The medal's obverse bears standing Athena/Minerva holding shield with one hand and oil lamp on pedestal with the other. In exergue, NATURAE SPECIES RATIOQUE
The medal's reverse bears six portrait busts, each surrounded by a wreath and labeled with last name: LAPHAM / PECKHAM / CHAMBERLIN / HOY / IRVING / ALLEN; below, THE WISCONSIN ACADEMY OF / SCIENCES ARTS AND LETTERS / 1870 - 1920; signed in bottom right corner, LC
The Latin phrase on the obverse translates to "Nature and her law." Athena, or Minerva in her Roman incarnation, is the goddess of wisdom and together with the oil lamp symbolizes the quest for knowledge and understanding.
References: MACo 1920-003