The main reason for observing the rule of thirds is to discourage placement of the subject at the center, or prevent a horizon from appearing to divide the picture in half.
"And to give the utmost force and solidity to your work, some part of the picture should be as light, and some as dark as possible: These two extremes are then to be harmonized and reconciled to each other."
This rule would likewise apply in breaking a length of wall, or any other too great continuation of line that it may be found necessary to break by crossing or hiding it with some other object : In short, in applying this invention, generally speaking, or to any other case, whether of light, shade, form, or color, I have found the ratio of about two thirds to one third, or of one to two, a much better and more harmonizing proportion, than the precise formal half, the too-far-extending four-fifths—and, in short, than any other proportion whatever.
I should think myself honored by the opinion of any gentleman on this point; but until I shall by better informed, shall conclude this general proportion of two and one to be the most pictoresque medium in all cases of breaking or otherwise qualifying straight lines and masses and groupes [sic], as Hogarth's line is agreed to be the most beautiful, (or, in other words, the most pictoresque) medium of curves.
But, however occasionally useful, it is neither accurate nor universal, the true mean of nature requiring compensation, which, in the case of warmth and coolness, is in about equal proportions, while, in regard to advancing and retiring colours, the true balance of effect is, approximately, three of the latter to one of the former; nevertheless, the proportions in both cases are to be governed by the predominance of light or shade, and the required effect of a picture, in which, and other species of antagonism, the scale of equivalents affords a guide.Smith's discussion of this "rule" is independent of the history and use of the term in composition and photography.