Chicago’s famous and efficient numbering system (one block=100 numbers, 8 blocks or 800 numbers=mile, 0 n-s is Madison, 0 e-w is State, all streets on the same alignment share the same name even if the street is not continuous) was instituted only in 1909, despite the fact that the city was laid out in a consistent grid pattern from the original 1830s plat forward!
The pre-1909 numbering system was a grade-A nightmare. There was completely different numbering for the North, South, and West Divisions.* The east-west numbering, and in two divisions the north-south numbering, was based on distance from the lake or river, but both the river and the lake shore meander. And yes, that means there could be two different 100 W. Kinzie Streets (luckily, I don’t think any streets ran into all three Divisions), that the numbers could do a large leap forwards or backwards simply by crossing a bridge, and that a building on a given corner of one street could have a different number than the building on the same corner one or two blocks down their common street (IOW, now 500 W. Madison and 500 W. Adams are both between Canal and Clinton, but before 1909 you couldn’t count on that at all).
*The Chicago River heads essentially due west from the lake and then splits into north and south branches. South of the main river and east of the south branch was the South Division. North of the main river and east of the south branch was the North Division. West of the north and south branches of the river was the West Division. Few people use these terms anymore, but in the 19th Century they were in common use.
You can go at least as far northeast as Philadelphia and still have townships, and I’ve never heard “town” used in the same sense. Is that just a New England thing?
In Ontario province, at least, residences that don’t have municipally-assigned numbers are assigned an “emergency” number, which is placed on a small standardized sign at the entrance to the property.
The numbers are unique, and serve to unambiguously identify residences to emergency services. The alternative is to say, “Third farm on the left side of the road after the bridge.” Which bridge? Or was that a culvert? And what end of the road are you counting from?).
These numbers are (I believe) directly related to geographical coordinates. The number for a particular place can be directly read from a topographical map that shows the place; and, given a number, you can find the place on the map.
Thus some people have street addresses like “72567 Highway 60”, even though their mail actually goes to a box at the local general store, and the mailing address would be more like “Post Office Box GK345, Town Name, Ontario, K0X 1W0”.
In Mass, we no longer have “counties” as a governmental entity. They (well, all but one, I think) are all now run by the state, and, even when they DID exist, never ran Police forces (well, not in the 20 years that I’ve been alive. Back in the day, I’m sure they did). The “County Sherriff”, who is now paid by the state, does nothing except for run the prisons, even to the point where I’m fairly sure they don’t have the authority to give you a speeding ticket.
All police that make arrests are the city/town (A town is just a city without a mayor. It’s still incorporated, they just have town meetings instead of a city council).
I remember about 5 years ago, a guy ran in the (what turned out to be last) race for county commissioner with the slogan “Abolish County Government.” He succeeded
The San Gabriel Valley, just northeast of Los Angeles, is a patchwork of many incorporated suburbs. Street names generally do not change as roads traverse multiple cities. However, each city staunchly maintains its own numbering system.
Most of 'em follow the prevailing practice out here of the centered grid described very nicely by Mr2001, but of course every few miles it resets as you enter a new city. It’s a complicated mosaic of city limits, but it’s absolutely crucial to note the city name of your target, or you could wind up miles away (but on the right road).
