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United States v. Carroll Towing Co.

Citation. 159 F.2d 169 (2d Cir. 1947)
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Brief Fact Summary.

While the bargee was away from the barge, the towing company tried to move the barge to another dock. The attempt accidentally loosed the barge and caused it to drift away and eventually sank.

Synopsis of Rule of Law.

If the probability is P; the injury, L; and the burden, B; liability depends upon whether B is less than L multiplied by P: i.e., whether B less than PL.


Connors Company (plaintiff) owned a barge that was moored to the end of the pier. The barge carried a cargo of flour owned by United States (plaintiff). Connors hired Carroll Towing Company to tow the barge. On January 4, 1944, while Connors’ employee who was supposed to watch the barge had gone ashore, Carroll’s tug boat tried to move the barge to another dock. This attempt failed and also released all other boats at the dock. Connors’ barge drifted away and eventually sank, destroying all four.


Whether the bargee who was absent while the accident happened was negligent?


Yes. Judgment reversed as the Court reassessed the parties’ liability for damages according to the Learned Hand formula and remanded the case for further proceedings.


The Carroll case is most famous for Judge Hand’s algebraic formula in determining liability.

The Court explained that there were three variables that need to be considered in this case:

  1. The probability that the barge will break away (“P”);
  2. the gravity of the resulting injury (“L”); and
  3. the burden of adequate precautions (“B”).

Therefore, the Learned Hand formula to liability B=PxL states that liability arises if B is less than L multiplied by P. In this case, P and L depended on specific circumstances. For example, if a storm threatened or the harbor was crowded, the danger would be greater. However, the court did not answer these questions specifically and left those to be reassessed on a new trial.

This Court also addressed the Conners’ bargee’s failure to care for the barge. Even it was impossible for the bargee to stay on board all the time, his absence was not excused in this case for him leaving the barge for 21 hours. The Court held and only held one thing, that in this case, it was a fair requirement that the Conners Company should have a bargee aboard during the working hours of daylight.

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