made one of the most important discoveries in the history of science. As Descartes had wedded algebra and geometry, so did Boole accomplish the marriage of logic and algebra.
Analogy in the Theory of Undulations.
There is no class of phenomena which more thoroughly illustrates alike the power and weakness of analogy than the waves which agitate every kind of medium. All waves, whatsoever be the matter through which they pass, obey the principles of rhythmical or harmonic motion, and the subject therefore presents a fine field for mathematical generalisation. Each kind of medium may allow of waves peculiar in their conditions, so that it is a beautiful exercise in analogical reasoning to decide how, in making inferences from one kind of medium to another, we must make allowance for difference of circumstances. The waves of the ocean are large and visible, and there are the yet greater tidal waves which extend around the globe. From such palpable cases of rhythmical movement we pass to waves of sound, varying in length from about 32 feet to a small fraction of an inch. We have but to imagine, if we can, the fortieth octave of the middle C of a piano, and we reach the undulations of yellow light, the ultra-violet being about the forty-first octave. Thus we pass from the palpable and evident to that which is obscure, if not incomprehensible. Yet the same phenomena of reflection, interference, and refraction, which we find in some kinds of waves, may be expected to occur, mutatis mutandis, in other kinds.
From the great to the small, from the evident to the obscure, is not only the natural order of inference, but it is the historical order of discovery. The physical science of the Greek philosophers must have remained incomplete, and their theories groundless, because they did not understand the nature of undulations. Their systems were based upon the notion of movement of translation from place to place. Modern science tends to the opposite notion that all motion is alternating or rhythmical, energy flowing onwards but matter remaining comparatively fixed in position. Diogenes Laertius indeed correctly compared the propagation of sound with the spreading of waves on the surface of water when disturbed by a stone, and Vitruvius displayed a more complete comprehension of the same analogy. It remained for Newton to create the theory of undulatory motion in showing by mathematical deductive reasoning that the particles of an elastic fluid by vibrating backwards and forwards, might carry a pulse or wave moving from the source of disturbance, while the disturbed particles return to their place of rest. He was even able to make a first approximation by theoretical calculation to the velocity of sound-waves in the atmosphere. His theory of sound formed a hardly less important epoch in science than his far more celebrated theory of gravitation. It opened the way to all the subsequent applications of mechanical principles to the insensible motion of molecules. He seems to have been, too, upon the brink of another application of the same principles which would have advanced science by a century of progress, and made him the undisputed founder of all the theories of matter. He expressed opinions at various times that light might be due to undulatory movements of a medium occupying space, and in one intensely interesting sentence remarks6 that colours are probably vibrations of different lengths, “much after the manner that, in the sense of hearing, nature makes use of aërial vibrations of several bignesses to generate sounds of divers tones, for the analogy of nature is to be observed.” He correctly foresaw that red and yellow light would consist of the longer undulations, and blue and violet of the shorter, while white light would be composed of an indiscriminate mixture of waves of various lengths. Newton almost overcame the strongest apparent difficulty of the undulatory theory of light, namely, the propagation of light in straight lines. For he observed that though waves of sound bend round an obstacle to some extent, they do not do so in the same degree as water-waves.7 He had but to extend the analogy