534? Royal Astronomical Society: Anniversary, 1844. 



ment which he enjoyed during the few remaining years of his life, 

 in consideration, as the warrant stated, of his attainments in science 

 and literature, and his valuable services, up to a very advanced pe- 

 riod of life, first in the Military College, and afterwards at the Uni- 

 versity of Edinburgh. 



For some years after his establishment at Edinburgh, a consider- 

 able portion of his time was occupied in the preparation of his lec- 

 tures, on which he bestowed great pains. When the new edition 

 of the Encyclopaedia Britannica was commenced, he undertook the 

 revision of all the mathematical papers he had contributed, as well 

 as some of those which had been written by Dr. Robison ; and se- 

 veral of the more important treatises, particularly Algebra, Conic 

 Sections and Fluxions, were remodelled and almost entirely re- 

 written. To the Transactions of the Royal Society of Edinburgh he 

 contributed a paper in 1823, on the Investigation of Formulae for 

 finding the logarithms of trigonometrical quantities from one another; 

 one in 1831, entitled "Account of the Invention of the Pantograph, 

 and a Description of the Eidograph ;" and one in 1839, on the Analo- 

 gous Properties of Elliptic and Hyperbolic Sectors. His last contri- 

 bution to that Society, published in vol. xiv. of the Transactions, 

 was entitled, " Solution of a Functional Equation, with its Applica- 

 tion to the Parallelogram of Forces, and to Curves of Equilibration." 

 This paper, in addition to the investigation of series adapted for cal- 

 culation, contains a set of tables, to ten decimal places, of the cor- 

 responding values of the amplitude, ordinate, and arc of a catenary, 

 which are important in an engineering point of view, as they afford 

 the data required for constructing arches having the forms of equili- 

 brated curves. Similar tables, to eight places, had previously been 

 given by Mr. Davies Gilbert in a paper on the mathematical theory 

 of suspension bridges, in the Philosophical Transactions for 1826 ; but 

 the numbers were found by Mr. Wallace to be erroneous, generally, 

 in the last three decimal figures. 



Mr. Wallace is the author of a paper in vol. ix. of our Memoirs 

 containing two elementary solutions of Kepler's problem by the an- 

 gular calculus. In the Transactions of the Philosophical Society of 

 Cambridge, vol. vi., there is also a paper by him under the title of 

 " Geometrical Theorems and Formulas particularly applicable to some 

 Geodetical Problems." For this subject he had a particular predi- 

 lection ; and in 1838, while confined to a sick-bed, he composed, 

 and afterwards published at his own expense, a separate work, enti- 

 tled " Geometrical Theorems and Analytical Formulae, with their 

 application to the Solution of certain Geodetical Problems." This 

 volume, which he appropriately dedicated to his friend Colonel Colby, 

 contains the substance of his paper in the Cambridge Philosophical 

 Transactions, with the addition of a considerable number of extremely 

 elegant formulae, most of them new, and some of them important in 

 the practice of the higher geodesy. 



Professor Wallace took great delight in all the practical ajDplica- 

 tions of his science, and had a strong turn for mechanical invention. 

 His attention having been directed to the imperfections of the Pan- 



