Few more details about his service, I've been able to uncover.........
He joined 26th July 1875 and was posted to X Division.
27.07.1895 146J posted to L Division as 181L.
10.08.1895 181L posted back to J Division as 198J.
23.04.1897 Pensioned as 97J (so it would appear that he went back to the 97J number, at some point between 1895 and 1897. Perhaps as a mark or respect to his Ripper days?).
I've still got a few more avenues to explore. But I think at this point I can confirm with a level of certainty that he didn't serve out his entire career in J Division as has previously been documented in Ripper lore.
I believe they worked 8 hour shifts in those days, so three rota's would have been required to cover the 24 hours. But exactly what those hours were I don't know.
I can't vouch for the 19th century but, for many years, the police did work the sort of rota system you describe (four shifts working a four week cycle with one shift on Rest Day - basically a week of mornings, a week of afternoons and a week of nights, separated by two days off)- it was still in force (just) when I started in Nottinghamshire in 1974. This created a difficulty, in that every officer was entitled to two days off every week - not possible when a total of 21 days had to be worked in every 28 days to provide the cover. Therefore one paid rest day was worked in every four weeks. The hours, when I started were 6am-2pm, 2pm-10pm & 10pm-6am.