Thompson wrote On Growth and Form in the maturity of a career that lay somewhat outside the mainstream of the biological sciences of his day. The book is in large part a contribution to morphology, the study of organic form. This branch of the biological sciences had a flowering in the early and mid-nineteenth century but subsequently receded from the forefront of influential research. As an aspect of natural philosophy, morphology can be traced back at least to the Greek philosopher Aristotle, although the term itself is credited to the German poet-philosopher Johann Wolfgang von Goethe. In broad terms, the study was concerned with relationships of structure between diverse plant and animal species and proposed various theories to explain the observed continuity of organic forms. For example, Goethe, whose scientific and poetic work D’Arcy Thompson knew well, had asserted that all plants were modifications of an archetypal plant and that all plant organs were variations of a single fundamental organ, the leaf. The most arresting issues in morphology, however, lay in zoology and paleontology; with the appearance of Charles Darwin’s On the Origin of Species in 1859 the fundamental problems of morphology seemed to have been resolved by reference to paths of evolutionary descent within the animal kingdom.

Thompson’s early education took place during the widespread debate over the merits of the Darwinian evolutionary theories, and his scientific career, though not running altogether counter to concepts of evolution and natural selection, had a pronounced bias toward alternative perspectives on many issues. On Growth and Form is essentially an attempt to establish a theory of organic form based upon the physical and mathematical laws governing the development and function of organisms instead of upon the operation of the mechanisms of heredity and natural selection. In its progression of topics, On Growth and Form demonstrates organic form as principally determined by material forces operating upon biological structures. In the first two chapters, titled “Introductory” and “On Magnitude,” the foundation of the book is set solidly upon the laws of Newtonian physics, yet Thompson carefully avoids giving the reader the impression that his personal philosophy is mechanistic:The waves of the sea, the little ripples on the shore, the sweeping curve of the sandy bay between the headlands, the outline of the hills, the shape of the clouds, all these are so many riddles of form, so many problems of morphology, and all of them the physicist can more or less easily read and adequately solve: solving them by reference to their antecedent phenomena, in the material systems of mechanical forces to which they belong, and to which we interpret them as being due. They have also, doubtless, their immanent teleological significance; but it is on another plane of thought from the physicist’s that we contemplate their intrinsic harmony and perfection, and “see that they are good.”

Thompson’s appreciation of natural beauty is clearly attuned to his love for mathematics, an affinity which appeared early in his career and set him apart from the majority of his colleagues in the biological sciences.

Despite his reputation as a zealous geometer, Thompson avoids mere mathematical abstraction in his approach by emphasizing process in living form. Biological entities, he writes, “can never act as matter alone, but only as seats of energy and as centres of force.” The author’s conception of the vitality of biological form is implicit in his use of the word “growth” in the title of the book; he understands that the idea of “form” by itself can be too easily detached from the “dynamical” aspect of objects and phenomena. Thompson’s prose often exhibits a dynamism uniquely attuned to his subject, as in the following discussion of scale:A certain range, and a narrow one, contains mouse and elephant, and all whose business it is to walk and run; this is our own world, with whose dimensions our lives, our limbs, our senses are in tune. The great whales grow out of this range by throwing the burden of their bulk upon the waters; the dinosaurs wallowed in the swamp, and the hippopotamus, the sea-elephant and Steller’s great sea-cow pass or passed their lives in the rivers or the sea. The things which fly are smaller than the things which walk and run; the flying birds are never as large as the larger mammals, the lesser birds and mammals are much of a muchness, but insects come down a step in the scale and more.

Thompson here evokes not only the energy and movement of organisms but also the dynamism of time on complementary scales of individual and historical development.

The third chapter of On Growth and Form, “The Rate of Growth,” introduces the notion that “the form of an organism is determined by its rate of growth in various directions.” After a promising but brief exposition of this concept, Thompson is diverted into a somewhat superfluous argument regarding a passage from Darwin and then launches informative but pedestrian accounts of human growth and population statistics, the growth rates of insects and animal organs, and environmental factors affecting growth. This long chapter, alone among the seventeen which make up the 1942 edition, concludes with a one-page summary of its contents; its next-to-last sentence, a resigned “But enough of this discussion,” lends credibility to John Tyler Bonner’s editing of this chapter for the revised edition of 1961.

The fourth and fifth chapters of On Growth and Form concern the cell. Chapter 4, “On the Internal Form and Structure of the Cell,” begins with a brief historical review of the morphological approach to cell structure, beginning with the first decades of the nineteenth century. After observing that the visible structure of the cell has been studied more exhaustively than the “purely dynamic problems” associated with cells, Thompson goes on to state, with somewhat uncharacteristic dogmatism, that the “mere study” of cell structure is essentially exhausted—a judgment that was extremely premature. In the absence of sufficiently intricate observations by which he might account for the complexity of cellular activity, he reassures the reader that “very great and wonderful things are done by means of a mechanism (whether natural or artificial) of extreme simplicity.” His aim in this chapter is to emphasize the operations of “physical forces” in cells and thereby to avoid a static, mechanical model of the cell, but Thompson is here writing from a position of weakness. Historically, the study of cell structure and physiology was on the verge of far-reaching developments which might well have inspired a fresh treatment of the topic by Thompson only a few years later; on the professional side, however, his background as a naturalist with virtually no experience in experimental biology left him particularly vulnerable to the obsolescence inherent in this more specialized and more quickly advancing field of...

(The entire section is 2903 words.)