Obituary. Professor Wallace. 531 



of Dr. Robison, he contributed the article " Porism" to the third 

 edition of the Encyclopaedia Britannica ; and, a few years later, when 

 a new and greatly enlarged edition of that work was undertaken, he 

 was enlisted as a regular contributor, and undertook to furnish the 

 principal mathematical papers. 



During the vacations of the Perth academy he paid regular visits 

 to Edinburgh, where he continued to cultivate the friendship of Ro- 

 bison, Playfair, and other scientific men, to whom his now recognised 

 talents and mathematical attainments procured him introductions. 

 The first mark of literary distinction he received was that of Cor- 

 responding Member of the Edinburgh Academy of Physics ; a so- 

 ciety which, though not known by its published transactions, was at 

 that time remarkable by reason of the cluster of talented persons of 

 whom it was composed, several of whom have since attained the 

 highest distinction in literature, philosophy, and public affairs. 

 Such association could not fail to have a powerful effect in the de- 

 velopment of his mind, even though his residence at a distance from 

 Edinburgh prevented him from attending many of the meetings. 



In 1802 he presented a second paper to the Royal Society of 

 Edinburgh, containing a new method of expressing the coefficients 

 of the development of the algebraic formula which represents the 

 disturbing effect of the mutual action of two planets on each other. 

 This was a contribution of great merit, and, immediately upon its 

 publication, established his reputation as a mathematician of the first 

 order. The volume of the Transactions in which it appeared was 

 reviewed in the second number of the Edinburgh Review ; and an 

 able analysis of Mr. Wallace's paper was concluded with the follow- 

 ing encomium : — " We cannot conclude without expressing our sin- 

 cere admiration of this excellent performance — excellent in every 

 respect ; and, trifling as it may appear to mathematicians, remark- 

 able for a pure, perspicuous, and not inelegant style. It is a paper, 

 equal, in our opinion, to whatever has been most admired of the 

 greatest analysts. We remember nothing in the works of Euler or 

 Lagrange which belongs to a higher order of excellence in the 

 science." Mr. Wallace's method of development depended ulti- 

 mately upon the proportions which the perimeters of two ellipses 

 bear to those of their circumscribing circles ; and in order to faci- 

 litate its application, he gave, in an appendix, a very beautiful and 

 quickly converging series for the rectification of the ellipse, applica- 

 ble to every case of eccentricity, and to every length of an arc that 

 can possibly occur in calculation. His merit with respect to this 

 paper cannot be considered as having been diminished by the disco- 

 very he made some time after its publication, that in certain respects 

 he had been anticipated by Legendre. The very little intercourse 

 which at that time existed between this country and France, and the 

 position of the author in a remote provincial town, are sufficient ex- 

 cuses for his not having been more accurately acquainted with the 

 state of mathematical discovery on the Continent. 



Mr. Wallace had been for several years a contributor to some of 

 the periodical publications in England in which mathematical ques- 



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