X 



fell upon his lungs and terminated fatally. He died on the 8th of Decem- 

 ber, 1864. 



Dr. Boole was a man of great goodness of heart. By those who knew 

 him intimately he was regarded with a feeling akin to reverence. " Apart 

 from his intellectual superiority," says one of his colleagues, "there was 

 shed around him an atmosphere of purity and moral elevation, which was 

 felt by all who were admitted within its influence. And over all his gifts 

 and graces there was thrown the charm of a true humility, and an apparent 

 total unconsciousness of his own worth and wisdom." 



Many illustrations might be given of the versatility of Boole's talent, his 

 love of poetry and music, his fine appreciation of the beauties of external 

 nature, his profound reverence for truth, especially religious truth, and 

 many other qualities of his intellect and heart which have not been so much 

 as touched upon ; but the limits within which it is proper that this sketch 

 should be contained forbid any elaborate estimate of his character. 



Boole's mathematical researches have exercised a very considerable in- 

 fluence upon the study of the higher branches of the analysis, especially 

 in this country. They have stimulated and directed the efforts of other 

 investigators to an extent that is not perhaps generally known. Out of 

 his theory of linear transformations has grown the more general theory of 

 covariants (due to Professor Cayley), with all its important geometrical and 

 other applications. By his invention of an algebra of non- commutative 

 symbols, a great impulse has been given to the cultivation of the calculus 

 of operations. His general method in analysis is the most powerful in- 

 strument which we possess for the integration of differential equations, 

 whether total or partial. To Sir John Herschel is due the high praise of 

 having first applied the method of the separation of symbols to the solution 

 of linear differential equations with constant coefficients. But it was re- 

 served for Duncan F. Gregory and Boole to set the logical principles of that 

 method in a clear and satisfactory light ; and to Boole alone belongs the 

 honour of having extended the theory to the solution of equations with 

 variable coefficients. His principal discoveries in this department will be 

 found in his 'Differential Equations,' and the Supplementary volume 

 (edited by Mr. Isaac Todhunter), works which though primarily intended 

 for elementary instruction, may be read with advantage by the advanced 

 mathematical student. Other original investigations will be found in the 

 same volumes, and more especially in those parts wdiich relate to Riccati's 

 equation, to integrating factors, to singular solutions, to the inverse pro- 

 blems of geometry and optics, to partial differential equations, and to 

 the projection of a surface on a plane. 



The calculus of logic, upon the invention of which Boole's fame as a 

 philosophical mathematician may be permitted to rest, is most fully deve- 

 loped in his ' Investigation of the Laws of Thought.' The design of this 

 work is — to use the author's own words — ^' to investigate the fundamental 



