considering the case “exceptional” under 35 U.S.C. § 285. The District Court, noting in substance that the issue of patent-ability was close and that the infringement issues were fairly debatable and litigated in good faith, refused to increase the damages and ordered that each party bear its own attorney fees. The court’s ruling was consistent with our decisions under section 284, Union Carbide Corp. v. Graver Tank Mfg. Co., 282 F.2d 653, 675 (7th Cir. 1960), cert. denied, 365 U.S. 812, 81 S.Ct. 692, 5 L.Ed.2d 691 (1961), and section 285, Allen v. W. H. Brady Co., 508 F.2d 64, 67 (7th Cir. 1974).
  Interest
  The District Court allowed interest commencing on the date the master’s
  report was filed. Plaintiffs’ argument that interest should run from the end of each year in which infringement occurred on the amount of damages incurred in that year is based on statements in the House and Senate Reports on prior versions of what became section 284, cited in Aro Mfg. Co. v. Convertible Top Co., 377 U.S. 476, 505-506, 84 S.Ct. 1526, 12 L.Ed.2d 457 (1964), to the effect that “interest from the time infringement occurred” is recoverable. H.R. Rep. No. 1587, 79th Cong., 2d Sess. 1-2 (1946); S.Rep. No. 1503, 79th Cong., 2d Sess. 2 (1946), U.S.Code Cong. Serv. p. 1387. The language in the bill which these statements describe was deleted, however, before the bill was enacted. See General Electric Co. v. Sciaky Bros., Inc., 415 F.2d 1068, 1077 (6th Cir. 1969). The argument that the language of the committee reports was nevertheless given sanction by the citation in the Aro case was rejected by the Second Circuit in Georgia-Pacific Corp. v. U. S. Plywood-Champion Papers Inc., 446 F.2d 295, 301 n. 7 (2d Cir. 1971), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971). But cf. Marvel Specialty Co. v. Bell Hosiery Mills, Inc., 386 F.2d 287, 290 — 291 (4th Cir. 1967), cert. denied, 390 U.S. 1030, 88 S.Ct. 1409, 20 L.Ed.2d 286 (1968). We agree with the Second Circuit on this point. That court adopts the further view in the Georgia-Pacific case that the 1946 Amendment to the statute, which speaks of “interest ... as fixed by the court,” altered the rule of Duplate Corp. v. Triplex Safety Glass Co., 298 U.S. 448, 459, 56 S.Ct. 792, 80 L.Ed. 1274 (1936) to the extent of giving the District Court “its traditional discretionary power in equity”. 446 F.2d at 302. This circuit, however, has continued, after the 1946 Amendment, to apply the rule of Duplate that interest should run from the date damages are liquidated absent exceptional circumstances. Union Carbide Corp. v. Graver Tank & Mfg. Co., supra, 282 F.2d at 677. We defer to the law of the circuit and decline to disturb the District Court’s ruling on interest.
  Costs
  The order of reference to the master included a direction to determine the costs recoverable by plaintiffs. The master included in his report findings of costs in the amount of $20,240, and the District Court awarded costs in that amount. Neither side complains of the reference of the issue of costs to a master.
  Under Rule 54(d), Fed.R.Civ.P., costs are to be allowed to the prevailing party except when otherwise provided by statute or unless the district court directs otherwise. 28 U.S.C. § 1920 provides for the taxing of costs:
  A judge or clerk of any court of the United States may tax as costs the following:
  (1) Fees of the clerk and marshal;
  (2) Fees of the court reporter for all or any part of the stenographic transcript necessarily obtained for use in the case;
  (3) Fees and disbursements for printing and witnesses;
  (4) Fees for exemplification and copies of papers necessarily obtained for use in the case;
  (5) Docket fees under section 1923 of this title.
  A bill of costs shall be filed in the case and, upon allowance, included in the judgment or decree.
  28 U.S.C. § 1924 requires that before costs are taxed, they must be verified by an affidavit that states the items are correct and were necessarily incurred in the case.
  The Supreme Court, construing Rule 54(d) in Farmer v. Arabian American Oil Co., 379 U.S. 227, 235, 85 S.Ct. 411, 416, 13 L.Ed.2d 248 (1964), stated:
  “We do not read that Rule as giving district judges unrestrained discretion to tax costs to reimburse a winning litigant for every expense he has seen fit to incur in the conduct of his case. Items proposed by winning parties as costs should always be given careful scrutiny. Any other practice would be too great a movement in the direction of some systems of jurisprudence, that are willing, if not indeed anxious, to allow litigation costs so high as to discourage litigants from bringing lawsuits, no matter how meritorious they might in good faith believe their claims to be. Therefore, the discretion given district judges to tax costs should be sparingly exercised with reference to expenses not specifically allowed by statute. Such a restrained administration of the Rule is in harmony with our national policy of reducing insofar as possible the burdensome cost of litigation.”
  Our difficulty with the assessment of costs begins with plaintiffs’ failure to file an affidavit of costs, as required by 28 U.S.C. § 1924. As a result of this omission and the failure to offer any authenticating testimony at the hearing before the master, there was no proper authentication of any items of costs.
  In addition, it does not appear that the items proposed as costs were given “careful scrutiny,” or that the discretion to allow costs was “sparingly exercised with reference to expenses not specifically allowed by statute,” as required by Farmer. We therefore remand the case to the District Court with directions to redetermine the allowable costs in the light of the admonition of Farmer and in accordance with the additional standards set forth below.
  At the hearing on costs before the master, plaintiffs offered as Exhibit 78 a group of bills from the New York law firm that represents them in this case dated during the period June 1, 1963 to April 1, 1970. These bills were admitted over objection despite the absence of any authentication and were the basis for the assessment of some $11,061 of the costs allowed. Some of the disbursements shown in the bills were made in connection with this litigation but others were made for other unrelated litigation. Plaintiffs, instead of identifying the case to which each disbursement related, prorated the disbursements on each bill among the various cases, based apparently on the proportion of legal services shown on the bill to have been rendered in each case. Thus, if, in the bill for a given month, services in this case were charged at $1,000 and in another case at $500, two-thirds of the disbursements would be charged to this case. This method of proving costs led to some absurd results. For example, one of the other cases for which services and disbursements were jointly billed was another patent infringement case between the same parties relating to a hopper patent, in which defendant prevailed. Wahl v. Carrier Mfg. Co., 452 F.2d 96 (7th Cir. 1971), cert. denied, 405 U.S. 990, 92 S.Ct. 1255, 31 L.Ed.2d 457 (1972). The bill of December 31, 1967 includes a disbursement, which related to the hopper case, of $874.50 paid to court reporter. A portion of this disbursement was charged to defendant, notwithstanding that it prevailed in the hopper case.
  The assessment of costs based on the arbitrary allocation of disbursements made by plaintiffs was unwarranted. To be recoverable as a part of costs, a disbursement must be shown to have been made in connection with the case in which the costs are allowed. Such a showing is normally made by an affidavit under 28 U.S.C. § 1924. The affidavit may be based on the affiant’s knowledge or on business records available to him, but a mere oral assertion of the attorney for the prevailing party is manifestly inadequate.
  Most of the bills contain a lump sum charge for “miscellaneous disbursements for” various described items including “copies of patents,” “postage,” “telephone calls,” “photoprints,” and “typing.” Typically the enumeration ends with “etc.” In the first place, such a listing in explanation of a single sum was an inadequate basis for allowing costs, because it shows neither the amount of the individual expenditures nor the cases in connection with which they were made. Secondly, costs are not allowable for many of the expenditures listed. While charges for copies of patents, file wrappers and photoprints reasonably necessary for use in the case are recoverable as costs (W. F. & John Barnes Co. v. International Harvester Co., 145 F.2d 915, 918-919 (7th Cir. 1944), cert. denied, 324 U.S. 850, 65 S.Ct. 687, 89 L.Ed. 1410 (1945); 6 J. Moore, Federal Practice ¶ 54.77[6], at 1737 (2d ed. 1974)), charges for telephone calls and, ordinarily, for postage are not (Lee National Corp. v. Kansas City Southern Industries, Inc., 50 F.R.D. 412, 413 (S.D. N.Y.1970); Department of Highways v. McWilliams Dredging Co., 10 F.R.D. 107, 108 (W.D.La.1951), aff’d, 187 F.2d 61 (5th Cir. 1951)). Typing charges, which are presumably incidental to attorneys’ services, are not taxable.
  The bills in Exhibit 78 also contain disbursement items for other expenses of attorneys, including traveling expenses incurred in attending depositions, pretrial conferences, and trial, as well as expenses incurred in making investigations. These expenses are not recoverable as costs. Kiefel v. Las Vegas Hacienda, Inc., 404 F.2d 1163, 1170 (7th Cir. 1968), cert. denied, 395 U.S. 908, 89 S.Ct. 1750, 23 L.Ed.2d 221 (1969); 6 J. Moore, Federal Practice, supra, ¶ 54.-77[4], at 1725, and ¶ 54.77[8], at 1751.
  The bills also include disbursements for legal services of local counsel. The District Court having specifically held that plaintiffs were not entitled to recover attorney fees, these expenditures were not recoverable as fees, and they were plainly not recoverable as costs.
  The charges of the court reporter for transcripts of the trial and of depositions reasonably necessary for use in the case even though not used at trial are recoverable upon a proper showing as provided in 28 U.S.C. § 1924. E. g., Hope Basket Co. v. Product Advancement Co., 104 F.Supp. 444, 449 (W.D.Mich.1952); 6 J. Moore, Federal Practice, supra, ¶ 54.77[4], at 1720. This is true of charges for services of the official court reporter as well as those of a private reporter. Fleischer v. A.A.P. Inc., 36 F.R.D. 31, 36 (S.D.N.Y.1964).
  Some $7,384 of the costs recovered by plaintiffs relates to the expenses of demonstration models, preparation of exhibits, stands, and equipment used to operate exhibits, and transportation of exhibits. The amounts of these items were determined by estimates, an unsatisfactory method of proving expenses and disbursements if invoices and other kinds of more reliable evidence are available. Estimates should be received only upon a showing that such other evidence is not available through no fault of the claimant.
  Turning to the allowability of expenses of this kind as costs, this court has allowed costs for models and charts. W. F. & John Barnes Co. v. International Harvester Co., supra, 145 F.2d at 916, 918. Other circuits have refused to allow such costs for lack of statutory authority. Specialty Equipment & Mach. Corp. v. Zell Motor Car Co., 193 F.2d 515, 520-521 (4th Cir. 1952); Johns-Manville Corp. v. Cement Asbestos Products Co., 428 F.2d 1381, 1385 (5th Cir. 1970). While we do not overrule our prior decision in the Barnes case, which has been the law in this circuit for over 30 years, we must require district courts, in ruling on applications for allowance of expenditures for models and demonstration exhibits as costs, to heed the admonition of the Farmer case (379 U.S. at 235, 85 S.Ct. at 416) that “the discretion given district judges to tax costs should be sparingly exercised with reference to expenses not specifically allowed by statute.” Ordinarily, it will be best to follow Professor Moore’s suggestion that prior approval of the district court be obtained, if a party wishes to use an expensive model or exhibit, the expense of which he will seek to have taxed as costs. 6 J. Moore, Federal Practice, supra, ¶ 54.77[6], at 1739-1741. We shall not impose that requirement in a case already tried. It does not appear here, however, that in allowing exhibit and model expenses as costs the District Court sparingly exercised its discretion. These elements of costs should be reexamined on remand. We add that the expense of transporting exhibits is not a proper element of costs. Twentieth Century Fox Film Corp. v. Goldwyn, 328 F.2d 190, 224 (9th Cir. 1964), cert. denied, 379 U.S. 880, 85 S.Ct. 143, 13 L.Ed.2d 87 (1964).
  The judgment of the District Court is affirmed in all respects except the award of costs. As to costs, the action is remanded to the District Court for further proceedings consistent with this opinion.
  Affirmed in part; reversed and remanded in part.
  . The master, in rejecting plaintiffs’ argument, relied specifically on testimony of defendant’s accountant that some additional overhead and labor costs would necessarily be incurred in the production of the additional machines and the testimony of Vibra Screw’s chief engineer that the back-up man in the assembly shop had other duties to perform. The master’s analysis on this point is reasonable and supported by sufficient evidence.