His earliest memoir, read before the Royal Society of Edinburgh, on the 7th of November 1796, and published in its Transactions, shows, not only that at this time he was well acquainted with the works, and possessed the methods of the most celebrated of the continental writers, but that he could advance independently in the track which they had discovered and so successfully pursued. This memoir, entitled " A New Series for the Rectification of the Ellipse, together with some Observations on the Evolution of the Formula (a~ -\- — ^o.h cos0)'^" besides displaying considerable analytical skill in the accomplishment of its immediate object, shows that the solution of the highest class of physical problems had already en- gaged the author's attention.
Two other memoirs, communicated by Mr. Ivory to the same So- ciety, one in 1799, " A New Method of resolving Cubic Equa- tions," and the other in 1802, "A New and Universal Solution of Kepler's Problem," both indicate great originality of thought and powers of investigation. The approximation which he gives in the latter memoir for the determination of the excentric anomaly is re- markable for its simplicity, universality, and accuracy.
At this period, Mr. Ivory was in correspondence with Professor Playfair, Mr. Leslie (afterwards Sir John I^eslie), Mr. Wallace and Mr. Brougham (now Lord Brougham), and with these eminent persons his intercourse was ever after continued until interrupted by the death of one of the parties. To the well-founded recom- mendation of Lord Brougham he was indebted for the grant of a pension of £300 per annum, in 1831, by King William IV.
Released from the anxieties of mercantile speculations by the dissolution of the company of which he had been the manager, he, in 1804, applied for, and immediately obtained, one of the Mathe- matical Professorships in the Royal Military College at Marlow (afterwards removed to Sandhurst). During the time that he was connected with this institution, he acquired the esteem and regard of the authorities of the College, of his colleagues, and of his pupils. In the discharge of his public duty he appears to have been alto- gether exemplary ; and he was universally considered to be one of the best and most successful instructors that had ever been con- nected with the College.
He now became better known in the scientific world, and while he discharged the important duties of his Professorship to the ad- vantage of the College and the advancement of its character, he com- municated to the public many important memoirs on various scien- tific subjects, which appeared in the Philosophical Transactions, in Leybourn's Mathematical Repository, Maseres's Scriptores Logarith- mic!, and the Supplement to the sixth edition of the Encyclopsedia Britannica.
About the year 1816, his health began to give way under the confinement consequent upon close application to his professorial duties, and devoted attachment to scientific inquiry ; and he was compelled by bad health to resign his Professorship. The estimation in which he was held by the authorities of the College cannot
