General observations on early urban policing
In 1800, only four cities in the US had populations of around 25,000 or more - the largest of these was New York with 60,000 (the others were Philadelphia, Baltimore and Boston) - so the challenges of policing in the US up to the early 1800s were much less than in the major cities of Europe where London was just short of 1 million, with Paris over 500,000. However, population growth over the following decades was rapid and from around the 1830s, city authorities began to make major changes in the organization of law enforcement.
Looking in general at the early history of urban policing,
Police are relative newcomers to the Anglo-American criminal justice
system. The Constitution does not mention them. Early city charters do
not mention them, either, for the simple reason that, as we know them,
police had not been invented. Instead, cities had loosely organized
night watches and constables who worked for the courts, supplemented
by the private prosecution of offenders through lower-level courts
(Steinberg 1989). The night watch and day constable, dating from the
Middle Ages...
were not replaced until the 1820s, when London police were reorganized
by Robert Peel. The police precedent for the United States, as is well
known, came from the establishment of the Metropolitan Police of
London in 1829.
Source: Eric H. Monkkonen, 'History of Urban Police'. In Crime and Justice, Vol. 15, Modern Policing (1992), pp. 547-580
On these early constables and the night watch,
Constables were responsible to civil and criminal courts. They supported themselves by fees, which came from serving warrants and civil
papers and arresting offenders. The victim of an offense had to seek a
constable, paying for his actions...
Night watch did just that: they were to raise the hue and cry in case
of an offense or to sound an alarm for a fire. The usual criticism of
them was that they slept, used their noisy rattles to warn off
potential offenders, and ran from real danger....the night watch, who were either citizens doing required volunteer service or, more likely, their paid substitutes, were not in any way a serious crime-fighting organization.
Source: Monkkonen
Also 'imported' from Britain, and operating in American cities from at least the 17th century, were thief catchers and coroners. The former were often, but not always, thieves themselves; despite their name, their job was primarily to recover stolen property and act as informers rather than actually catch thieves. Coroners, on the other hand, played a more active role in actually examining evidence and determining cause of death.
New York
The NCJRS' website has an article on the development of the city's law enforcement, History of New York City Police Department
In the Dutch era from 1625 to 1664, the first professional police
department was created in New Amsterdam. Police officers used hand
rattles as they patrolled the streets to discourage crime and
apprehend criminals. Under British rule from 1664 to 1783, constables
were charged with keeping the peace. They focused on such offenses as
excessive drinking, gambling, prostitution, and church service
disturbances. During the Revolutionary War, the British appointed a
military governor and employed citizen patrols to protect New York
City residents. After independence, New York adopted the London police
model and established a paid professional police force in 1828. The
first set of printed rules and regulations was issued to the police
force in 1845, and full uniforms were adopted in 1853.
Note that New York had a small population even in 1800, around 60,000 - making it the US' largest city. This was up from just 25,000 in 1776 and just 5,000 in 1700.
Going into more detail and starting from the early days of Dutch settlement (then New Amsterdam, 1625 to 1664), the new arrivals
formed a council to make and interpret the law. The council then
appointed a schout-fiscal - Dutch for legal officer - to see that its
edicts were obeyed. It was the schout-fiscal's job to punish each
lawbreaker in a manner befitting the crime. He served as both sheriff
and prosecutor throughout New Netherland, an area covering what is now
lower New York State and eastern New Jersey.
Then they got a bit more organized:
In 1651, the first professional police department was created in New
Amsterdam – the Rattlewatch. It was a voluntary patrol composed of
citizens appointed by the council. In addition to muskets, its members
were equipped with the hand rattles that gave the fledgling police
force its name. They strolled the streets to discourage crime and
search for lawbreakers. In times of emergency, they noisily spun their
rattles to summon assistance from fellow Rattlewatch members.
In late 1658, the eight members of the Rattlewatch began drawing pay,
making them the first municipally funded police organization.
This seems to have worked reasonably well as, when the British took over in 1664, few changes were made. One was that,
Instead of a schout-fiscal, there was an English constable. His job was
to keep the peace, suppress excessive drinking, gambling,
prostitution, and prevent disturbances when church services were in
progress.
However, this soon changed due to the French and Indian wars:
During the late 1600's, with the first of the French and Indian wars
underway, the military assumed responsibility for maintaining law and
order in the City. Officials appointed a bellman to do the job. His
title came from the bell he rang while making his rounds and calling
out the hours. In addition to the bell, he was issued a gun, uniform,
badge, shoes and stockings, becoming the City's first uniformed
policeman.
In the next stage of development,
The start of the 18th century brought radical changes to the City's
system of public protection. The post of bellman was abolished and the
English introduced the constable's watch to protect New York's 6,000
residents. What is now lower to mid-Manhattan was divided into six
sectors, with a High Constable and 12 sub-constables sworn to "take
care, and keep and preserve the peace" throughout the area. In 1731, a
watch-house - or Jail - was built at the corner of Wall and Broad
Streets. Punishment for "ruffians and evildoers" was carried out in
the "cage, stocks, whipping post or ducking stool" in front of City
Hall.
Things seem to have worsened after the revolution, though:
By the time the Revolutionary War ended, the City's population had
grown to 60,000 - and police protection had become a major problem.
But little was done to deal with it. Crime continued to increase
through the late 1820's. Although more watchmen were hired, they were
widely regarded as incompetent and the protection they provided was
considered inadequate. . . For years the situation remained this way.
Nothing was done until contempt for the City's weak police force
finally gave way to fear - fear that the City's social disintegration
was imminent. And with that fear came the realization that something
had to be done about providing New York with a strong, effective
police department.
Philadelphia
The US' second largest city in 1800 had no professional police force at the time. Like New York, policing evolved as the population grew, from the Town Watch in around 1700 to the first paid (but limited) police agency in 1751:
This agency, comprised of wardens and constables, patrolled the city
on a limited basis, usually stationed in "watch boxes."
Then, in 1830,
An ordinance of December 30 of that year first established a "police
patrol" which served throughout the day as well as night. Many
ordinances extended the scope of the system; in 1833 the City
Commissioners' function of lighting the streets was transferred to it
and in 1841 a full-scale Police Department was created under the
direction of the Mayor.
In common with New York, it steadily developed with guidelines becoming more clearly defined and responsibilities sometimes added and then later transferred:
...in 1859 a Detective Division was formed within the Department and
in the following year a River and Harbor Police were added to it. In
1864 the office of Fire Marshal was created within the Department,
where it remained until 1937.