The Action for Proportion of General Average

"If goods are thrown overboard in order to lighten a ship, the loss incurred for the good of all shall be made good by the contribution of all. The French ordinance [observed in the US and Great Britain] in express terms excludes from the benefit of general average, goods stored upon the deck of the ship . . . [that is,] the owners of the cargo under cover are not required to contribute to the jettison of the goods on deck. . . . [Thus, in the US,] the master is only authorized to load on deck by special contract with the shipper.

" . . . That the case of jettison . . . was . . . understood to be put as a mere illustration of a more general principle, Mr. Justice Story thinks is abundantly clear from the context of the Roman law, where a ransom paid to pirates to redeem teh ship is declared to be governed by the same rule. The same rule, he remarks, was applied to the case of cutting away or throwing overboard of the masts or other tackle of the ship to avert the impending calamity, and the incidental damage occasioned thereby to other things.
. . . . .
"The principle is, that all ordinary loss and damage sustained by the ship must be borne by the ship owners; but if upon a particular emergency articles are used or expenses incurred for the general benefit of all the parties interested in the ship, cargo, and freigh, then all of those for whose benefit teh same are used or incurred, should contribute to pay therefore . . . . And wages to the crew employed in rendering services toward such recovery may be included among those expenses."
. . . .
"[In addition, the doctrine requires] that by that sacrifice [of the jettisoned cargo] the safety of the other property should be presently and successfully attained [for the duration of the voyage].
. . . . .
"In New York it is a settled rule that a party who is obliged to pay and bear charges, as owner of the ship, is entitled, even if a case of contribution exists, to recover the whole of it, in the first instance, of the insurer upon the ship, and to leave it to him to call upon the ownesr or insurerers of the cargo and freigh for their contributory shares."

2 Robinson's Practice 386--394 (1855) (citations omitted).

Recoveries were available at both law (via an implied promise) and equity. Mr. Robinson did not specify the method for apportioning the contribution obligation, but one assumes that it would be pro rata based upon the value of the preserved cargo.