In his initial letter, Magellan outlined the required conditions for the Premium bearing his name. The basic appearance of the Premium would be an inscribed gold oval plate. Every member of the APS should be able to examine and comment on each entry (unless that member was also a candidate). The winner should have his entry published in its entirety in the next volume of the Society's Transactions. The Premium should be open to any eligible person without restriction. All entries should be kept for evaluation for five years, after which they should be published.

Model of a Temporary Rudder

Using these conditions as a starting point, a committee of APS members established more extensive rules for the Premium. The rules, which were approved by Magellan, required that entries should be sent to the president or vice-president of the Society (who would pay the postage). Entries were to be outwardly identified by a motto or device, with the real name and address of the author enclosed in a sealed envelope that was to be opened only after winning the Premium. Entries were not to have been previously published or publicly awarded. Members were allowed to view entries at one of the Society's stated meetings (though they were not to take an entry home). However, the entries were to be judged by a twelve-member committee and the Society's elected officers. All entries would be held for five years, after which they would be burned without breaking the seal contrary to the initial desires of Magellan.

Manuscript drawing of the Elliptograph

At various times during the nineteenth century the Committee for the Premium met to discuss the administering of the award. Around 1820 they came up with 36 "Prize Questions" that they felt would make worthy candidates for the Premium - and stated that any member was welcome to make additions. In 1899 the Society resolved to use the unexpected income from the Premium's fund to purchase books for the library relating to the areas of science in which the premium is offered.

By the middle of twentieth century the Premium Committee had elected to change how the prize was awarded. Rather than advertise for the submission of entries it was decided to award the Premium to a person or persons for an accomplishment or lifetime achievement in navigation, astronomy, or natural philosophy. Today, in addition to the medal, recipients also receive a cash award.