L. HAND, Circuit Judge.

These appeals concern the sinking of the barge, "Anna C," on January 4, 1944, off Pier 51, North River. The Conners Marine Co., Inc., was the owner of the barge, which the Pennsylvania Railroad Company had chartered; the Grace Line, Inc., was the charterer of the tug, "Carroll," of which the Carroll Towing Co., Inc., was the owner. The decree in the limitation proceeding held the Carroll Company liable to the United States for the loss of the barge's cargo of flour, and to the Pennsylvania Railroad Company, for expenses in salving the cargo and barge; and it held the Carroll Company also liable to the Conners Company for one half the damage to the barge; these liabilities being all subject to limitation. The decree in the libel suit held the Grace Line primarily liable for the other half of the damage to the barge, and for any part of the first half, not recovered against the Carroll Company because of limitation of liability; it also held the Pennsylvania Railroad secondarily liable for the same amount that the Grace Line was liable. The Carroll Company and the Pennsylvania Railroad Company have filed assignments of error.

The facts, as the judge found them, were as follows. On June 20, 1943, the Conners Company chartered the barge, "Anna C," to the Pennsylvania Railroad Company at a stated hire per diem, by a charter of the kind usual in the Harbor, which included the services of a barge, apparently limited to the hours 8 A.M. to 4 P.M. On January 2, 1944, the barge, which had lifted the cargo of flour, was made fast off the end of Pier 58 on the Manhattan side of the North River, whence she was later shifted to Pier 52. At some time not disclosed, five other barges were moored outside her, extending into the river; her lines to the pier were not then strengthened. At the end of the next pier north (called the Public Pier), lay four barges; and a line had been made fast from the outermost of these to the fourth barge of the tier hanging to Pier 52. The purpose of this line is not entirely apparent, and in any event it obstructed entrance into the slip between the two tiers of barges. The Grace Line, which had chartered the tug, "Carroll," sent her down to the locus in quo to "drill" out one of the barges which lay at the end of the Public Pier; and in order to do so it was necessary to throw off the line between the two tiers. On board the "Carroll" at the time were not only her master, but a "harbormaster" employed by the Grace Line. Before throwing off the line between the two tiers, the "Carroll" nosed up against the outer barge of the tier lying off Pier 52, ran a line from her own stem to the middle bit of that barge, and kept working her engines "slow ahead" against the ebb tide which was making at that time. The captain of the "Carroll" put a deckhand and the "harbormaster" on the barges, told them to throw off the line which barred the entrance to the slip; but, before doing so, to make sure that the tier on Pier 52 was safely moored, as there was a strong northerly wind blowing down the river. The "harbormaster" and the deckhand went aboard the barges and readjusted all the fasts to their satisfaction, including those from the "Anna C," to the pier.

After doing so, they threw off the line between the two tiers and again boarded the "Carroll," which backed away from the outside barge, preparatory to "drilling" out the barge she was after in the tier off the Public Pier. She had only got about seventy-five feet away when the tier off Pier 52 broke adrift because the fasts from the "Anna C," either rendered, or carried away. The tide and wind carried down the six barges, still holding together, until the "Anna C" fetched up against a tanker, lying on the north side of the pier below — Pier 51 — whose propeller broke a hole in her at or near her bottom. Shortly thereafter: i.e., at about 2:15 P.M., she careened, dumped her cargo of flour and sank. The tug, "Grace," owned by the Grace Line, and the "Carroll," came to the help of the flotilla after it broke loose; and, as both had syphon pumps on board, they could have kept the "Anna C" afloat, had they learned of her condition; but the bargee had left her on the evening before, and nobody was on board to observe that she was leaking. The Grace Line wishes to exonerate itself from all liability because the "harbormaster" was not authorized to pass on the sufficiency of the fasts of the "Anna C" which held the tier to Pier 52; the Carroll Company wishes to charge the Grace Line with the entire liability because the "harbormaster" was given an over-all authority. Both wish to charge the "Anna C" with a share of all her damages, or at least with so much as resulted from her sinking. The Pennsylvania Railroad Company also wishes to hold the barge liable. The Conners Company wishes the decrees to be affirmed.

The first question is whether the Grace Line should be held liable at all for any part of the damages. The answer depends first upon how far the "harbormaster's" authority went, for concededly he was an employee of some sort. Although the judge made no other finding of fact than that he was an "employee," in his second conclusion of law he held that the Grace Line was "responsible for his negligence." Since the facts on which he based this liability do not appear, we cannot give that weight to the conclusion which we should to a finding of fact; but it so happens that on cross-examination the "harbormaster" showed that he was authorized to pass on the sufficiency of the fasts of the "Anna C." He said that it was part of his job to tie up barges; that when he came "to tie up a barge" he had "to go in and look at the barges that are inside the barge" he was "handling"; that in such cases "most of the time" he went in "to see that the lines to the inside barges are strong enough to hold these barges"; and that "if they are not" he "put out sufficient other lines as are necessary." That does not, however, determine the other question: i.e., whether, when the master of the "Carroll" told him and the deckhand to go aboard the tier and look at the fasts, preparatory to casting off the line between the tiers, the tug master meant the "harbormaster" to exercise a joint authority with the deckhand. As to this the judge in his tenth finding said: "The captain of the Carroll then put the deckhand of the tug and the harbor master aboard the boats at the end of Pier 52 to throw off the line between the two tiers of boats after first ascertaining if it would be safe to do so." Whatever doubts the testimony of the "harbormaster" might raise, this finding settles it for us that the master of the "Carroll" deputed the deckhand and the "harbormaster," jointly to pass upon the sufficiency of the "Anna C's" fasts to the pier. The case is stronger against the Grace Line than Rice v. The Marion A.C. Meseck, was against the tug there held liable, because the tug had only acted under the express orders of the "harbormaster." Here, although the relations were reversed, that makes no difference in principle; and the "harbormaster" was not instructed what he should do about the fasts, but was allowed to use his own judgment. The fact that the deckhand shared in this decision, did not exonerate him, and there is no reason why both should not be held equally liable, as the judge held them.

We cannot, however, excuse the Conners Company for the bargee's failure to care for the barge, and we think that this prevents full recovery. First as to the facts. As we have said, the deckhand and the "harbormaster" jointly undertook to pass upon the "Anna C's" fasts to the pier; and even though we assume that the bargee was responsible for his fasts after the other barges were added outside, there is not the slightest ground for saying that the deckhand and the "harbormaster" would have paid any attention to any protest which he might have made, had he been there. We do not therefore attribute it as in any degree a fault of the "Anna C" that the flotilla broke adrift. Hence she may recover in full against the Carroll Company and the Grace Line for any injury she suffered from the contact with the tanker's propeller, which we shall speak of as the "collision damages." On the other hand, if the bargee had been on board, and had done his duty to his employer, he would have gone below at once, examined the injury, and called for help from the "Carroll" and the Grace Line tug. Moreover, it is clear that these tugs could have kept the barge afloat, until they had safely beached her, and saved her cargo. This would have avoided what we shall call the "sinking damages." Thus, if it was a failure in the Conner Company's proper care of its own barge, for the bargee to be absent, the company can recover only one third of the "sinking" damages from the Carroll Company and one third from the Grace Line. For this reason the question arises whether a barge owner is slack in the care of his barge if the bargee is absent.

As to the consequences of a bargee's absence from his barge there have been a number of decisions; and we cannot agree that it is never ground for liability even to other vessels who may be injured. As early as 1843, Judge Sprague in Clapp v. Young, held a schooner liable which broke adrift from her moorings in a gale in Provincetown Harbor, and ran down another ship. The ground was that the owners of the offending ship had left no one on board, even though it was the custom in that harbor not to do so. Judge Tenney in Fenno v. The Mary E. Cuff, treated it as one of several faults against another vessel which was run down, to leave the offending vessel unattended in a storm in Port Jefferson Harbor. Judge Thomas in The On-the-Level, held liable for damage to a stake-boat, a barge moored to the stake-boat "south of Liberty Light, off the Jersey shore," because she had been left without a bargee; indeed he declared that the bargee's absence was "gross negligence." In the Kathryn B. Guinan, Ward, J., did indeed say that, when a barge was made fast to a pier in the harbor, as distinct from being in open waters, the bargee's absence would not be the basis for the owner's negligence. However, the facts in that case made no such holding necessary; the offending barge in fact had a bargee aboard though he was asleep. In the Beeko, Judge Campbell exonerated a power boat which had no watchman on board, which boys had maliciously cast loose from her moorings at the Marine Basin in Brooklyn and which collided with another vessel. Obviously that decision has no bearing on the facts at bar. In United States Trucking Corporation v. City of New York, the same judge refused to reduce the recovery of a coal hoister, injured at a foul berth, because the engineer was not on board; he had gone home for the night as was apparently his custom. We reversed the decree, but for another reason. In The Sadie, we affirmed Judge Coleman's holding that it was actionable negligence to leave without a bargee on board a barge made fast outside another barge, in the face of storm warnings. The damage was done to the inside barge. In The P.R.R. No. 216, we charged with liability a lighter which broke loose from, or was cast off, by a tanker to which she was moored, on the ground that her bargee should not have left her over Sunday. He could not know when the tanker might have to cast her off. We carried this so far in The East Indian, as to hold a lighter whose bargee went ashore for breakfast, during which the stevedores cast off some of the lighter's lines. True, the bargee came back after she was free and was then ineffectual in taking control of her before she damaged another vessel; but we held his absence itself a fault, knowing as he must have, that the stevedores were apt to cast off the lighter. The Conway No. 23 went on the theory that the absence of the bargee had no connection with the damage done to the vessel itself; it assumed liability, if the contrary had been proved. In The Trenton, we refused to hold a moored vessel because another outside of her had overcharged her fasts. The bargee had gone away for the night when a storm arose; and our exoneration of the offending vessel did depend upon the theory that it was not negligent for the bargee to be away for the night; but no danger was apparently then to be apprehended. In Bouker Contracting Co. v. Williamsburgh Power Plant Corporation, we charged a scow with half damages because her bargee left her without adequate precautions. In O'Donnell Transportation Co. v. M. J. Tracy, we refused to charge a barge whose bargee had been absent from 9 A.M. to 1:30 P.M., having "left the vessel to go ashore for a time on his own business."

It appears from the foregoing review that there is no general rule to determine when the absence of a bargee or other attendant will make the owner of the barge liable for injuries to other vessels if she breaks away from her moorings. However, in any cases where he would be so liable for injuries to others, obviously he must reduce his damages proportionately, if the injury is to his own barge. It becomes apparent why there can be no such general rule, when we consider the grounds for such a liability. Since there are occasions when every vessel will break from her moorings, and since, if she does, she becomes a menace to those about her; the owner's duty, as in other similar situations, to provide against resulting injuries is a function of three variables: (1) The probability that she will break away; (2) the gravity of the resulting injury, if she does; (3) the burden of adequate precautions. Possibly it serves to bring this notion into relief to state it in algebraic terms: if the probability be called P; the injury, L; and the burden, B; liability depends upon whether B is less than L multiplied by P: i.e., whether B PL. Applied to the situation at bar, the likelihood that a barge will break from her fasts and the damage she will do, vary with the place and time; for example, if a storm threatens, the danger is greater; so it is, if she is in a crowded harbor where moored barges are constantly being shifted about. On the other hand, the barge must not be the bargee's prison, even though he lives aboard; he must go ashore at times. We need not say whether, even in such crowded waters as New York Harbor a bargee must be aboard at night at all; it may be that the custom is otherwise, as Ward, J., supposed in "The Kathryn B. Guinan," supra; and that, if so, the situation is one where custom should control. We leave that question open; but we hold that it is not in all cases a sufficient answer to a bargee's absence without excuse, during working hours, that he has properly made fast his barge to a pier, when he leaves her. In the case at bar the bargee left at five o'clock in the afternoon of January 3rd, and the flotilla broke away at about two o'clock in the afternoon of the following day, twenty-one hours afterwards. The bargee had been away all the time, and we hold that his fabricated story was affirmative evidence that he had no excuse for his absence. At the locus in quo — especially during the short January days and in the full tide of war activity — barges were being constantly "drilled" in and out. Certainly it was not beyond reasonable expectation that, with the inevitable haste and bustle, the work might not be done with adequate care. In such circumstances we hold — and it is all that we do hold — that it was a fair requirement that the Conners Company should have a bargee aboard (unless he had some excuse for his absence), during the working hours of daylight.

The decrees will be modified as follows. In the libel of the Conners Company against the Pennsylvania Railroad Company in which the Grace Line was impleaded, since the Grace Line is liable in solido, and the Carroll Company was not impleaded, the decree must be for full "collision damages" and half "sinking damages," and the Pennsylvania Railroad Company will be secondarily liable. In the limitation proceeding of the Carroll Company (the privilege of limitation being conceded), the claim of the United States and of the Pennsylvania Railroad Company will be allowed in full. Since the claim of the Conners Company for "collision damages" will be collected in full in the libel against the Grace Line, the claim will be disallowed pro tanto. The claim of the Conners Company for "sinking damages" being allowed for one half in the libel, will be allowed for only one sixth in the limitation proceeding. The Grace Line has claimed for only so much as the Conners Company may recover in the libel. That means that its claim will be for one half the "collision damages" and for one sixth the "sinking damages." If the fund be large enough, the result will be to throw one half the "collision damages" upon the Grace Line and one half on the Carroll Company; and one third of the "sinking damages" on the Conners Company, the Grace Line and the Carroll Company, each. If the fund is not large enough, the Grace Line will not be able altogether to recoup itself in the limitation proceeding for its proper contribution from the Carroll Company.

Decrees reversed and cause remanded for further proceedings in accordance with the foregoing.