On google books it has a snippet of the Differential Officer Battery. it included data on knowledge of military tactics and technology, physical science, social science, sports and other activities. That may be something to look into.
The organisation began in Omaha, Nebraska in 1881 with its first six lodges (later expanding to 350) chartered in July 1882. Initially only open to men with Danish parents or heritage, it provided a forum for nurturing Danish culture and language as well as providing financial assistance to members in case of death or illness.
After 1920, as Danish immigration lessened and the number of eligible males dwindled, lodges opened their membership to include American-born daughters and later spouses and children of lodge members. The DBIA gradually evolved into a social organization for the entire family.
In August 1995, the organisation’s insurance function was merged into Woodmen of the World and/or Assured Life Association. A number of lodges remain active today as organizations that promote pride in Danish culture and origin.