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The Pennsylvania Railroad Company chartered the Anna C from Conners Marine Company, which was loaded with flour owned by the United States. Before the accident, the Anna C was moored at Pier 52 on the North River along with several other barges. The barges at Pier 52 were tied together by mooring lines and one barge at Pier 52 was tied to another set of barges at the adjacent Public Pier. On the day of the accident the tug Carroll was sent to remove a barge from the Public Pier. In the process of removing the barge, the line between the barges at Pier 52 and the barges at the Public Pier was removed. After the removal of the line, the barges at Pier 52 broke free. This resulted in the sinking of Anna C. The United States, lessee of the Anna C, sued Carroll Towing Co., owner of the Carroll in an indemnity action.


  1. Was reasonable care taken by the defendants to prevent accidents of this nature?
  2. Is the probability multiplied by the liability greater than or less than the burden of adequate precautions?


Appeal dismissed.


Learned Hand, writing for the court, held Carroll's liability is stated to depend on three factors:

  1. the probability of the occurrence (P);
  2. the gravity of the resulting liability (L); and
  3. the burden of adequate precautions (B).

If the product of the first two were greater than the burden, then taking the precaution would have been reasonable (PL > B). If the product of the first two were less than the burden, then the care would not have been reasonable (PL < B). This is the "Hand Formula".


In determining if reasonable care was taken, the judge or jury should attempt to measure three things:

  1. magnitude of the loss if an accident occurs (L);
  2. probability of the accident’s occurrence (P); and
  3. burden of taking precautions that would avert it (B).

If the product of the first two terms is greater than the burden of precautions, then the failure to take those precautions is a failure to use reasonable care, and you are negligent.

If PL > B, it would be negligent not to expend the funds to prevent the accident. Therefore the defendant should be liable. If PL < B, then it would not be appropriate to hold the defendant liable.