Frederick Methvan Whyte designed a system for classifying steam locomotives by wheel arrangement that came into use in the early 20th century. Whyte's system counts the number of leading wheels, then the number of driving wheels, and finally the number of trailing wheels.
Thus, a locomotive with two leading axles (and thus four wheels) in front, then three driving axles (six wheels) and followed by one trailing axle (two wheels) is classified as a 4-6-2.
It's important to stress that wheels, not axles, are what is counted in this system. Other classification schemes in use elsewhere (such as in France) count axles.
The system had to be extended with the advent of articulated locomotives. The scheme generally adopted is that locomotives such as Garratts, where there are, in effect, two seperate locomotives joined by a common boiler, are classified by using a plus sign in between the arrangements of each engine. Thus, a 'double Pacific' type Garratt is a 4-6-2+2-6-4.
Simpler articulated types such as Mallets, where there are no unpowered axles in between powered axles, are just written by adding extra numbers in the middle; each number represents a grouping of wheels. Thus a Big Boy is written under this modified Whyte notation as a 4-8-8-4; there are two leading axles, one group of four driving axles, another group of four driving axles, and then two trailing axles.
The limitations of the Whyte system led to the design of other forms of classification. Most commonly used in Europe is the UIC Classification scheme, based on German practice, which can more completely define the exact layout of a locomotive.
In American (and to a lesser extent British) practice, most wheel arrangements in common use were given names.
Here is a list of the most common wheel arrangements: in the illustration, which should be read left to right, with the front of the locomotive to the left, small o is a carrying axle, and a big O is a driving axle.
Arrangement Whyte Classification Name
OO 0-4-0 Four-Coupled
oOO 2-4-0 Porter
oOOo 2-4-2 Columbia
ooOO 4-4-0 American, Eight-Wheeler
ooOOo 4-4-2 Atlantic
ooOOoo 4-4-4 Reading, Jubilee
OOO 0-6-0 Six-Coupled
oOOO 2-6-0 Mogul
oOOOo 2-6-2 Prairie
ooOOO 4-6-0 Ten-Wheeler
ooOOOo 4-6-2 Pacific
ooOOOoo 4-6-4 Hudson, Baltic
OOOO 0-8-0 Eight-Coupled
OOOOo 0-8-2 Transfer
oOOOO 2-8-0 Consolidation
oOOOOo 2-8-2 Mikado
oOOOOoo 2-8-4 Berkshire, Kanawha
ooOOOO 4-8-0 Mastodon
ooOOOOo 4-8-2 Mountain, Mohawk
ooOOOOoo 4-8-4 Northern, Niagara, Confederation,
Dixie, Greenbrier, Pocono,
oooOOOOooo 6-8-6 (used only on Pennsylvania Railroad steam turbine)
OOOOO 0-10-0 Ten-Coupled
OOOOOo 0-10-2 Union
oOOOOO 2-10-0 Decapod
oOOOOOo 2-10-2 Santa Fe
oOOOOOoo 2-10-4 Texas, Selkirk
ooOOOOOo 4-10-2 Southern Pacific, Overland
OOOOOO 0-12-0 Twelve-Coupled
oOOOOOO 2-12-0 Centipede
ooOOOOOOo 4-12-2 Union Pacific
ooOO OOoo 4-4-4-4 Duplex
oooOO OOooo 4-6-4-4 Pennsylvania
ooOO OOOoo 4-4-6-4 (PRR Q2)
ooOOO OOoo 4-6-4-4 (PRR Q1)
OO OO 0-4-4-0
OOO OOO 0-6-6-0 Erie
oOOO OOO 2-6-6-0 Denver & Salt Lake
oOOO OOOo 2-6-6-2
oOOO OOOoo 2-6-6-4 Norfolk & Western
oOOO OOOooo 2-6-6-6 Allegheny
ooOOO OOOoo 4-6-6-4 Challenger
OOOO OOOO 0-8-8-0 Angus
oOOOO OOOO 2-8-8-0 Bull Moose
oOOOO OOOOo 2-8-8-2 Chesapeake
oOOOO OOOOoo 2-8-8-4 Yellowstone
ooOOOO OOOOo 4-8-8-2 (SP Cab Forward)
ooOOOO OOOOoo 4-8-8-4 Big Boy
Garratts are pretty much always two identical engine frames back to back; double Pacifics, double Northerns, etc.