Quantitative Agrobiology: IV. Apparent Exceptions to the Mitscherlich Law 1

IT IS characteristic of the law of diminishing increments of yield in agriculture that when increments of growth factors are applied to a "poor" but otherwise normal soil the resulting yield should conform to the rule of halved increments. Such conformity is ipso facto proof of the constancy of the Baule coefficient 0.301, into which the effect factors of all growth factors are subsumed. But for more than 40 years uninformed critics have been pointing to "many exceptions" which are alleged to deprive the Mitscherlich equation of the character of a general law and reduce it to a mere empirical expression applicable only to fortuitous cases. Quantitative agrobiologists are ready to admit that smooth, normal Mitscherlich curves are not obtained every time a field test is made in disregard of any and all environmental circumstances. It should seem hardly necessary to point out that there does not exist a system of natural law that cannot be distorted or masked by the intrusion of an extraneous major force. Thus, it is natural (normal) for a ray of light to project itself along a straight path. However, a ray of light can be bent out of its course by a strong gravitational field. (cf. Einstein). But the intrusion of this extraneous circumstance does not invalidate the principle that light normally travels in a straight line. The point here is that an apparent aberration, if known to be due to accidental and avoidable circumstances, is not a true exception to a general rule. No experienced experimenter expects to obtain smooth yield curves from a small group of plots where soil variability is extreme. The variations may be physical, as manifested by differences in texture and porosity that affect moisture retention and aeration; or chemical, as where neighboring plots have different original contents of plant nutrients or pH. Under such conditions the experimental results may be so confused that it is impossible to represent them by any regular curve, and an uninformed plant culturist' may well conclude that the Mitscherlich equation has no practical application to his soil. His experiment will not, however, be wholly labor-lost; it will at least have demonstrated the existence of soil heterogeneity, and the plant culturist may consider whether, and how, he may establish soil uniformity on his field. Where physical soil heterogeneity is randomly distributed and where the number of replications is sufficiently large,