London: Society for Promoting Christian Knowledge, 1876.
First edition, rare on the market in this condition, of Maxwell's textbook on dynamics, “a masterpiece of natural philosophy, notable especially for introducing into physics the term relativity in a passage that combines strenuous scientific insight with a mystical awareness … [It] had a strong influence on [Henri] Poincaré” (Routledge Encyclopedia of Philosophy, p. 209). “More light is thrown on Maxwell’s own opinions about the problem of relative and absolute motion and the connection between dynamics and other branches of physics by the delightful monograph Matter and Motion, published in 1876” (DSB). This book also contains, within a discussion of causality, a foreshadowing of modern ideas about chaos theory.
Matter and Motion has sometimes been represented in the past as a largely non-mathematical summary of Newtonian dynamics but it is now recognized that it contains an incisive analysis of concepts such as space, time and acceleration that is a clear precursor of Einstein’s work that lead to the special theory of relativity. Article 18, ‘Absolute Space,’ includes the statement: “All our knowledge, both of time and place, is essentially relative.” Maxwell also emphasizes from the beginning of the work the notion of ‘configuration’ of a set of points, which he defines as “the assemblage of relative positions” − this avoids the arbitrary choice of an ‘origin’ or ‘axes’ which would be needed to specify the Cartesian coordinates of the points. In art. 29 he represents such a configuration by a set of bright dots on a black field, to emphasize that there are no absolute measures of distance between the points. This can be viewed as an anticipation of Einstein’s use of generalized coordinate systems in his general theory of relativity.
Later, in art. 102, Maxwell summarizes the first five chapters of the book as follows: “Our whole progress up to this point may be described as a gradual development of the doctrine of relativity of all physical phenomena. Position we must evidently acknowledge to be relative, for we cannot describe the position of a body in any terms which do not express relation. The ordinary language about motion and rest does not so completely exclude the notion of their being measured absolutely, but the reason of this is, that in our ordinary language we tacitly assume that the earth is at rest … There are no landmarks in space; one portion of space is exactly like every other portion, so that we cannot tell where we are. We are, as it were, on an unruffled sea, without stars, compass, sounding, wind or tide, and we cannot tell in what direction we are going. We have no log which we can case out to take a dead reckoning by; we may compute our rate of motion with respect to the neighbouring bodies, but we do not know how these bodies may be moving in space.”
The latter part of the book is concerned with the problem of the aether, the hypothetical material that physicists at the time believed must exist in order for heat and light to be transmitted through empty space. “Maxwell writes: “Energy cannot exist except in connection with matter.” But energy, in the form of light and heat, traverses the space between the sun and the earth. Hence, there must be matter “existing in the interplanetary spaces” and, in fact, “disseminated through the whole of the visible universe” (art. 108). This “matter,” the “aether”, cannot be gravitational in proportion to its mass. Yet Newton, by means of experiments reported in the Principia, demonstrated that all matter exerts a gravitational force corresponding to its mass. Beginning with Chapter VII, Maxwell therefore very carefully reviews the theory of the pendulum and its application to the measurement of the gravitational constant. In Chapter VIII he concludes, notwithstanding the experimental evidence, that “it is still extremely doubtful whether the medium of light and electricity is a gravitating substance, though it is certainly material and has mass” (art. 145). The implicit question, standing as it does simply as an enigma, in effect sets the stage for much of the physics of the twentieth century” (thomasksimpson.com/matter.pdf).
The foundations of chaos theory are usually located in a famous paper by Edward Lorenz published in 1963. But the necessary conditions for deterministic chaos were foreseen by Maxwell in the present work. “The possibility of small causes having large effects (in a perfectly deterministic universe) was anticipated by many scientists before Lorenz, and even before the birth of dynamical systems theory, which is generally accepted to have its origins in Poincaré’s work on differential equations towards the end of the 19th century. Maxwell [Matter and Motion, art. 19] wrote: “There is a maxim which is often quoted, that “The same causes will always produce the same effects.”” After discussing the meaning of this principle, he adds: “There is another maxim which must not be confounded with [this], which asserts that “Like causes produce like effects.” This is only true when small variations in the initial circumstances produce only small variations in the final state of the system.” He then gives the example of how a small displacement of railway points sends a train on different courses” (Van der Heuden, p. 85).
“Maxwell’s Matter and Motion first appeared in 1876 and was reprinted before the year was out. The first American edition was printed in 1878. Following several reprints on both sides of the Atlantic, Sir Joseph Larmor added notes and appendices to produce a new edition in 1920. This edition was reprinted in 1925 and at least half-a-dozen times since 1952” (Flood, McCartney & Whitaker, James Clerk Maxwell: Perspectives on his Life and Work (2014), p. 27).
Van der Heuden, ‘Butterfly effect,’ pp. 84-6 in Encyclopedia of Nonlinear Science (A. Scott, ed.), 2004.
16mo (158 x 100 mm), pp. viii, -128, [4 advertisements]. Original brown cloth decorated in black, a little rubbed.