ANALOGY. 293 



between the forms of mathematical and logical expressions, 

 we undoubtedly owe the greatest recent advance in logical 

 science. Boole based his extension of logical processes 

 entirely upon the notion that logic was an algebra of two 

 quantities, o and i. His profound genius for the investi- 

 gation of symbolic methods led him to perceive by analogy 

 that there must exist a general system of logical deduc- 

 tion, of which the old logicians had seized only a few stray 

 fragments. Much mistaken as he was in placing algebra 

 as a higher science than logic, no one can deny that the 

 development of the more complex and dependent science 

 had advanced far beyond that of the simpler science, and 

 that Boole, in drawing attention to the connexion, made 

 one of the most important discoveries in the history of 

 science. As Descartes had wedded algebra and geometry, 

 so did Boole substantially 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 

 certain common principles of rhythmical or harmonic motion, 

 and the subject therefore presents a vast field for mathema- 

 tical generalization. At the same time each kind of medium 

 may allow of waves peculiar in their conditions, so that it 

 is a beautiful exercise in analogical reasoning to observe 

 how, in making inferences from one kind of medium to 

 another, we must make allowance for difference of circum- 

 stances. 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 



