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Torts · The Hand formula · Case brief

United States v. Carroll Towing Co.

159 F.2d 169 (2d Cir. 1947) · United States Court of Appeals for the Second Circuit · 1947
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Facts

A barge, the Anna C, was moored in New York Harbor with several other barges when a tug's operations caused the flotilla to break loose. During the shifting of lines, the Anna C's lines were cast off and not properly secured again, and the barge drifted away and collided with a tanker. The tanker sank, and the United States, as owner of the cargo, sought damages. The barge owner had no bargee aboard at the time, and the case concerned whether that absence contributed to the loss.

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Issue

Was the barge owner negligent for failing to have a bargee aboard the Anna C, such that the owner's omission contributed to the accident and resulting damages?

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Rule

Negligence depends on whether the burden of taking precautions is less than the probability of harm multiplied by the gravity of the resulting injury. If B < P × L, failure to take the precaution is negligent.

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Holding

Yes. The court held that the barge owner was contributorily negligent because the absence of the bargee during working hours on a busy harbor created an unreasonable risk under the circumstances.

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Reasoning

Judge Learned Hand reasoned that there is no fixed rule requiring a bargee's constant presence; the duty depends on the likelihood and seriousness of possible harm weighed against the inconvenience of precautions. In a crowded wartime harbor, barges were frequently shifted, and the risk of lines coming loose was substantial. Because the burden of having a bargee aboard during the relevant daytime period was slight compared with the probability and magnitude of loss, the owner's failure to provide one was negligent. The court therefore allocated fault rather than placing all responsibility on the tug operators.

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Significance

The case is famous for articulating the Hand formula, B < P × L, one of the most influential economic expressions of the negligence standard in American tort law. It is a foundational case for risk-utility analysis in breach determinations and is regularly paired with cases such as Vaughan v. Menlove, 132 Eng. Rep. 490 (C.P. 1837), and Bolton v. Stone, [1951] A.C. 850, on the objective standard of care and probability of harm. It also foreshadows modern comparative fault thinking by emphasizing apportionment based on relative fault.

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