Kan. Stat. § 19-1409
In the subdivision of sections of land, as surveyed by the United State surveyors into quarter sections, the following method shall be followed, to wit: The surveyor shall proceed to connect the points of position of the monuments marked "one quarter S.," commonly known as quarter-section corner monuments, which are upon opposite sides of the section, by tracing a straight line from one to the other; he shall then ascertain the point of intersection of the two straight lines as above mentioned, and the said point of intersection shall be the point of position of the corner common to the four quarters of the section subdivided. The provisions of this article shall not apply to center corners of sections already established according to law.
K.S.A. 19-1409