A more thorough explanation:

An adjutant general is the administrative head of a military unit that has a general staff. They are responsible for overseeing the day-to-day operations of the unit and ensuring that everything runs smoothly. In addition, an adjutant general may also be an officer in charge of the National Guard of a state.

For example, the Adjutant General of the United States Army is responsible for overseeing the Army's administrative and logistical functions. They work closely with other military leaders to ensure that the Army is prepared to carry out its missions.

Ad largum is a Latin term that means "at large" or "at liberty." It is often used in legal contexts to describe someone who is free to act as they please, without any restrictions or limitations.

For example, if a suspect is released from custody and allowed to go ad largum, it means that they are free to go about their business and are not required to stay in a particular location.

Adlegiare is a Latin term that means "to purge oneself of a crime by oath." It was a common practice in medieval times for someone accused of a crime to swear an oath of innocence in front of witnesses in order to clear their name.

For example, if someone was accused of theft, they might be required to adlegiare by swearing an oath that they did not steal the item in question. If they were believed, they would be cleared of the crime and allowed to go free.