BENJAMIN PEIRCE. 451 



By virtue of his office he was a member of the Transit of Venus 

 Commission, and by his suggestions and active effort he greatly aided 

 that undertaking. Two parties from the Coast Survey were sent out 

 by him, — one to Nagasaki, and the other to Chatham Ishind, to take 

 part in the work. 



The "Quaternion Analysis" of Hamilton seemed to Professor 

 Peirce to promise a very fruitful future. " I wish I was young again," 

 he said, " that I might get such power in using it as only a young man 

 can get." He took great pains to interest his students in it, and in 

 his later years formed a class for its earnest practical study, with good 

 results. His own thought was turned especially to the logic that un- 

 derlies all similar systems, and to the limits and the extensions of 

 fundamental processes in mathematics. 



At the first session of the National Academy of Sciences, in 1864, 

 he read a paper on the elements of the mathematical theory of quality. 

 Between 1866 and 1870 various papers were read to that Academy, 

 or to this Academy, on " Linear Algebra." " Algebras," " Limitations 

 and Conditions of Associated Linear Algebras," " Quadruple Linear 

 Associative Algebra," etc. These papers were not printed in form 

 as read, but instead in 1870-71 appeared his "Linear Associative 

 Algebra." 



His own feeling about this contribution to science is expressed in 

 the salutatory to his friends : " This work has been the pleasantest 

 mathematical effort of my life. In no other have I seemed to myself 

 to have received so full a reward for my mental labor in the novelty 

 and breadth of the results." 



An analysis of this treatise was given by Doctor Spottiswoode to 

 the London Mathematical Society, which is characterized by Professor 

 Peirce as " fine, generous, and complete." Such an analysis can onl5^ 

 come from one who has made a special study of the laws of mathemati- 

 cal thought. To some mathematicians, and other men of science, it 

 may yet be a question, if the time has come for them to say with entire 

 certainty whether this work is to share the fate of Plato's barren specu- 

 lations about numbers, or to become the solid basis of a wide extension 

 of the laws of our thinking. Those who have thought most on the 

 course which contemporary mathematical science is taking will prob- 

 ably agree that the new ground thus broken can hardly fail to bring 

 forth precious fruit in the future by adding to the powers of mathe- 

 matics as an instrument. 



In any case, the Associative Algebra can never lose its value as an 

 important and most beautiful addition to Ideal Mathematics, and must 



