Why do many vinyl albums of classical music have Sides 1 / 4 on the first record and 2 / 3 on the second? An example of this is the RCA Red Seal recording of Beethoven's 9th Symphony by the Boston Symphony Orchestra.
Many phonographs were able to play multiple records in sequence with a mechanism that would hold one or more records on the turntable, and one or more additional records elevated on the center post.
At the end of one record, the mechanism sensed the tone arm reaching close to the center of the record, and then lifted it, pulled it out beyond the edge of the records. The system then dropped the bottom record of those on the center post, leaving the rest of them. Then the tone arm mechanism moved the tone arm to the outside of the record and lowered it to the record.
The mechanism was pretty ingenious, but it couldn't flip records over. So, to play a long piece, it would play one side of each record until the stack was exhausted. Then it was up to a person to flip the stack to play the opposite sides in sequence.
So, when playing records 1A/1B, 2A/2B, 3A/3B, 4A/4B in such a mechanism, the play order would be 1A, 2A, 3A, 4A, (flip), 4B, 3B, 2B, 1B. The "B" sides would go the other way because flipping the whole stack would put them in the opposite order.
Purists would take offense at the idea of letting records drop like that, but it was an irresistible convenience to people who could tolerance slightly quicker wear of their records.