pro computer days. The process was the cheques went from your bank to their local clearing centre, from there to the other branch if a local branch of the same bank; the clearing centre nearest to the branch it's drawn on if another branch off another centre; to the clearing centre of the other bank if on another bank - then copy the same as for your bank. Depending on how many centres it went through, add a day. Eventually it ends up in the bank the cheque is drawn on (over night if a nearby branch of your bank) where a member of staff checks there's enough in the account and the signature is right and there is no stop payment on it. Then the cheque is cleared for payment.

If there is an issue they write to the depositing bank and inform them it's being bounced, allow a day for the mail.

Now the process for the physical movement of the cheque is exactly the same today as then, except it's a state wide clearing centre where all the banks meet now. So they have a policy to allow the maximum time for a notice of being bounced to arrive.

My first job was in a bank back in 1970 and at one time I was the fellow who did the signature checking and the like, so I know how it worked then as I was intimately involved.