260 



Society, and is printed in the Philosophical Transactions of that year. 

 This was followed on Jane 4, 1829, by another paper, " On the 

 geometrical representation of the powers of quantities, whose indices 

 involve the square roots of negative quantities." Having previously 

 confined his attention to representing geometrically quantities of the 

 form a-\-h\^ — 1, in the last memoir he succeeded in representing 

 geometrically quantities of that form affected with an index of the 

 same form {a-\-h^/ — lm + ?i\^ "~ 0' close of it stated that 



" it will be manifest from what has been demonstrated, that all alge- 

 braic quantity may be geometrically represented, both in length and 

 direction, by lines drawn in a given plane from a given point." This 

 extension of the subject Mourey had hinted at, but had not then 

 published. 



Mr. Warren's mathematical productions are limited to those above 

 mentioned, with the exception of a short communication to the Cam- 

 bridge Philosophical Society on a correction of Mourey's proof that 

 every equation has as many roots as it has dimensions, which may 

 be regarded as an instance of the scrupulousness with which he was 

 accustomed to seek for exactness in mathematical demonstration. 

 In the latter part of his life, when his time was chiefly taken up with 

 ecclesiastical duties, he did not wholly lay aside mathematics, but 

 with friends would converse largely on favourite topics, showing re- 

 markable power in carrying on a mathematical demonstration vivd 

 voce. He continued to entertain a high estimate of the capabilities 

 of the geometrical representation of impossible quantities, which he 

 made some attempts to extend to space of three dimensions, and he 

 even contemplated the possibility of applying it to the solution of 

 the problem of three bodies. On these questions, however, he has 

 left nothing in v/riting. 



Mr. Warren was Chancellor of the Diocese of Bangor, and was the 

 rector of Graveley in Cambridgeshire, and Caldecott in Huntingdon- 

 shire. He was also owner of the advowson of Caldecott, which, as 

 well as an adjoining parish, was without a resident clergyman. In 

 order to remedy this evil, he was desirous that the union of the two 

 parishes might be effected. With this view he sold the advowson 

 of Caldecott to the patron of the other parish, and gave up the pur- 

 chase-money for the purpose of building a parsonage-house for the 

 united parishes. It is not intended in this sketch to enter into de- 

 tails with respect to Mr. Warren's private history, but the above in- 

 cident in his life is deemed ^vorthy of record as being characteristic 

 of the man. He was a clergyman of unaffected piety, simple habits 

 and generous disposition . 



On the motion of Sir R. H. Inglis, Bart., the best thanks of the 

 Society were given to the President for his excellent Address, and 

 his Lordship was requested to permit the same to be printed. 



The Statutes relating to the election of Ofhcers and Council having 

 been read, and Sir C. Lemon, Bart., and Mr. W. Tooke having, with 



