"To form a just estimate on the state of any branch of natural history at a given period, it is necessary to view it in two positions; first, in regard to the principles upon which it is prosecuted, and secondly, how far these principles have been applied to practical use, or in other words, to the clear determination of the species. The first of these views contemplates ornithology as an inductive science, and its rank in the scale of human knowledge will be determined by the greater or lesser accordance of its fundamental principles with those which regulate every other branch of the physical sciences,—by the simplification and reduction of its innumerable facts to a few universal laws,—and by the analogy which can be traced between these laws, and such others that have been determined in higher and more extended portions of creation. For although the study of this branch of zoology is so vast, compared to our limited faculties, that an ordinary life would hardly be sufficient for thoroughly understanding it, yet it is but a very small point in the circle of the physical sciences, which embraces all matter and all creation. When, therefore, we have advanced in the philosophy of any branch of natural history, so far as to assimilate its laws with others that have been determined in conterminous branchs, we have demonstrative evidence that our assumptions are correct; but if two or three of these laws can be still farther traced throughout the visible creation, and even to extend themselves to all that is known of the spiritual world, our evidence is of a much higher cast. The truths of the one, become not only connected, but, as it were, amalgmated, with the truths of the other; they cannot, in minds accustomed to inductive reasoning, be separated; and we become as much inclined to question the circular progress of the planets round the sun, as the circular development of the variation of forms in the animal and the vegetable creation.
"Ornithology, no less than other branches of zoology, is rapidly approaching, in its fundamental principles, to the state of demonstrative certainty just intimated. Enough has been already published to show that the principles upon which it is now founded, as a science, are safe and sure. The circularity of the primary groups, upon the whole, has been successfully established, by Mr. Vigors, and very many of the natural families rightly located; but as this was the result of synthesis,—in other words, an implicit adoption of the theory of Mr. Macleay, so it naturally followed that the theoretic errors of one would be transferred to the other ..."
William Swainson, 1836. On the natural history and classification of birds. Vol. I. (pp 192–194) London.
William Swainson was a leading proponent of the Quinarian system of classification invented by William Macleay, which held that taxa naturally group into circles of five, as opposed to the dichotomous trees that we favor today. The Quinarian system fell out of favor long before Darwin published Origin of Species.
“Quinarian systematists believed that two sorts of relationship—affinity and analogy—obtained among taxa, that taxa existed in natural groups of five, that circular chains of affinity connected taxa within each group of five, and that relationships of analogy obtained among taxa occupying corresponding positions in different circles of affinity.” Robert J. O'Hara.