LEWIS R. MORGAN, Circuit Judge:

Golf City, Inc., a golf specialty retail store located in New Orleans, Louisiana, brought this antitrust action more than seven years ago after numerous golf equipment manufacturers refused to sell to Golf City their prestige lines, or "pro-lines," of golf equipment. Golf City alleged that the refusals to deal arose out of a conspiracy involving the manufacturers and the Professional Golfers' Association of America (PGA).

The original defendants were PGA and fourteen of the manufacturers. All but one of the manufacturers, Wilson Sporting Goods Co. (Wilson), settled with Golf City along the way. After extensive discovery, the case against Wilson and PGA was tried to the district court sitting without a jury. In February, 1975, the court issued what it styled a Memorandum of Reasons, finding that Wilson and PGA had violated section 1 of the Sherman Act. Then, in May, 1975, the court issued another Memorandum of Reasons awarding Golf City treble damages, interest, and attorneys' fees.

Appellants Wilson and PGA launch a broad attack on the district court's decision. On the question of liability, they urge that the district court's findings of fact, required by Rule 52(a) of the Federal Rules of Civil Procedure, do not give a clear understanding of the basis of the court's decision. Appellants contend alternatively that the finding of liability was clearly erroneous in the face of certain uncontradicted defense evidence. With respect to damages, Wilson and PGA seek to impugn the adequacy of Golf City's figures. Moreover, appellants challenge the district court's calculation of net profit as clearly erroneous and question the district court's complete failure to deal with the question of mitigation of damages. Finally, Wilson and PGA assert that the district court made an error of law in its award of interest and awarded excessive attorneys' fees. PGA, in a separate argument, challenges an earlier district court decision holding that PGA had transacted business in the Eastern District of Louisiana within the meaning of the federal venue statute.

Golf City contends in a cross-appeal that the district court should have awarded additional damages and attorneys' fees.

I. FACTS

A. The Golf Equipment Industry

Golf equipment merchandising in the United States is two-tiered. One tier is pro-line equipment and the other tier is store-line equipment. Some manufacturers offer only pro-line equipment, and others offer both pro-line and store-line equipment. The manufacturers generally restrict the sale of their pro-line equipment. Since 1930, for example, appellant Wilson has sold its pro-line equipment "only to pro shops located at outdoor golf courses or driving ranges." The pro-line golf equipment is heavily advertised by the manufacturers in golf magazines and in other publications, and these advertisements generally state that the equipment is available only at pro shops. Because pro shops operated by golf professionals are the common beneficiaries of the manufacturers' restrictive distribution policies for pro-line equipment, the policies are referred to as pro only sales policies.

Store-line equipment ordinarily is sold to any retail outlet that meets certain credit requirements. The manufacturers do very little direct advertising of their store-line equipment.

B. PGA

PGA is a self-described trade association of golf professionals. According to PGA, approximately 4,600 PGA members were head professionals at the 10,870 golf clubs or courses in the United States as of September 1, 1974. Thus, PGA members accounted for nearly 50 per cent of the pro shop outlets in the country as of that date.

C. Golf City

As we have stated, Golf City is a golf specialty retail establishment located in New Orleans, Louisiana. Golf City's owner is James H. "Buddy" Orange, a former automobile executive who became a golf enthusiast in the 1960's and who, in 1968, developed an interest in entering the golf equipment retailing business.

Orange obtained the initial inventory for Golf City from Burt Dargie, the owner of a golf specialty store in Memphis, Tennessee. Orange testified that he had modeled Golf City after Dargie's operation and that the two stores shared such attributes as special machines for evaluating one's golf swing, large display areas, and a complete repair facility. After Golf City opened in April, 1969, Orange sought to increase the store's inventory of pro-line merchandise by purchasing some directly from the manufacturers. Orange was repeatedly rebuffed. In December, 1969, Golf City sued.

II. LIABILITY

A. Injury

Golf City brought its action under section 4 of the Clayton Act, which grants a private cause of action for antitrust violations to any person "injured in his business or property" by the anticompetitive conduct. Golf City identifies the injury to its business or property as "the inability to purchase [pro-line equipment] directly from the manufacturers." Brief for Golf City at 46.

B. Conspiracy

The injury alleged must be caused by an antitrust violation. See Brunswick Corp. v. Pueblo Bowl-O-Mat, Inc., 429 U.S. 477, 97 S.Ct. 690, 50 L.Ed.2d 701 (1977). Golf City contends that the refusals of the manufacturers to deal with it in pro-line merchandise were born of a conspiracy involving the manufacturers and PGA, a conspiracy "designed to exclude from the market direct competitors of some members of the combination", E. A. McQuade Tours, Inc. v. Consolidated Air Tour Manual Committee, 467 F.2d 178, 186-87 (5th Cir. 1972), cert. denied, 409 U.S. 1109, 93 S.Ct. 912, 34 L.Ed.2d 690 (1973), and therefore a conspiracy unlawful per se under section 1 of the Sherman Act.

Appellants Wilson and PGA maintain, as they have throughout the course of the litigation, that the pro only sales policies which dictated the refusals to deal with Golf City were adopted unilaterally by each manufacturer and are so maintained. Appellants contend that the pro only sales policies are in wide use because they are an effective form of non-price competition — consumers like to purchase prestige golf equipment available only at pro shops. Appellants' point, if factually correct, would be a complete defense to the section 1 allegation, because

[s]ection 1 . . . is directed only at joint action. [citation omitted] It does not prohibit independent business actions and decisions. A person still has the right to refuse to do business with another, provided he acts independently and not pursuant to an unlawful understanding, tacit or expressed.

Modern Home Institute, Inc. v. Hartford Accident Indemnity Co., 513 F.2d 102, 108 (2d Cir. 1975).

The mere fact that substantially all of the manufacturers approached by Golf City refused to deal does not permit the inference of conspiracy. We quote again from the Second Circuit's Modern Home Institute:

Both sides agree that parallel behavior alone is not sufficient evidence of conspiracy to find a Sherman Act § 1 violation. [citations omitted] The mere fact that all defendant companies were initially enthusiastic about plaintiff's proposal and then rejected it, even if they knew the other defendant companies were doing likewise, is not enough to defeat the motion for summary judgment. [citation omitted] Such parallel conduct is consistent with independent competitive decisions or at most reflects a non-consensual decision not to compete. Additional facts or circumstances are needed to show that the decisions were interdependent and thus raise the inference of a tacit agreement to boycott. [citations omitted]

513 F.2d at 110.

The "additional facts or circumstances" offered by Golf City to raise the inference of conspiracy were adduced in a series of documents designated collectively in the record as exhibit P-76. The P-76 documents were obtained from PGA during discovery. They are chiefly letters and reports and, for the most part, they chronicle PGA's efforts between 1967 and 1969 to stop golf pros from participating in what is called the bootleg market in pro-line equipment. Apparently many pros are willing to sell some of the pro-line equipment they have bought from the manufacturers to outlets like Golf City that cannot obtain the goods directly. This bootleg market is also called leakage.

The main character in the events revealed in the P-76 documents was William Clarke, who then was chairman of a PGA committee called the Manufacturers' Relations Committee. Another key character was Joe Wolfe, a Wilson executive who chaired a committee of manufacturers' representatives that was the industry counter-part of the Clarke Committee. There is no doubt that these documents show a continuing effort in the late sixties by Clarke and Wolfe to stop leakage.

This antileakage evidence naturally drew the parties to a 1966 Supreme Court case, United States v. General Motors Corp., 384 U.S. 127, 86 S.Ct. 1321, 16 L.Ed.2d 415 (1966), and the district court made General Motors the legal centerpiece for its decision on liability. In General Motors, the big auto maker's Chevrolet dealers in the Los Angeles area complained to GM that some dealers were reselling their cars to discount houses that purportedly were offering the Chevrolets to the public at prices below those of the GM franchisees. The Supreme Court held that the efforts by GM and its dealers to stop this leakage transgressed section 1 of the Sherman Act. The Court summarized the key findings of the district court:

That in the summer of 1960 the Losor Chevrolet Dealers Association, `through some of its dealer-members,' complained to General Motors personnel about sales through discounters . . .; that at a Losor meeting in November 1960 the dealers there present agreed to embark on a letter-writing campaign directed at enlisting the aid of General Motors . . .; that in December and January General Motors personnel discussed the matter with every Chevrolet dealer in the Los Angeles area and elicited from each a promise not to do business with the discounters . . .; that representatives of the three associations of Chevrolet dealers met on December 15, 1960, and created a joint investigating committee . . .; that the three associations then undertook jointly to police the agreements obtained from each of the dealers by General Motors; that the associations supplied information to General Motors for use by it in bringing wayward dealers into line, and that Chevrolet's O'Connor asked the associations to do so . . .; that as a result of this collaborative effort, a number of Chevrolet dealers were induced to repurchase cars they had sold through discounters and to promise to abjure such sales in future. . . .

These findings by the trial judge compel the conclusion that a conspiracy to restrain trade was proved.

384 U.S. at 140-42, 86 S.Ct. at 1328.

The instant case is not on all-fours with General Motors. As we shall discuss infra, the Golf City theory of liability does not seem to include the antileakage efforts themselves as a separate source of injury to Golf City. Golf City points to the antileakage evidence only as proof that the lack of direct availability of pro-line goods from the manufacturers was the product of conspiracy. To make General Motors analogous, one would have to change its facts as follows: first, the automobile discounters would be the plaintiffs; second, their complaint would be that GM refused to sell them Chevrolets directly; third, their theory of liability would be that the franchise distribution system used by GM was the product of a conspiracy involving GM, other automobile manufacturers, and the dealers; and fourth, the proof of a franchise system conspiracy would be the antileakage evidence actually adduced in the General Motors case. As our discussion of the district court's findings infra indicates, we have some difficulty with this scenario.

C. The District Court's Findings

After noting the uniform refusals to deal with Golf City by the manufacturers and after setting out a portion of the antileakage evidence, the district court found that

PGA and manufacturers are working together in a rather tight conspiracy to restrict the sale of pro line goods to pro shops only, to police leakage into stores like the plaintiff's.

Appendix, vol. I, at 218. Then later in its Memorandum of Reasons on liability the court made the general finding that "plaintiff's lack of pro-line goods causes a loss of business." Id. at 225.

PGA and Wilson attack these findings two ways. First, they argue that the findings do not give a clear understanding of the basis of the district court's decision and therefore are inadequate under Rule 52(a) of the Federal Rules of Civil Procedure. Alternatively, PGA and Wilson contend that the finding of liability was clearly erroneous. Since we agree that the findings fail to give a clear understanding of the basis of the court's decision, we do not reach the clear error issue.

1. Rule 52(a): General Principles. — Rule 52(a) mandates that in all civil actions tried without a jury "the court shall find the facts specially . . . ." One purpose of the rule is to aid the appellate court by affording it a clear understanding of the ground or basis of the decision of the trial court. Silberblatt, Inc. v. United States, 353 F.2d 545, 549 (5th Cir. 1965). Another purpose of the rule, identified forthrightly by Judge Frank, is to engender care on the part of the trial judge in ascertaining the facts:

It is sometimes said that the requirement that the trial judge file findings of fact is for the convenience of the upper courts. While it does serve that end, it has a far more important purpose — that of evoking care on the part of the trial judge in ascertaining the facts. For, as every judge knows, to set down in precise words the facts as he finds them is the best way to avoid carelessness in the discharge of that duty: Often a strong impression that, on the basis of the evidence, the facts are thus-and-so gives way when it comes to expressing that impression on paper. The trial court is the most important agency of the judicial branch of the government precisely because on it rests the responsibility of ascertaining the facts. When a federal trial judge sits without a jury, that responsibility is his. And it is not a light responsibility since, unless his findings are `clearly erroneous,' no upper court may disturb them. To ascertain the facts is not a mechanical act. It is a difficult art, not a science. It involves skill and judgment. As fact-finding is a human undertaking, it can, of course, never be perfect and infallible. For that very reason every effort should be made to render it as adequate as it humanly can be.

United States v. Forness, 125 F.2d 928, 942-43 (2d Cir.), cert. denied, 316 U.S. 694, 62 S.Ct. 1293, 86 L.Ed. 1764 (1942) (footnotes omitted). See United States v. Merz, 376 U.S. 192, 199, 84 S.Ct. 639, 11 L.Ed.2d 629 (1964) (more careful consideration of problem assured if finder of fact required to state not only end result, but also process by which result reached).

The "facts" that 52(a) admonishes must be found specially are not all of one kind. They lie along a conceptual line from those termed "subsidiary" to those labeled "ultimate." For example, in the instant case a subsidiary fact might be that appellant Wilson notified Golf City on a certain date that Wilson would not sell Golf City pro-line golf equipment. An ultimate fact might be that PGA and the manufacturers conspired to prevent Golf City from obtaining pro-line goods. Ultimate facts generally are derived from subsidiary facts through a cause-effect reasoning process. That is, when subsidiary facts A, B, and C are shown to exist, then, because of the fact-finder's knowledge of the way the world works, he is able to conclude that, more likely than not, ultimate fact X also exists. He infers X from A, B, and C.

Rule 52(a) does not require that the trial court set out findings on all the myriad factual questions that arise in a case. As we have said: "Courts need not indulge in exegetics, or parse or declaim every fact and each nuance and hypothesis." Gulf King Shrimp Co. v. Wirtz, 407 F.2d 508, 516 (5th Cir. 1969). On the other hand, parsimony in setting out subsidiary facts may run afoul of the rule:

We have concluded that the findings of the district court do not provide a sufficiently definite predicate for proper appellate review. Many of the findings are couched in conclusory terms. Some were announced solely as ultimate findings without support which clearly reflected a choice between conflicting accounts of events or between alternate legal interpretations of those events. This court cannot be left to guess. The findings and conclusions we review must be expressed with sufficient particularity to allow us to determine rather than speculate that the law has been correctly applied.

Hydrospace-Challenger, Inc. v. Tracor/MAS, Inc., 520 F.2d 1030, 1034 (5th Cir. 1975). See Lettsome v. United States, 434 F.2d 907, 909 (5th Cir. 1970). Wright and Miller observe that "[i]deally findings of fact should be clear, specific, and complete, without nonrealistic and uninformative generality on the one hand, and on the other without an unnecessary and unhelpful recital of nonessential details of evidence." 9 Wright Miller, Federal Practice and Procedure § 2579, at 711 (1971). Relating the degree-of-thoroughness question to the purposes of Rule 52(a), the findings of the trial court must be sufficiently detailed to give us a clear understanding of the analytical process by which ultimate findings were reached and to assure us that the trial court took care in ascertaining the facts.

Compliance with Rule 52(a) is not a jurisdictional requirement for appeal:

[A]n appellate court may decide the merits of an appeal in the absence of fact findings in the rare case in which `a full understanding of the issues [can] be reached without the aid of findings.'

Davis v. United States, 422 F.2d 1139, 1142 (5th Cir. 1970). Whether a full understanding is possible goes "not . . . to jurisdiction but to our discretion . . . ." Gilbert v. Sterrett, 509 F.2d 1389, 1397 (5th Cir.) (Godbold, J., dissenting), cert. denied, 423 U.S. 951, 96 S.Ct. 373, 46 L.Ed.2d 288 (1975).

Rule 52(a) also provides that "[f]indings of fact shall not be set aside unless clearly erroneous . . . ." Justice Reed's definition of "clearly erroneous" has proved durable over the years:

A finding is `clearly erroneous' when although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed.

United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746 (1948). Findings that are sufficiently thorough to comply with Rule 52(a) must also survive the "clearly erroneous" crucible if so challenged on appeal.

2. Rule 52(a): Application Here. — For three reasons, all of them more or less related to the district court's treatment of the antileakage evidence, we conclude that the district court's findings on liability do not provide us with a clear enough understanding of the basis of its decision to enable us confidently to carry out our task of appellate review.

First, the findings are susceptible of the interpretation that the court predicated treble damage liability not only on the manufacturers' refusals to deal with Golf City, but also on the antileakage efforts. The interpretation is suggested by the portions of the court's opinion quoted supra and is strengthened by the following passage from the opinion:

The law . . . condemns collaborative manufacturers that uniformly refuse to deal with merchants. And our case goes further. The manufacturers and the PGA dominated pro shops work together to restrict pro shop sales to consumers only. The watch word of the golf industry is `Don't sell pro line merchandise to stores like the plaintiff.' In fact, this prohibition in the golf industry has developed its own nomenclature so that knowledgeable golf people say `We must stop leakage.' This attempt by a manufacturer to control the destiny of its golf clubs after sold to pro shops is also a violation of the Sherman Act. Even without a conspiracy a manufacturer's attempt to retain dominion over its products by controlling to whom the products are sold is illegal.

Appendix, vol. I, at 228. This language is puzzling, because the district court made no finding that Golf City was denied free access in any degree to the bootleg market as a result of conspiracy. In fact, the opinion is silent on whether appellee even attempted to purchase equipment in the bootleg market.

Wilson and PGA interpret the district court's opinion as predicating liability on the antileakage efforts as well as the manufacturers' refusals to deal. They expend much of their briefing space to a contention that, while Wilson and PGA agreed in principle to cooperate against leakage, no antileakage effort was implemented to Golf City's detriment, and Golf City, faced with the contention, does not really attempt to defend the court's finding. Referring to appellants' position that no antileakage effort was implemented, the Golf City brief states:

Such an assertion, however, amounts to nothing more than an effort to create a `straw man' which Wilson feels it can knock down. This is a case of `refusals to deal', and the `impact' of concerted action in the basic decisions not to sell pro-line golf products to Golf City comes from the lack of direct availability. The anti-leakage efforts of the PGA, and the `full cooperation by the manufacturers' . . are only corroborative of a basic conspiracy to keep the `pro-only' product from the `stores'. The `injury' was sustained from the inability to purchase directly from the manufacturers and the antileakage program is merely `salt on the wound', and not the wound itself.

Brief for Golf City at 46. The Golf City brief suffers from some of the same ambiguity that is the cause of our confusion about the court's findings, but certainly the passage quoted cannot be characterized as a vigorous defense of a finding of antileakage liability. On remand, if the court finds liability, it should clarify the role of the antileakage evidence in its factual analysis. If the evidence is used only as urged by Golf City, that is, to infer that the manufacturers' refusals to deal were tainted by conspiracy, then the findings should state that clearly. If, however, the court concludes that the antileakage efforts themselves injured Golf City, then the findings must set out the instances of injury.

Second, the district court failed to explain at all its chain of factual reasoning from the antileakage evidence to the conclusion that the manufacturers' pro only sales policies were born or maintained in conspiracy. Sometimes, of course, no such explanation is needed. The court need only set out the subsidiary facts and the path to the inference is self-evident. Not so here. We see no intuitive link between the antileakage evidence and the conclusion that the pro only sales policies were the product of conspiracy.

Clearly there is a link between the fact of antileakage and the fact of pro only sales policies. The two share the object of restricting to pro shops the sale of pro-line golf equipment. We do not understand, however, the nature of the link between antileakage and the question of whether the pro only sales policies were born or maintained in conspiracy. If the inference is based only on the notion that persons who engage in one conspiracy probably engaged in another, then the inference is improper. Cf. Theatre Enterprises, Inc. v. Paramount Film Dist. Corp., 346 U.S. 537, 543-44, 74 S.Ct. 257, 98 L.Ed. 273 (1954). We have trouble understanding why antileakage efforts would not be just as compatible with the scenario urged by appellants that the pro only sales policies were formulated unilaterally and were prompted by the utility of the policies as a form of non-price competition.

Third, we think the court's findings are inadequate because they fail to deal with uncontradicted, substantial defense evidence tending to show that the pro only sales policies indeed were formulated unilaterally. In 1967, for example, PGA's Clarke wrote to a PGA member and stated:

Everyone has talked for some time of a `pro-only' policy but as you well know we have none. The manufacturers up to now . . . [have] set their own policy and in most cases this has varied.

Exhibit P-76, Exhibits, vol. II, at 170. Moreover, appellants point out that each manufacturer adopted its policy at a different time, Wilson's policy was inaugurated thirty years before the antileakage discussions began, and no manufacturer limits pro-line sales to PGA pros. Reply Brief for PGA at 3. Finally, there is no finding on whether pro only policies are of a nature that no one manufacturer can maintain one unless all the other manufacturers go along. If it would be in any manufacturer's competitive self-interest not to have a pro-only distribution policy, then the continued use of the policies by nearly all the manufacturers would be suspicious:

Actions against the apparent individual economic self-interest of the alleged conspirators may raise an inference of interdependent action . . . [and] actions . . . only in one's self-interest if done in concert with others may also provide the basis for an inference of illegal conspiracy.

Modern Home Institute, supra, 513 F.2d at 111 (citations omitted).

While it is true, as we have noted, that the court need not deal with every piece of evidence or every argument raised, it is equally true that

[t]he reviewing court deserves the assurance that the trial court has come to grips with apparently irreconcilable conflicts in the evidence . . . and has distilled therefrom true facts in the crucible of his conscience.

Keystone Plastics, Inc. v. C P Plastics, Inc., 506 F.2d 960, 962 (5th Cir. 1975). We do not hold that the inference of a conspiratorial taint to the refusals to deal with Golf City was clearly erroneous. We decide only that, in (1) failing to provide us with the reasoning chain by which it made the inference and (2) failing to deal with crucial defense evidence, the district court has not given us a clear understanding of the basis of its decision. It may be that the antileakage evidence, either alone or coupled with other evidence in the record, will support a finding of conspiracy with respect to the pro only sales policies. If such a theoretical matrix exists, then the parties should have the opportunity to argue it to the district court, and the district court should make explicit its reasoning in setting out findings of fact. We must be able to understand why the ultimate fact of liability, if liability is again found, follows from the subsidiary facts decided.

III. DAMAGES

A. Net Profit Calculation

The district court awarded lost profit damages to Golf City because of Golf City's inability to obtain pro-line golf equipment. In computing the lost profit, the court calculated that Golf City could have generated additional sales of more than $260,000 for $6,000 in additional rent, salaries and other operating expenses. Appellants suggest that the district court used the $6,000 after plaintiff's counsel proposed at oral argument that the record would support it. Appellants point to the testimony of Golf City's proprietor, Mr. Orange, as showing the $6,000 calculation to be incredibly low.

On cross-examination, Orange testified that he would have needed (1) one additional sales person at about $5,000 per year, (2) no more than $1,500 to $2,000 in additional advertising, and (3) one additional assistant in the repair department at about $5,000 per year. These additional expenses would equal "an additional 12,000 per year" over a period of "five years less two months," totalling "slightly lower" than $60,000. Orange later adjusted his estimates slightly, but the figure remained well over the $6,000 used by the district court. We hold that the district court's finding on incremental operating cost is clearly erroneous.

B. Duty to Mitigate Damages

An antitrust plaintiff has a duty to mitigate damages. Here, Golf City might have mitigated its damages in either of two ways: (1) It might have purchased "leaked" pro line equipment from pro shops. (2) It might have attempted to increase its volume of store-line merchandise to compensate for the inability to obtain pro-lines goods.

The district court made absolutely no findings about mitigation of damages. Golf City contends that the bootleg market in leaked goods was not dependable and that leaked goods cost more. Moreover, Golf City claims there is little cross-elasticity of demand between store-line and pro-line merchandise. Certainly these points would bear on the amount of mitigation Golf City could be expected to accomplish. They do not, however, absolve Golf City of its duty to mitigate. Because the district court failed to make findings about mitigation, we have no clear understanding of how the court reached the conclusion it did on quantum.

IV. VENUE

Section 12 of the Clayton Act allows an antitrust action against a corporation to be brought in any judicial district where the corporation (1) is an inhabitant, (2) may be found, or (3) transacts business. The district court held that PGA could be sued in the Eastern District of Louisiana because it had transacted business there. The court based this conclusion on the following factors: (a) There are 55 PGA members in the State of Louisiana, along with an undetermined number of dues-paying apprentices who are working toward full membership in the PGA. (b) A golf magazine, circulating in the State of Louisiana and presented to the court, was shown to have carried, albeit without charge to the PGA, institutional advertising as to the service performed by golf professionals and containing in it the name "The Professional Golfer's Association of America," and the PGA emblem. (c) The PGA makes available in Louisiana the necessary applications and forms for membership in PGA by professional golfers, and by those seeking to become professional golfers. (d) The PGA recently has conducted in Baton Rouge, Louisiana, a five day "business school" for its members and apprentices in connection with the business of the administration of golf shops. (e) PGA regularly acknowledges golf feats by amateurs in the State of Louisiana by awarding them "membership" in the PGA "Hole-In-One-Club," such "membership" being given exclusively to those who score "holes-in-one" at golf clubs and courses served by PGA golf professionals. (f) A separate legal entity, the PGA Tournament Players Division Corporation, sponsors golf tournaments in various parts of the country, including Louisiana.

We address the last of these factors first. Certainly the conducting of a golf tournament by a corporation in a particular judicial district would constitute the transaction of business in that district within the meaning of the Clayton Act. The Supreme Court has stated that the test is whether "in fact, in the ordinary and usual sense, [the corporation] `transacts business' [in the district] of any substantial character." Eastman Kodak Co. v. Southern Photo Materials Co., 273 U.S. 359, 372-73, 47 S.Ct. 400, 403, 71 L.Ed. 684 (1927); see United States v. Scophony Corp., 333 U.S. 795, 807, 68 S.Ct. 855, 92 L.Ed. 1091 (1948). A golf tournament would clearly be transaction of business of a substantial character.

The district court conceded, however, that the Tournament Players Division was a separate legal entity, and we conclude for that reason that the contacts of that entity cannot be attributed to PGA for the purpose of fixing venue. The district court sought to connect the two corporations on the bases that (1) three of the ten members of the Tournament Players Division governing board are officers of PGA and (2) the PGA logo appears on membership applications for the Tournament Players Division. Those links are not sufficient. In San Antonio Telephone Co. v. American Telephone and Telegraph Co., 499 F.2d 349 (5th Cir. 1974), we rejected the contention that, because venue was proper for ATT in a particular judicial district, it was proper also for certain telephone operating companies associated with ATT. We said:

While it is true that venue may be established through a relationship between corporations when they in effect comprise a single entity . . . the evidence in this case does not demonstrate such a total disregard for the separate corporate entities. Rather it appears that, while ATT may dictate general policies of the operating companies, the daily business affairs are the responsibility of the different companies.

499 F.2d at 352 (citations omitted). The district court certainly did not find a "total disregard for the separate corporate entities" in the relationship between PGA and the Tournament Players Division. Thus, the Louisiana golf tournaments conducted by the Tournament Players Division cannot be added to the PGA venue brew.

We are left, then, with the findings we have designated a through e, and we hold these "too tenuous a connection . . . to constitute transacting business in the ordinary and usual sense." San Antonio Telephone Co. v. ATT, supra, 499 F.2d at 351 (footnote omitted). First, a professional association does not "transact business" in a judicial district merely because some of its members reside in the district and receive the association's publications there. Friends of Animals, Inc. v. American Veterinary Medical Ass'n, 310 F. Supp. 620, 624 (S.D.N.Y. 1970); Midwest Fur Producers Ass'n v. Mutation Mink Breeders Ass'n, 102 F. Supp. 649, 652 (D.Minn. 1951). Second, free advertising of the PGA in a golf magazine distributed in Louisiana is the most attenuated of contacts with the district. See San Antonio Telephone Co. v. ATT, supra, 499 F.2d at 351 n. 5. Third, the availability of PGA membership applications in the district adds only minutely to the PGA's contact with the district. Fourth, the conducting of a single five day business school in Baton Rouge, which is not within the Eastern District of Louisiana, cannot be more, and seems less, than an occasional sporadic contact with the Eastern District. Finally, we cannot believe that PGA's granting of "Hole-In-One-Club" memberships in the district so enhances the quality of PGA's contact with the district to render it amenable to suit there under the section 12 standard.

We have dealt with the contacts seriatim and have found them wanting. The harder task remains. Do the contacts, taken together, constitute the transaction of business in the district in the ordinary and usual sense? This aspect of the inquiry is most responsible for the observation that "the only rule of law which is uniformly applicable to all cases involving venue [is that] the decision depends entirely upon the particular facts involved." Courtesy Chevrolet, Inc. v. Tennessee Walking Horse Breeders' Exhibitors' Ass'n of America, 344 F.2d 860, 863 (9th Cir. 1965). We hold that, on the particular facts of this case as found by the district court in its venue opinion, the contacts as a whole are too tenuous to subject PGA to suit in the Eastern District of Louisiana pursuant to section 12 of the Clayton Act.

V. OTHER ISSUES

A. Price-Fixing

In one section of its opinion, the district court concludes that the actions of the appellants were motivated by a purpose to fix prices. We find it unnecessary to reach this point. If the district court on remand finds that the refusals to deal with Golf City were dictated by a conspiracy to prevent such stores from obtaining pro-line equipment, then liability will be established irrespective of any price-fixing question. Moreover, Golf City makes no argument that damages would be affected in the least by a price-fixing finding.

B. Interest

The district court awarded interest "on the untrebled portion of the judgment" from the date of judicial demand. Appendix, vol. I, at 233. By statute, 28 U.S.C. § 1961, interest runs on a judgment not from the date of judicial demand, but from the date of the judgment.

C. Cross-Appeal

Golf City's cross-appeal contentions about damages and attorneys' fees may be presented to the district court on remand, if the district court finds liability. Appellants' remaining contentions with respect to damages also may be presented to the district court.

VI. CONCLUSION

The judgment of the district court is reversed in part, vacated in part, and remanded for proceedings consistent with this opinion.