156 IVORY. 



appointment to a professorship of mathematics in the Eoyal Military 

 College at Marlow, in Buckinghamshire (afterwards removed to 

 Sandhurst), with which establishment he remained until his retire- 

 ment from public service. This was the most active period of his 

 life, for while fulfilling assiduously the duties of his professorship he 

 continued unremittingly his scientific studies. His earliest writings 

 were three memoirs, which he communicated in the years 1796, 

 1799, and 1802, to the Royal Society of Edinburgh. The first of 

 these was entitled, 'A New Series for the Rectification of the Ellipse;' 

 the second, ' A New Method of Resolving Cubic Equations ;' and the 

 third, ' A New-and Universal Solution of Kepler's Problem ; ' all of 

 them evincing great analytical skill, as well as originality of thought. 

 Mr. Ivory contributed fifteen papers to ' The Transactions of the 

 Royal Society of London,' nearly all of them relating to physical 

 astronomy, and every one containing mathematical investigations 

 of the most refined nature. The first, published in the ' Transactions 

 of 1809,' and entitled, ' On the Attractions of Homogeneous Ellip- 

 soids,' is his most celebrated paper, in which he completely and 

 definitely resolved the problem of attraction for every class of ellip- 

 soidal bodies. Many of Ivory's remaining contributions, ranging 

 through a period of nearly thirty years, related to the subject of 

 the attraction of spheroids and the theory of the figure of the Earth, 

 and some of them are considered masterpieces of anylitical skill. 

 One of the last subjects which occupied his attention was the pos- 

 sible equilibrium of a spheroid with three unequal axes when re- 

 volving about one of the axes, a fact which Jacobi had discovered. 

 This Ivory demonstrates in the volume for 1838 of the ' Philosophical 

 Transactions.' The volumes in 1823 and 1838, contain Ivory's 

 two papers on the ' Theory of Atmospheric Refraction,' a subject 

 which, next to the Theory of Attractions, engaged most seriously 

 his attention on account of its great importance in astronomy and 

 the curious mathematical difficulties which its investigation pre- 

 sents. For each of these papers he was awarded the Royal medal 

 by the Society. Of all his contributions to the ' Transactions,' only 

 one is purely mathematical; this is contained in the volume for 

 1831, and is entitled, ' On the Theory of Elliptic Transcendants.' 

 Besides these contributions to the Royal Society, Ivory wrote se- 

 veral papers in the Philosophical Magazine of 1821-27 ; in Maseres's 

 * Scriptores Logarithmic! ; ' in Leybourne's ' Mathematical Reposi- 

 tory;' and in the Supplement to the sixth edition of the Encyclo- 

 paedia Britannica. In the beginning of 1819 Ivory, finding that his 

 health began to decline under the great exertions which he made in 

 carrying on his scientific researches, and performing his duties as 

 professor, resigned his professorship at Sandhurst and retired into 

 private life. In consideration, however, of his great merit, the 

 pension due for the full period of service required by the regulations 

 was granted to him, although that period had not been completed. 



