In the U.S., Chaining is a method by which railroads precisely measure and specify locations along the line. It measures distances from a fixed point, called chaining zero, following the twists and turns of the railroad line, so that the distance described is understood to be the "railroad distance," not the distance by the most direct route (as the crow flies).
This article describes chaining on the New York City Subway system, where each "chain" is 100 feet (~30.5 m) long. This is as opposed to the milepost or mileage system, where distances are usually measured in miles and hundredths.
Chaining zero
Chaining zero is a fixed point from which the chaining is measured on a particular chaining line. A chaining number at a specific ___location (called a chaining station) on a line of 243, say, identifies that the point is 24,300 feet (~4.6 miles or ~7.4 km) from chaining zero, usually measured along the center line of the railroad.
Once chaining is established, it is rare but not unheard of to change the ___location or route to chaining zero on a given line. However, it is not uncommon for a line's chaining numbers to refer to a chaining zero that no longer exists or along a physical line that no longer exists, because of abandonment or demolition. It is less common but not impossible for a reroute to alter the accuracy of chaining numbers, if only slightly.
Exceptions exist to the principle that chaining numbers represent a railroad distance to the zero point. On the original 
India chaining zero for the original system is a political rather than physical ___location, and there is no railroad at or near the zero point. Sometimes trackage (usually but not always short distances) is chained backwards from a tie point with another line.
Chaining lines
Chaining lines are routes on physical railroad lines that are usually described by one or two letters for the purpose of identifying locations on those lines.
Chaining lines are not necessarily the same as the physical lines they run on. One physical line may have several chaining letters, and one chaining line may cover several physical lines.
The letters assigned to a chaining line have nothing whatever to do with the letters displayed on trains and public maps and timetables. These latter are subway service letters . See: New York City Subway line, route and station nomenclature and Category:New York City Subway services.
For example, the BMT A chaining line begins at BMT South chaining zero north of 57th Street on the Broadway-BMT Line, but is interrupted north of the Canal Street stations, where the express tracks becomes BMT H for the trip over the Manhattan Bridge south side tracks and the local tracks become BMT B for Lower Manhattan and the Montague Street Tunnel. The BMT A line begins again in the middle of the Manhattan Bridge span on the north side tracks, passes through DeKalb Avenue and then becomes the Brighton Line for that line's entire distance to Coney Island Terminal.
Track numbers on chaining lines
Each track on a chaining line is given a number, letter or (rarely) a combination of both to identify a particular track on a particular line.
BMT / IND practice
On the Template:BMT and India an odd numbered mainline track is going railroad south and an even numbered mainline track is going railroad north. In many locations a track may be going "railroad" north or south where the compass direction is different or even opposite. This may be because it is an essentially east-west line (e.g., the Jamaica Line), so railroad north means towards Manhattan and railroad south means away from Manhattan. It may also be because a line continuing from a north-south line turns in another direction (.e., the Fulton Street Line) but the railroad direction remains the same.
These track numbers provide a definitive way of determining whether a particular direction on a particular line is going "railroad" north or south. Especially it shows that "south" on several lines (including the BMT Jamaica Line, the IND Fulton Street Line and the BMT Myrtle Avenue Line) that run in an easterly to northerly compass direction for their entire route are nevertheless running railroad south.
The local (usually outside) tracks on a given Template:BMT/ India line are numbered 1 (south) and 2 (north). The express tracks are numbered 3 (south) and 4 (north). If there are an odd number of mainline tracks, the center track is (for example) track 3/4. The signals heading southbound will show the ___location as track 3 and northbound track 4. Additional tracks on the same chaining line are usually numbered higher by the same rules. On the four track Template:BMT Brighton Line, the tracks from west to east are:
A1 - A3 - A4 - A2
On the three track West End Line, they are:
D1 - D3/4 - D2
On the two track Canarsie Line, they are:
Q1 - Q2
IRT practice
On the the tracks are numbered differently, the southbound tracks are 1 (local) and 2 (express) and the northbound are 3 (express) and 4 (local). On a four track line, the tracks are numbered:
1 - 2 - 3 - 4
On a three track line, M is used for the middle track, and 1 and 4 are still the local tracks"
1 - M - 4
And on a two-track line, there are no express tracks, so the two tracks are:
1 - 4
Chaining zero locations
Each division of the subway system has one or more chaining zero locations.
IND
The original India system has only one chaining zero, and the only one based on a physical ___location that is not and has never been on the subway or elevated system. IND zero was calculated by extending a straight line drawn from the centerline of the West Fourth Street-Washington Square Park station in Greenwich Village to the point in Lower New York Bay where that line intersects the New York-New Jersey border. That ___location, which is south of the entire City of New York, roughly north of Keansburg, New Jersey, was established as the IND chaining zero. The southern end of the Eighth Avenue Line platforms at West 4th Street station was established as chaining point 969+25, being 96,925 feet (18.357 miles) from the zero point.
The entire IND system was chained by increasing the chaining numbers moving railroad north from that point, and reducing the numbers going railroad south. As a result the principle that chaining stations along any line reflect the accurate distance to a chaining zero point via the physical railroad is not true on the IND.
When the IND Division incorporated the formerly Template:BMT Culver Line into its system in 1954, the line was resignalled from BMT chaining line C to IND chaining line B, all the way to the end of Culver chaining at the approach to West Eighth Street-New York Aquarium and the chaining distances recalculated from IND zero.
When the IND Division was extended out the former Template:BMT Fulton Street Elevated in Queens in 1956, the BMT chaining, both zero point and BMT chaining letter (K), were kept intact. The Rockaway Line, which was opened at the same time as part of the IND, retained the Long Island Rail Road chaining distances, measured from Long Island City LIRR station via the old Montauk and Rockaway Bay lines.