TKANSACTIONS OF THE SECTIONS. 15 



Logic of Quality apart from Quantity," Mr. Jevonshas urged various objections to 

 certain parts of Boole's system, more particularly to the numerical calculus. The 

 author of this paper has briefly considered those objections in the concluding por- 

 tion of an article on " Boole's Life and Writings," which he contributed to the July 

 Number of the BritishQuarterly Review for 1866 (pp. 141-181). 



Hamilton's theory of quaternions, as expounded by Prof. Tait, has its logical basis 

 in principles which were tirst brought clearly to light in the com-se of Boole's remark- 

 able inquiries. No one can read the earlier chapters of Prof. Tait's ' Quaternions,' 

 and compare them with the earlier chapters of Boole's ' Laws of Thought,' without 

 being struck with the similarity, not to say the identity, of many of the processes 

 employed in both works. Treating of the properties of the quaternion symbols 

 S, K, V, the expoimder of Hamilton's system remarks, "It is cm-iovis to compare 

 the properties of these quaternion symbols with the Elective Symbols of Logic, 

 as given in Boole's wonderful treatise on the 'Laws of Thought,' and to think 

 that the same grand science of mathematical analysis, by processes remarkably 

 similar to each other, reveals to us tru^ths in the science of position far beyond the 

 powers of the geometer, and truths of deductive reasoning to which xmaided thought 

 could never have led the logician." (Tait's Quaternions, p. 50, footnote.) 



Sir Benjamin Brodie has endeavoured to do for chemistiy what Boole has done 

 for logic, — to reduce it under the domain of mathematics, using the term " mathe- 

 matics " in the enlarged sense, explained in the .author's former communication. 

 Of the validity of Sir Benjamin's proposed " method for the investigation, bv means 

 of symbols, of the laws of the distribution of weight in chemical change," it is not 

 necessary to speak here. But that method is interesting, as being undoubtedly the 

 iirst attempt to " free the science of chemistry from the trammels imposed upon it 

 by accumulated hj'potheses, and to endow it with the most necessaiy of all the in- 

 struments of progTessive thought, an exact and rational language." Sir Benjamin's 

 system was evidently suggested by Boole's ' Laws of Thought.' Whether the soil 

 into which he has transplanted Boole's ideas be congenial or not, remains to be 

 seen. 



But the most remarkable amplification of Boole's conceptions which the author 

 has hitherto met with is contained in a recent paper by Mr. C. S. Peirce, on the 

 "Logic of Relatives" (Memoirs of the American Academj-, vol. ix.). Mr. Peirce 

 divides logical terms into three grand classes. " The first embraces those whose 

 logical form involves only the conception of quality, and which therefore re- 

 present a thing simply, as 'a .' These discriminate objects in the most rudi- 

 mentary way, whicli does not involve any consciousness of discrimination. They 

 regard an object as it is in itself as stech (quale) ; for example, as horse, tree, or 

 man. These are absolute terms. The second class embraces terms whose logical 

 form involves the conception of relation, and which require the addition of another 

 term to complete the denotation. These discriminate objects with a distinct con- 

 sciousness of discrimination. They regard an object as o^er against another, that 

 is, as relative ; as father of, lover of, or servant of. These are simjile relative terms. 

 The third class embraces terms whose logical form involves the conception of 

 bringing things into relation, and which require the addition of more than one 

 term to complete the denotation. They discriminate, not only with consciousness 

 of discrimination, but with consciousness of its origin. They regard an object as 



medium or third between two others ; that is, as conjugative, as given of to 



, or buyer of for from . These may be termed conjugative 



terms." " Boole's logical algebra," says Mr. Peirce, " has such singular beauty, so 

 far as it goes, that it is interesting to inquire whether it cannot be extended over 

 the whole realm of formal logic, instead of being restricted to that simplest and 

 least useful part of the subject, the logic of absolute terms, which, when he wi-ote, 

 was the only formal logic known." The object of Mr. Peirce's paper is to show that 

 this extension is possible. Some account was given of the notation and processes 

 employed. 



On Musical Intervals. By William SpottisWoode, M.A., P.B.S. 



