Professor Forbes's Address to the British Association. 255 



undertook his report in the early days of the Association, when 

 its friends were yet few and its success dubious ; its execution 

 has been delayed by the extent of the subject and labour of 

 the task. The report on the differential and integral calculus, 

 which was intended to form the basis of it, is delayed, and the 

 present one is devoted to a discussion chiefly of algebraic me- 

 thods, and a close examination of the metaphysical principles 

 upon which this interpretation of analysis is founded. The 

 author has thus been led to extend the views which, in his re- 

 cent systematic treatise, he had developed in regard to the signs 

 of aflPection of algebraic quantities, including those of imaginary 

 quantities, of discontinuous functions, and the interpretaticHis 

 of zero and infinity. The author has then treated of Series, as 

 regards their fitness for giving directly conclusive results, par- 

 ticularly when such series are divergent^ leaving to the other 

 part of the report a detail of the progress in the application of 

 series, which is more practical than metaphysical. The author 

 then treats historically of the elementary works in use on Al- 

 gebra and Trigonometry ; and devotes the last part of the re- 

 port, consisting of above fifty pages, to the Theory of Equar 

 tions, in which he has minutely analysed some of the most re- 

 markable papers on this abstruse subject. Altogether this re- 

 port (especially when completed), cannot fail to fulfil, in a 

 striking manner, the two great objects of such works ; first, 

 to supply those engaged in collateral branches of science 

 with the means of referring to and obtaining the information 

 they may require upon methods which perhaps are of daily 

 utility in physico-mathematical inquiries ; but with which, from 

 the vast extent of the science of pure mathematics, the short- 

 ness of human life prevents the possibility of a complete and 

 systematic acquaintance, unless it be made the special object of 

 study ; and, in the second place, to point out, where chasms of 

 reasoning occur, what mathematical methods are impregnable, 

 and what rest upon a still dubious basis, in a metaphysical 

 point of view, several of which are very specifically treated of 

 in Mr Peacock's report. It is much to be desired that nothing 

 may longer postpone the conclusion of a work which cannot 

 fail to reflect honour upon the Association, 



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