Mo. Rev. Stat. § 60.345

The quarter-section corners of sections south of the township line and east of the range line, and not established by the original government survey will be established according to the conditions represented upon the official government plat using single proportionate measurement between the section corners belonging to the same section as the quarter-section corner being established, the section corners having first been identified or reestablished. The proportional position shall be offset, if necessary, in a cardinal direction to the true line defined by the nearest adjacent corners on opposite sides of the quarter-section corner to be established.