THE SCIENTIFIC SPIRIT IN ENGLAND. 



247 



of this document, of which he knew by a reference in 

 another work. At last he got possession of a copy which 

 had probably during all this time been buried in the 

 library of a prominent mathematical tutor at Cam- 

 bridge, with whom he had been in frequent intercourse. 

 Thomson then took it with him to Paris, where Sturm 

 and Liouville at once recognised its merits. He then 

 published it in ' Crelle's Journal,' where it has ever 

 since been referred to as a fundamental essay on the 

 so-called potential theory. 1 One of the most original 

 thinkers on mathematics, who introduced a novel prin- 

 ciple into algebraical science, George Boole, never at- 21. 



Boole. 



tained to a higher position than that of teacher at a 

 remote Irish provincial College. 2 But perhaps the most 

 signal example of the want of support which the 



1 See note 1 to p. 231 ; also Sir 

 William Thomson, reprint of papers 

 on " Electrostatics and Magnet- 

 ism," 2nd ed., London, 1884, p. 2, 

 note ; p. 126, note. 



2 George Boole (1815-64), a native 

 of Lincolnshire, was one of the few 

 gi-eat and original mathematicians 

 who, like Leibniz and Grassmann, 

 and to some extent Gauss, looked 

 at the logical as well as the purely 

 arithmetical side of the language 

 of symbols. Though his treatises 

 on ' Differential Equations ' (1859) 

 and on 'Finite Differences' (1860) 

 have become well-known text-books, 

 and his 'Laws of Thought' (1854), 

 in which he examined the found- 

 ations of the mathematical theories 

 of logic and probabilities, remains a 

 unique work, his principal services 

 to science lie in the direction of 

 the "calculus of operations." In 

 this branch of mathematics, which 

 is peculiar to England, the sym- 

 bols indicating an arithmetical op- 



eration are separated from those 

 denoting quantity and treated as 

 distinct objects of calculation. In 

 connection with these investiga- 

 tions, many of which have now 

 penetrated into ordinary text- 

 books, Boole was led to examine 

 the conditions under which and the 

 forms in which algebraical expres- 

 sions, whilst undergoing changes 

 and transformations, remain, never- 

 theless, unaltered (invariant) (1841). 

 By introducing this point of view 

 he has, so to speak, created modern 

 algebra ; founding the extensive 

 and fruitful science of " Invari- 

 ants." Of this we shall treat 

 later on. I now only refer to the 

 further development of this sub- 

 ject in the hands of Cayley and 

 Sylvester, and to the valuable 

 sketch of the history of this branch 

 of mathematics by Dr F. Mayer in 

 the first volume of the ' Jahres- 

 bericht der deutschen Mathemati- 

 ker-Vereinigung,' Berlin, 1892. 



