This explanation assists with using our map co-ordinate converters.
In principle there is a mathematical basis for the Alberta Township System (ATS) variant of the Dominion Land Survey (DLS) system as implemented in Canada. In fact, the implementation in Western Canada reflects a number of slightly different approaches, as well as a large number of errors.
Below is a brief description of how to lay out the DLS grid for Alberta.
Lay off six-mile ticks from the 49th parallel of latitude to the 60th parallel. This gives you 127 township lines.
The 49th parallel of latitude is the first base line of the ATS system. On it lay off six-mile ticks westwards starting at the 110th line of longitude (4th DLS meridian). Start over at the 114th and 118th lines of longitude (5th & 6th DLS meridians). Extend these ticks 12 miles due north (following a line of constant longitude) to the first correction line. This gets you your first set of range lines.
Starting at the 49th parallel (first base line) go 24 miles directly north. This gets you to the second base line. At the latitude corresponding to this distance from the 49th parallel lay off six-mile ticks westwards from 110th meridian as you did at the 1st base line. The circumference of the earth has decreased as you went northwards, so there will be fewer full ticks than there were one base line south. Extend 12 miles north and 12 miles south from these ticks. This gets you your next set of range lines. You will note there is an offset between the range lines extending north from the lower base line and those extending south from the current ones. This offset occurs along what is called a correction line.
Repeat the base line process every 24 miles northwards (to the 32nd).
All this will result in a mesh of cells nominally six miles on a side. Each such cell is called a Township (not to be confused with the township lines we laid off earlier). Subdivide the Township into 36 sections by laying off ticks of one sixth of each Township side and connecting them by north-south and east west lines. The sections are numbered sinusoidally starting from the southeast corner of the Township.
Sections can be similarly subdivided into quarters by placing and connecting ticks at the halfway point on each section side. Use the same process to subdivide sections into legal subdivisions (LSD) except place the tick at the one-quarter way points. LSDs are numbered sinusoidally starting at the southeast corner of the section.
Note that this method of determining subdivision of the Section is approximate in that it ignores complexities introduced by the placement of road allowances and differences in road allowance widths within Alberta.
The publication "Understanding Western Canada's Dominion Land Survey System" published by the Division of Extension and Community Relations, University of Saskatchewan, provides a readable, fairly detailed description of how things are laid out.
Alberta Geological Survey's approach is pragmatic. We use a form of the ATS grid, available from AltaLIS, to construct a spatially indexed ISAM-like set of files containing the section corner co-ordinates. These are used to perform quick forward and inverse lookups. Bilinear interpolations are applied to handle quarters, LSDs and residuals.
For more information on the Alberta Township System, visit the Alberta Land Surveyors' Association's page on the topic.