xxviii.] ANALOGY. C35 



metr}% so did Boole accomplish tlie marriage of logic and 

 alijebra. 



'o^ 



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 allow- 

 ance 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 in- 

 comprehensible. 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 pliilosophers must have remained incomplete, 

 and tlieir theories groundless, because they did not under- 

 stand 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 on- 

 wards but matter remaining comparatively fixed in position. 

 Diogenes Laertius indeed correctly compared the propaga- 

 tion of sound with the s])reading of waves on the surface 

 of water when disturbed by a stone, and Vitruvius dis- 



