Sol Gloriosa Marítima, S.A. (“Gloriosa”) and the M.T. KEIYOH MARU (“KEIYOH MARU”) appeal a judgment for Trinidad Corporation (“Trinidad”) and the S.S. FORT WORTH in this maritime collision case. The district court found the KEI-YOH MARU entirely at fault for the accident. Appellants claim that the district court’s ruling was unsupported by substantial evidence, incorrectly determined the applicable rules of navigation governing the maneuvers of the KEIYOH MARU, incorrectly applied the rule of The Pennsylvania, 86 U.S. (19 Wall.) 125 , 22 L.Ed. 148 (1878), concerning the burden of proof in collision cases, and abused its discretion in selecting a formula for prejudgment interest. We affirm.

BACKGROUND

A. The Scene

The KEIYOH MARU is a Panamanian registered ocean-going oil tanker, under bareboat charter by Gloriosa. The FORT WORTH is a United States registered ocean-going oil tanker, owned and operated by Trinidad. These two ships collided on February 1, 1981, just outside the Port of Los Angeles.

The Port of Los Angeles/Long Beach has a breakwater separating the harbor from the open sea. There are two gaps in the breakwater. The entrance to the Port of Long Beach is east of the entrance to the Port of Los Angeles. At each breakwater entrance sea buoys and charts indicate trapezoidal pilot boarding areas. By the published orders of the United States Coast Guard Captain of the Port, Order 1-78, 45 Fed.Reg. 30,431 (1980), these pilot boarding areas were restricted to only those vessels entering or exiting each port. The collision between the KEIYOH MARU and the FORT WORTH occurred in the pilot boarding area for the Port of Los Angeles.

Between the trapezoidal boarding areas is a restricted area designated Anchorage “G”. By published Coast Guard regulations, 33 C.F.R. § 110.214 (a)(7) (1987), this area was restricted to only those vessels intending to anchor or depart from anchorage in the area. The restrictions with respect to the pilot boarding areas and Anchorage “G” prohibited a vessel outbound from the Port of Long Beach to cut across either area en route to the northbound shipping lanes. The pilot boarding area restrictions and the restrictions with respect to entering Anchorage “G” were clearly noted on charts in use aboard the FORT WORTH and KEIYOH MARU. These restrictions were also in government publications of which both vessels were required to be aware. 33 C.F.R. § 164.33 (1987). No evidence was introduced that either vessel had reason to be unaware of these restrictions.

B. The Accident

All material events leading to the collision occurred between 0125 hours and 0150 hours on February 1,1981. Night visibility was described as extremely clear, although the officers of the FORT WORTH indicated that the background lights from the harbor area restricted visibility in that direction. Weather conditions otherwise were unremarkable. There was little or no wind. The sea was calm.

At 0125 hours, the FORT WORTH was in the southbound coastal shipping lane heading into the Port of Los Angeles. She intended to enter the restricted pilotage area for the Port of Los Angeles, take on board a pilot there, and proceed into port. The FORT WORTH’S course was confirmed by a reconstruction offered by an expert witness, and was found by the district court to conform with the relevant navigational requirements for entry into the Port of Los Angeles.

The appellants claim that the FORT WORTH failed to effectively use radar and *821 post a lookout. They also suggest that the speed of the FORT WORTH was excessive. Moreover, they argue that the FORT WORTH failed to make radio communications, signal when collision was unavoidable, and display special lights. Finally, they claim the FORT WORTH made no attempt to ascertain the presence of the KEIYOH MARU until the collision was unavoidable. The district court found that the FORT WORTH had not used radar or a lookout to track the movements of other vessels in the area. The district court made no findings concerning the other claimed defects in the FORT WORTH’S navigation.

As the FORT WORTH was maneuvering towards the Los Angeles pilotage area, the KEIYOH MARU was departing from the Port of Long Beach. At about 0125 the KEIYOH MARU passed through the Long Beach breakwater entrance. At this point, the KEIYOH MARU was under the command of a harbor pilot, Captain Trottier. Once the KEIYOH MARU was safely through the breakwater, Trottier radioed the pilot boat to come alongside to pick him up. The precise location where the KEI-YOH MARU boarded Capt. Trottier onto the pilot boat was subject to dispute. Nevertheless, the district court found that the point where the KEIYOH MARU left off its pilot was no more than a thousand yards from the breakwater entrance. This finding was important since it credited the testimony of another pilot, Capt. Franklin, on board the pilot boat leaving the KEI-YOH MARU and heading towards the FORT WORTH, that the KEIYOH MARU later navigated through the restricted Anchorage “G”. The Coast Guard investigation after the collision also found that the KEIYOH MARU traversed the restricted Anchorage “G”. A reconstruction of the KEIYOH MARU’s course also confirmed that it sailed through Anchorage “G”.

Apparently, Capt. Franklin on board the pilot boat was the first to realize that the KEIYOH MARU was attempting to cut across the bow of the FORT WORTH. Franklin reached the wheelhouse of the FORT WORTH just as the captain of the FORT WORTH gave orders for full astern and gave a five-blast emergency signal. These were the only evasive maneuvers taken by either vessel just before the collision. The vessels collided inside the restricted Los Angeles pilot boarding area with the KEIYOH MARU’s port bow tearing into and destroying the entire bow of the FORT WORTH. By published U.S. Coast Guard rules, the KEIYOH MARU was restricted from entering this area since she was neither entering nor exiting the Port of Los Angeles. The FORT WORTH was entitled to be in this area since she was intending to enter the Port of Los Angeles.

Immediately after the collision, Pilot Capt. Trottier made observations of the screwwash of both vessels. The screw-wash is the water turbulence generated by the propellers of each vessel. Captain Trottier noted that the FORT WORTH’S screwwash was going astern. By contrast, the KEIYOH MARU’s screwwash was going forward. The district court consequently found that the KEIYOH MARU was powering through the collision. The appellants vigorously dispute this finding. Counsel for the KEIYOH MARU do not, however, question the district court’s finding that it traversed the restricted anchorage and pilotage areas.

C. Prior Proceedings

The district court found the KEIYOH MARU entirely at fault for the collision. The court also found that the FORT WORTH’S failure to track the movements of the KEIYOH MARU by radar and lookout did not contribute to the accident.

The parties stipulated to the damages incurred by their respective vessels. They agreed that the FORT WORTH was entitled to recover at least $1,559,569.85 as a result of the subject collision due to liability on the part of defendants. Other consequential damages were awarded to the FORT WORTH and so the total damages amounted to $1,857,825.31. The district court also awarded prejudgment interest at a rate of 13.735% compounded annually, commencing July 1, 1981, to the date of entry of judgment. This rate was based on *822 the 52 week United States Treasury Bill rate. Post-judgment interest was also awarded.

The district court had jurisdiction over this controversy based upon 28 U.S.C. § 1333 (1982). Appellants filed a notice of appeal and an amended notice of appeal, both timely. This court ordered that the second notice of appeal be entertained. Trinidad Corp. v. M.T. KEIYOH MARU, 781 F.2d 1360, 1362 (9th Cir.1986). We have jurisdiction over this appeal pursuant to 28 U.S.C. § 1291 (1982).

ANALYSIS

A. Standard of Review

Findings of fact made by admiralty trial courts are subject to the clearly erroneous standard of review. In re White Cloud Charter Boat Co., Inc., 813 F.2d 1513, 1517 (9th Cir.1987); Seattle-First Nat’l Bank v. Bluewater Partnership, 772 F.2d 565 , 568 (9th Cir.1985). This standard also extends, under comparative negligence principles, to an admiralty court’s apportionment of fault. In re White Cloud, 813 F.2d at 1517 ; Alkmeon Naviera, S.A. v. M/V Manna L, 633 F.2d 789, 796 (9th Cir.1980). Under a clearly erroneous standard, we must affirm an apportionment of liability unless, after review of all the evidence, we are left with a “definite and firm conviction that a mistake has been committed.” In re White Cloud, 813 F.2d at 1517 . The district court's conclusions of law are, of course, reviewed de novo.

In maritime collision cases fault is now judged under a comparative negligence standard. United States v. Reliable Transfer Co., Inc., 421 U.S. 397, 411 , 95 S.Ct. 1708, 1715-16 , 44 L.Ed.2d 251 (1975). 1 Counsel for the KEIYOH MARU has conceded that they were at some fault for the accident. They therefore seek to overturn the district court’s ruling that they were entirely at fault. We, nonetheless, affirm the district court’s decision.

B. The KEIYOH MARU’s Navigation

The KEIYOH MARU’s chief argument is that the two vessels were, prior to the collision, in a crossing situation which demanded that the FORT WORTH take action to prevent the accident. This argument has two elements: (1) that the relevant rules of navigation for both vessels were the International Regulations for Preventing Collisions at Sea, 1972 (“72 COL-REGS”), 33 U.S.C.A. foil. § 1602, and not the local Coast Guard rules, and (2) that a crossing situation did, in fact, exist. We hold that the district court’s finding that no crossing situation ever materialized was not clearly erroneous.

1. The Applicable Nautical Rules of the Road

The COLREGS were adopted by the International Marine Consultative Organization (“IMCO”), now the International Maritime Organization, on October 20, 1972. They entered into force for the United States on July 15, 1977. 33 U.S.C. § 1602 (a). The COLREGS “apply to all vessels upon the high seas and in all waters connected therewith navigable by seagoing vessels.” 33 U.S.C.A. § 1602 R. 1(a). However, the COLREGS also provide that: “Nothing in these Rules shall interfere with the operation of special rules made by an appropriate authority for road-steads, harbours, rivers, lakes or inland waterways connected with the high seas and navigable by seagoing vessels. Such special rules shall conform as closely as possible to these Rules.” COLREGS R. 1(b).

Earlier in 1972, the United States had provided for the application of these local rules governing traffic in and out of ports and harbors. See 33 U.S.C. § 1223 (a)(1), (4), 1223(c) (1982). Pursuant to this authority, the United States Coast Guard enacted regulations for traffic in and out of the ports of Los Angeles and Long Beach. The regulations at issue in this case are *823 those prohibiting traffic through a pilotage area unless a vessel is moving in or out of a designated port, Captain of the Port Order 1-78, 45 Fed.Reg. 30,431 (1980), and that regulation prohibiting movement through Anchorage area “G”, 33 C.F.R. § 110.214 (a)(7) (1987). The KEIYOH MARU was governed by these two regulations because at all relevant times before the collision she was in the territorial waters of the United States, and thus under the jurisdiction of the United States. 33 U.S.C.A. § 1223 (a)(1) & (d). The Coast Guard’s regulations concerning restricted zones “conform as closely as possible” with the COLREGS. COLREGS R. 1(b). Therefore, the KEIYOH MARU was obliged to respect the rule against transiting Anchorage “G” and the Los Angeles pilotage zone, an obligation which the district court found that she had disobeyed.

2. Did a Crossing Situation Exist?

The appellants claim that the physical relationship of the two vessels as they approached one another created a crossing situation under the applicable COLREGS. Rule 15 of the COLREGS provides that: “When two power-driven vessels are crossing so as to involve risk of collision, the vessel which has the other on her starboard side shall keep out of the way and shall, if the circumstances of the case admit, avoid crossing ahead of the other vessel.” COL-REGS R. 15. Appellants claim that the FORT WORTH had the KEIYOH MARU on her starboard side at all times and was required to stay clear of her.

The district court ruled, however, that no crossing situation existed before the collision. In order to be considered a privileged vessel in a crossing situation, it must be on a steady course. “A ship is on a steady course, not only when her heading does not change, but whenever her future positions are certainly ascertainable from her present position and movements.” Commonwealth & Dominion Line v. United States, 20 F.2d 729, 731 (2d Cir.1927), rev’d on other grounds, 278 U.S. 427, 429 , 49 S.Ct. 183, 183 , 73 L.Ed. 439 (1929); see also United States v. S.S. Soya Atlantic, 330 F.2d 732, 737 (4th Cir.1964). The district court found that the KEIYOH MARU’s navigation did not satisfy this test. The district court said: “Due to the constantly changing engine orders and constantly changing headings of the KEIYOH MARU, the KEIYOH MARU never established itself on a constant course and speed in a crossing situation with the FORT WORTH.” Moreover, the KEIYOH MARU’s course could not possibly be characterized as “certainly ascertainable” because of her movement through the restricted anchorage area. 2 The FORT WORTH was entitled to assume that another vessel would not transgress a restricted area and embarrass its passage. The district court was correct in finding that no crossing situation existed. The FORT WORTH had, therefore, no duty to stay clear of the KEIYOH MARU. 3

*824 C. The FORT WORTH’S Navigation

All of the above discussion deals with the liability of the KEIYOH MARU. We now turn to the appellants’ claim that the district court incorrectly determined the measure of fault for the FORT WORTH. The district court determined that no fault was attributable to the FORT WORTH. Appellants argue that because the FORT WORTH was in violation of numerous statutory safety rules the district court was obliged to apply the rule of The Pennsylvania, 86 U.S. (19 Wall.) 125 , 22 L.Ed. 148 (1873).

The Supreme Court’s decision in The Pennsylvania established a stringent burden of proof for a vessel in violation of a statutory safety requirement. That case involved the collision between a bark and a steamer in a dense fog. Id. 86 U.S. (19 Wall.) at 126-27 . The bark was not sounding the appropriate fog signals, in contravention of an earlier act of Congress for preventing collisions at sea. Id.; Act of Apr. 29, 1864, ch. 69, art. 10, 13 Stat. 60 (1864). In weighing the fault of the bark, the Supreme Court, Justice Strong writing, said:

Id. at 136 ; see also The Martello, 153 U.S. 64, 75 , 14 S.Ct. 723, 727 , 38 L.Ed. 637 (1894) (applying The Pennsylvania rule in these words: “Can it be said in this case [that the statutory fault] could not by any possibility have contributed to the collision?”); Waring v. Clarke, 46 U.S. (5 How.) 441, 465 , 12 L.Ed. 226 (1847) (a vessel “will be held responsible for all losses until it is proved that the collision was not the consequence [of a statutory fault]”). This rule has often been applied in this circuit. See, e.g., Mathes v. The Clipper Fleet, 774 F.2d 980, 982 (9th Cir.1985); Ishizaki Kisen Co. v. United States, 510 F.2d 875, 879 (9th Cir.1975); The Denali, 105 F.2d 413, 418 (9th Cir.1939), cert. denied, 311 U.S. 687 , 61 S.Ct. 65 , 85 L.Ed. 444 (1940). 4

In order to satisfy the burden imposed by The Pennsylvania rule, the violator must show not merely that its fault might not have been one of the causes of the collision but that it could not have been one of the causes. This circuit has interpreted the phrase “could not have been” in The Pennsylvania to mean that “where a ship at the time of a collision is in violation of a statutory rule intended to prevent collisions, the burden of proof rests upon her to establish that the violation could not reasonably be held to have been a proximate cause of the collision.” States S.S. Co. v. Permanente S.S. Corp., 231 F.2d 82, 87 (9th Cir.1956); see also United States v. Joyce, 511 F.2d 1127, 1129 (9th Cir.1974); Pacific Tow Boat Co. v. State Marine Corp., 276 F.2d 745 , 749 (9th Cir.1960).

Courts in this circuit have periodically discussed an alternate formulation of *825 this rule, that to escape liability a ship in violation of a statutory safety rule “must prove beyond reasonable doubt that the collision would have occurred” anyway. Permanente S.S. Corp., 231 F.2d at 87 (iquoting Oriental Trading & Transp. Co. v. Gulf Oil Corp., 173 F.2d 108, 109 (2d Cir.), cert. denied sub. nom. Gulf Oil Corp. v. M/V The John A. Brown, 337 U.S. 919 , 69 S.Ct. 1162 , 93 L.Ed. 1729 (1949)); see also Ishizaki, 510 F.2d at 880 (settling on proximate cause test, but also quoting a student Comment, The Pennsylvania Rule: Charting a New Course for an Ancient Mariner, 54 B.U.L.Rev. 78, 80 (1974), which suggested that “a statutory violator would have to demonstrate beyond all doubt that his violation did not cause the loss”). The burden of proof imposed by The Pennsylvania rule has been described as “difficult, if not impossible” to discharge. Ishizaki, 510 F.2d at 879 (quoting The Princess Sophia, 61 F.2d 339, 347 (9th Cir.1932), cert. denied sub. nom. Brace v. Canadian R.R. Co., 288 U.S. 604 , 53 S.Ct. 396 , 77 L.Ed. 980 (1933)). Nevertheless, there must be a causal connection between the violation alleged and the injury. The Pennsylvania, 86 U.S. (19 Wall.) at 136 (“It must be conceded that if it clearly appears the fault could have had nothing to do with the disaster, it may be dismissed from consideration.”); Mathes, 774 F.2d at 983 . We believe that the burden imposed under The Pennsylvania rule is discharged by a clear and convincing showing of no proximate cause, rather than the stricter test of beyond a reasonable doubt. Pacific Tow, 276 F.2d at 749 (“The words ‘could not have,’ as used in [The Pennsylvania ] rule, do not require the vessel guilty of a statutory fault to prove that its fault could not by any stretch of the imagination have had any causal relation to the collision no matter how speculative, improbable, or remote.”) 5 Clear and convincing evidence suffices for a showing in satisfaction of The Pennsylvania rule.

To prove its argument that the district court misapplied The Pennsylvania rule, appellants must show that the FORT WORTH was, indeed, in violation of a statutory rule promoting safety at sea, and that the FORT WORTH failed to show, by clear and convincing evidence, that the violation could not be reasonably held to have been a proximate cause of the collision.

1. Did the FORT WORTH Violate any Statutory Rules?

Appellants claim that the FORT WORTH was in violation of a number of statutory rules, including failure to maintain a lookout, to use available radar, to maintain a safe speed, to give way in a crossing situation, to take action to avoid the collision, and to show the appropriate navigational lights. The district court found that the FORT WORTH was in violation of only two of these requirements: posting a lookout and using available radar. The rest of the appellants’ claimed statutory violations for the FORT WORTH are unsupported in the record. Substantial evidence indicated the FORT WORTH’S speed was safe, appropriate, and a “good” speed to pick up her *826 pilot. Additionally, all the evidence indicated that the FORT WORTH took immediate action in sounding a warning blast and turning hard to port in order to avoid the collision.

Having determined that the FORT WORTH failed to post a lookout and effectively use radar, we must determine whether these constitute statutory violations. Failure to effectively use radar is an unambiguous statutory violation for the purposes of The Pennsylvania rule. See 1972 COLREGS R. 7(b) (“Proper use shall be made of radar equipment if fitted and operational ... to obtain early warning of risk of collision_”); Afran Transp. Co. v. M/T Bergechief, 274 F.2d 469 , 475 (2d Cir.1960) (“the vessel that fails to use her radar has the burden of establishing that her failure to use radar did not contribute to the collision”).

The FORT WORTH contends the law of this circuit is that “[t]he lookout rule is not a statutory requirement within the purview of The Pennsylvania rule which would shift the burden of proof.” In re White Cloud, 813 F.2d at 1518 (original emphasis) (quoting Marport, 771 F.2d at 1218 n. 2 (citing Anthony v. International Paper Co., 289 F.2d 574, 581 (4th Cir. 1961))). We reject this contention. The discussion in White Cloud is not dispositive of this issue. The language in Marport, 771 F.2d at 1218 n. 2, is dicta, and the decision of the Fourth Circuit in Anthony was based not on the 1972 COLREGS (which were not yet in force), but on the Inland Rules of Navigation, 33 U.S.C.A. § 221 (Rule 29) (later repealed), which did not make posting a lookout an affirmative duty. Anthony, 289 F.2d at 577 . Rule 5 of the 1972 COLREGS provides that “[ejvery vessel shall at all times maintain a proper look-out by sight and hearing as well as by all available means appropriate in the prevailing circumstances and conditions so as to make a full appraisal of the situation and of the risk of collision.” 33 U.S.C.A. foil. § 1602, Rule 5. There is no question that posting a lookout is now a statutory duty. 6

This is the rule prevailing in other circuits. The statement in Anthony that posting a lookout does not constitute a statutory rule under the Inland Rules of Navigation, 289 F.2d at 581 , has been contradicted by three other circuits. Allied Chem. Corp. v. Hess Tankship Co., 661 F.2d 1044 , 1053 (5th Cir. Unit A Nov. 1981); Tug Ocean Prince, Inc. v. United States, 584 F.2d 1151, 1159-60 (2d Cir.1978), cert. denied, 440 U.S. 959 , 99 S.Ct. 1499 , 59 L.Ed.2d 772 (1979); First Nat’l Bank of Chicago v. Material Serv. Corp., 544 F.2d 911, 918 (7th Cir.1976) (concerning Great Lakes Rules). Moreover, the Supreme Court said in The Ariadne, 80 U.S. (13 Wall.) 475 , 20 L.Ed. 542 (1871), that:

Id. 80 U.S. (13 Wall.) at 478 . Lower courts in this circuit have also confirmed that failure to post a lookout raises a presumption of negligence under The Pennsylvania rule. See, e.g., Nehus v. Alaska Marine Towing, Inc., 519 F.Supp. 328, 331 (W.D.Wash.1981); Alaska Packers Ass’n, Inc. v. O/S Eastpoint, 421 F.Supp. 48, 52 (W.D. Wash.1976). We hold that the FORT WORTH’S failure to post a lookout and effectively use radar both constitute statutory violations for the purposes of The Pennsylvania rule.

2. Did the FORT WORTH Satisfy the Burden of The Pennsylvania Rule?

Appellants claim that the district court did not apply The Pennsylvania rule to the facts of this case. They argue that the district court made findings of fact only concerning the FORT WORTH’S failure to *827 effectively use radar. This is incorrect. The district court made the following findings of fact:

Plainly, the district court’s findings of fact deal with the FORT WORTH’S tracking of the KEIYOH MARU, whether by lookout or by radar.

This leaves the question whether the FORT WORTH could have avoided the collision if it had posted a lookout and used its radar. Once again, the standard is whether this was a proximate cause of the collision. We review the district court’s application of facts to The Pennsylvania rule under a clearly erroneous standard. In re White Cloud, 813 F.2d at 1517 . Appellants argue that had the FORT WORTH seen the oncoming KEIYOH MARU it could have taken action to avoid the collision. The district court disagreed, stating that the FORT WORTH could not possibly have anticipated that the KEIYOH MARU would have transgressed both the restricted Anchorage “G” and the Los Angeles pilotage area in its course. 7 Moreover, there was substantial evidence that even if a lookout or radar observer had tracked the movements of the KEIYOH MARU it would have been difficult if not impossible to have timely determined the KEIYOH MARU’s intentions.

Appellants’ argument is remarkably similar to that put forward by the defendant vessel in Bloomfield S.S. Co. v. Brownsville Shrimp Exch., 243 F.2d 869 (5th Cir.1957). In that case the offending vessel, a steamship, sailed through an armada of fishing vessels off the coast of Texas. The steamship alleged fault upon the fishing vessel it collided with for not having a lookout, in the words of the circuit court, “better to see how reckless was the navigation of the oncoming ship.” Id. at 872 . In our case, the FORT WORTH’S failure to post a lookout or effectively use its radar cannot be held to be a proximate cause of the collision. The FORT WORTH has shown by clear and convincing evidence that it could not reasonably have expected another vessel to transgress two restricted zones, and embarrass its passage. The district court’s ruling that the FORT WORTH satisfied its burden under The Pennsylvania rule was not clearly erroneous. Therefore, the KEIYOH MARU was entirely at fault for the accident.

D. Award of Prejudgment Interest

Appellants’ final argument is that the district court abused its discretion in awarding prejudgment interest. The district court set a constant rate of interest based on a rate equal to the coupon issue yield (as determined by the Secretary of *828 the Treasury) of the average accepted auction price for the last auction of 52 week United States Treasury Bills settled immediately prior to the date of payment by the underwriters. See Western Pacific Fisheries, Inc. v. S.S. President Grant, 730 F.2d 1280 , 1289 (9th Cir.1984). Appellants claim that instead of using a constant rate of return, the district court should have averaged the values indicated for the coupon yield rate every 52 weeks. The district court’s calculation of prejudgment interest resulted in a figure of 13.735%; appellants’ calculation of averages would result in a figure of 12.525%.

The award of prejudgment interest is within the discretion of the trial judge. This discretion must, however, be exercised with a view to the fact that prejudgment interest in an admiralty action is an element of compensation, not a penalty. Alkmeon Naviera, 633 F.2d at 797 ; Rosa v. Insurance Co. of Pennsylvania, 421 F.2d 390, 393 (9th Cir.1970). Although appellants are correct that appellees could have only earned a constant rate for a single year and, after expiration of the 52 week period, they would have had to reinvest their money at a new rate, their analysis ignores the fact that had appellees known that their money was to have been tied-up in excess of a year, they would have secured longer-term interest rates. Moreover, this circuit’s decision in Western Pacific Fisheries, 730 F.2d at 1289, does not mention the possibility of using an average, as opposed to a constant, rate of interest. Appellants rely on the Second Circuit decision in Ingersoll Milling Mach. Co. v. M/V Bodena, 829 F.2d 293, 311 (2d Cir.1987), cert. denied sub. nom. J.E. Bernard & Co. v. Ingersoll Milling Mach. Co., — U.S. -, 108 S.Ct. 774 , 98 L.Ed.2d 860 (1988), which merely upheld a district court’s decision to use an average rate of return under an abuse of discretion standard. We hold that it was not an abuse of discretion by the district court to use a constant rate of exchange, as opposed to averaging the yearly rates of return on Treasury Bills.

CONCLUSION

The decision of the district court is, therefore, AFFIRMED.

. Previously, a rule of divided damages prevailed. See The Schooner Catharine v. Dickinson, 58 U.S. (17 How.) 170 , 15 L.Ed. 233 (1854), which held that when both vessels were at fault in a collision, the damages would be equally divided between them. Id. 58 U.S. (17 How.) at 177 .

. The district court’s findings that the KEIYOH MARU traversed the restricted Anchorage "G” and the Los Angeles pilotage areas and that a crossing situation did not exist at any time were supported by substantial evidence. The finding that the KEIYOH MARU traversed restricted areas was based not only on the independent testimony of the pilot boat captain and crew, but also through technical recreations of the KEIYOH MARU’s course and headings. The finding that no crossing situation existed between the two vessels was supported by the same evidence, in addition to the complete and accurate log records of the FORT WORTH.

We decline the appellant’s invitation to subject the district court’s findings to closer scrutiny on appeal because the court allegedly adopted wholesale the appellee’s proposed findings of fact and conclusions of law. While some of the district court’s findings of fact were transcribed verbatim from the plaintiffs proposed findings, they do not so closely parallel and copy them as to raise a presumption that the district court did not engage in independent fact-finding.

. Because we rule that no crossing situation existed, we need not consider the FORT WORTH’S defense that because it was engaged in boarding a pilot it was restricted in its ability to maneuver and, therefore, the crossing rules were inapplicable. Consequently, we also reject the KEIYOH MARU’s claim that the district court erred in excluding impeachment evidence for the testimony of Captain White. White testified that the crossing rules do not apply to ships boarding pilots. Counsel for the KEIYOH MARU sought to admit evidence of an earlier collision where a contrary rule was promul *824 gated. Because we hold that no crossing situation existed, we need not consider whether the crossing rules would or would not apply to vessels picking up pilots.

. The FORT WORTH attempts to modify the rule of The Pennsylvania by quoting a passage from United States v. S.S. Soya Atlantic, 330 F.2d 732 (4th Cir.1964), that "[w]e are mindful of the principle that when the fault of one vessel is grave, obvious and inexcusable, fault ought not to be found on the part of another vessel, particularly when it is the privileged vessel, so as to require an apportionment, except upon clear and convincing evidence.” Id. at 740 . Ap-pellees are attempting to revive the major/minor fault rule of The Great Republic, 90 U.S. (23 Wall.) 20, 35 , 23 L.Ed. 55 (1874), and City of New York, 147 U.S. 72 , 85, 13 S.Ct. 211 , 216, 37 L.Ed. 84 (1893), which was expressly disavowed when the Supreme Court adopted the rule of comparative negligence in maritime collision cases. Reliable Transfer, 421 U.S. at 406 & n. 12, 95 S.Ct. at 1713 & n. 12. The FORT WORTH’S liability cannot be relieved simply on a showing that the KEIYOH MARU was more at fault.

. We, moreover, believe that to apply a “beyond a reasonable doubt" test to The Pennsylvania rule would be inconsistent with the system of pure comparative negligence under Reliable Transfer, 421 U.S. at 406 , 95 S.Ct. at 1713 . It would mean that a vessel charged with statutory fault would be judged by one standard for the purposes of establishing causation, while the other vessel (which may, in fact, be more blameworthy) is judged under a lighter burden. It must be borne in mind that “The Pennsylvania rule does not establish fault; it is limited to causation.” T. Schoenbaum, Admiralty and Maritime Law 452 (1987). The appropriate burden of proof under The Pennsylvania rule must, therefore, be keyed to the notion of proximate cause, the original rationale for the rule articulated by the Supreme Court in 1873. As the old rule of divided damages was eroded, and ultimately rejected in Reliable Transfer, so too has the burden of proof under The Pennsylvania come to reflect the essential purpose of the rule: to raise a presumption of causation where a vessel is in violation of a statutory safety rule. Pitts, Admiralty’s Pennsylvania Rule, 24 S.Tex. L.J. 541, 576-81 (1983); Comment, 54 B.U.L. Rev. at 80. We express no opinion here whether the rule of The Pennsylvania has outlived its usefulness under a pure comparative negligence system. But see California v. Italian Motorship ILICE, 534 F.2d 836, 840 (9th Cir.1976) (suggesting Reliable Transfer specifically overruled The Pennsylvania); Pitts, 24 S.Tex.L.J. at 546-50, 581-85; Casenote, 11 Tex.Int’l L.J. 159, 163 (1976).

. See also Pitts, 24 S.Tex.LJ. at 554 ("The 72 COLREGS and new Inland Navigational Rules, ... mak[e] a proper lookout a clear and mandatory statutory duty”).

. Needless to say, the KEIYOH MARU’s failure to observe the restrictions concerning Anchorage "G” and the Los Angeles Pilotage Area constituted a "statutory” violation for the purposes of The Pennsylvania rule. See Belden v. Chase, 150 U.S. 674, 698 , 14 S.Ct. 264, 271 , 37 L.Ed. 1218 (1893) (regulations promulgated pursuant to an agency’s statutory authority constitute safety rules under The Pennsylvania rule). Because we decide that the FORT WORTH discharged its burden of proof, we need not address here the proposition that The Pennsylvania rule has no applicability to situations where both vessels are guilty of a statutory fault. But see In re Gypsum Carrier, 465 F.Supp. 1050, 1063 (S.D.Ga.1979) (so ruling).