on Townships, Sections & Documents!
What the diagram shows is the typical way of the numbering of sections.
In land records or other listings, certain landowners may be simply listed as having property in section 1-36 or something along those lines. That's your clue as to where to look for the farm you're researching.
Each quater section might be divided into 4 more 40 acre sub-sections = 160 acres total. They might be labeled the NW 1/4, the NE 1/4 or SW 1/4 or SE 1/4.
In land ownership though, people might own 200 acres, 150 acres, 45 acres or about any number you might imagine. Sometimes small parcels were broken off of larger parcels.
Land descriptions can be very simple or they can become very complicated, referencing so many feet this way and so many feet that way with many variations.
For $700, Martin bought 35 acres in the SW 1/4 of the SE quarter of Section 35, Township 119, Range 21 (T119 R21) which is about 3/4 of a mile south of Palmer Lake.
The warranty deed described it in long-hand as:
"Beginning at the Southeast corner of the Southwest quarter of Section Thirty-Five (35), Township One Hundred and Nineteen (119) of Range Twenty One (21) and running thence north one hundred and sixty (160) rods to the center of said Section Thirty-Five (35): Thence at right angles west eighteen (18) rods and eleven and a half (11 1/2) feet: Thence at right angles South thirty-eight and one half (38 1/2) rod,: Thence at right angles East to the Centre of Bohanon Creek: Thence in a southerly direction down the centre of said crek to the south line of said Section Thirty Five (35) and thence east on said section line to the place of beginning, containing thirty five acres more or less."
A Warranty Deed typically conveys true ownership of land. A Quit Claim Deed my typically represent disclaiming any ownership from a private party or heirs of other prior owners. See a good lawyer for more detail on these finer points.