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and, on their return, left him in Paris, where the next winter was 

 occupied in attending lectures by Chasles, Lame, and others, and in 

 making the acquaintance of the leading French mathematicians. In 

 the winter of 1858-59 he was in Rome ; and subsequently he travelled 

 in Ttaly, making the acquaintance of many mathematicians, especially 

 of his friend Cremona. 



Returning to England in 1860, he was appointed mathematical 

 master at University College School ; and he held this post for a 

 period of five years, during which he made his first developments in . 

 teaching geometry. The experience of the results then attained led 

 him to join the Association for the Improvement of Geometrical 

 Teaching, when it was formed in 1871 ; and for the first seven years 

 of its existence he was its President and took an active part in its 

 work. 



He had been elected a Fellow of the Royal Society in 1861, and it 

 was from this date onwards that his researches are devoted to the 

 various branches of pure geometry which proved of most absorbing 

 interest to him. He was appointed Professor of Physics at University 

 College in 1865, and, on the death of Professor De Morgan in 1867, 

 he succeeded to the Professorship of Pure Mathematics ; but the 

 latter chair he resigned in 1870 to become Assistant Registrar in the 

 University of London. In 1873, the date of the establishment of the 

 Royal Naval College at Greenwich, he was appointed Director of 

 Naval Studies ; and he continued to discharge the duties of that 

 office for ten [years. The precarious condition of his health then 

 compelled him to resign : and he subsequently lived in comparative 

 retirement, spending most of his winters abroad, until his death on 

 16th February, 1892. 



Hirst took a prominent part in the foundation of the London 

 Mathematical Society in 1865, served as its President from 1872 to 

 1874, and was a member of its Council for over twenty years. His 

 active co-operation with the Society did much to extend its influence : 

 and it was largely to the pages of its Proceedings that his papers on 

 pure geometry were contributed. These are the papers containing 

 the particular researches for which a Royal Medal was awarded to 

 him in 1883 the year which practically marks the termination of 

 his public life. He had served on the Council of the Royal Society in 

 the years 1864-66, 1871-73, 1880-82 : after 1883, the only sign of 

 activity was the production of several papers, one of which in continua- 

 tion of his earlier researches is of considerable importance. 



The amount of Hirst's published work is not great ; but his work 

 is valuable, and an appreciable portion of it has been translated 

 into French and into Italian. His papers are singularly clear : and 

 side issues, that might lead him away from the main line of develop- 

 ment of his subjects, are severely excluded. It is evident that he 



