Diagram 5 illustrates how a section may be subdivided, although the Diagram only gives a few of the many subdivisions into which a section may be divided.  All Sections (except fractional Sections) are supposed to be 320 rods, or one mile, square and therefore contain 640 acres - a number easily divisible.  Sections are subdivided into fractional parts to suit the convenience of the owners of the land.  A half section contains 320 acres;  a quarter-section contains 160 acres;  half of a quarter contains 80 acres, and quarter of a quarter contains 40 acres, and so on.  Each piece of land is described according to the portion of the section which it embraces - as the Northeast quarter of Section 10;  or the Southeast quarter of the Southeast quarter of Section 10.  Diagram 5 shows how many of these subdivisions are platted, and also shows the plan of designating and describing them by initial letters as each parcel of land on the Diagram is marked with its description.

As has already been stated, all Sections (except Fractional Sections which are explained elsewhere) are supposed to contain 640 acres, and even though mistakes have been made in surveying, as is frequently the case, making sections larger or smaller than 640 acres, the Government recognizes no variation, but sells or grants each regular section as containing 640 acres "more or less."
The government Surveyors are not required to subdivide sections by funning lines within them, but they usually establish Quarter Posts on points marked A. B. C. and D. on Diagram 5.  After establishing Township corners, Section Lines are the next to be run, and section corners are established.  When these are carefully located the Quarter Posts are located at points as nearly equidistant between Section Corners as possible.  These corners when established by Government Surveyors cannot be changed, even though it is conclusively shown that mistakes have been made which cause some sections or quarter sections to be either larger or smaller than others.  The laws, however, of all the States provide certain rules for local surveyors to follow in dividing Sections into smaller parcels of land than has been outlined in the Governmental surveys.  For instance, in dividing a quarter section into two parcels, the distance between the Government Corners is carefully measured and the new post is located at a point equidistant between them.  This plan is followed in running out "eighties," "forties," "twenties," etc.  In this way, if the Government division overruns or falls short, each portion gains of loses its proportion.  This is not the case, however, with Fractional Sections along the North or West sides of a Township, or adjoining a lake or large stream. 

Source: Plat Book of Clinton County, Illinois. Compiled and Published by The Occidental Publishing Company, Geo. A. Ogle &
Company, Proprs., Chicago, 1892 which included the plats and the business directory

 Plat Township Lists
Clinton County Genealogy