The Museum of Alexandria was possessing the second library where it was depositing the remaining funds of the principal library. It was located in Serapis’s temple, founded by Ptolemy the IIIrd and was named as Serapeo. It used as bridge among the Egyptian culture and the Greek culture, and turned into center of scientific investigations after the destruction of the Museum. It was closed and destroyed after the edicts of the emperor Teodosio I against the pagan culture in 391 A.D.
The difference with mother-library is the following: SERAPEUM have a public character; and would be available to the entire city.
It seemed very appropriate name; a system of answered questions about; taxes and legal questions, accessible to all kinds of public. With rigor.