364 Matliematics. 



by their means greatly multiplied the cultivators of 

 this department of mathematical science. 



But this is not all; even those branches of ma- 

 thematics in which no great discoveries have been 

 made, and upon which no signal light has been 

 thrown within the last age, have yet received im- 

 provements of a less interesting and brilliant kind. 

 Former discoveries have been extended; old doc- 

 trines have been simplified and refined ; neater, 

 shorter, and more lucid ways of arriving at the 

 same results have been devised ; perspicuous, ele- 

 gant, and comprehensive theorems have taken the 

 place of those which were more prolix and obscure; 

 and many subtleties and refinements suggested by 

 the philosophers of the preceding age, but not suf- 

 ficiently developed by them, have been clearly and 

 satisfactorily unfolded. 



It is, also, worthy ofnc'cc, that in addition to 

 all the improvements wbxk have taken place in 

 mathematical science, as sucli, it has been applied 

 to many objects, during the last age, to the illus- 

 tration and accomplishment of which it had never 

 before been directed. A great number of diffi- 

 cult and most interesting problems in astronomy 

 have been resolved by the Anal}ftic Method, first 

 applied to this object by Euler. His calcula- 

 tions, by this method, of the perturbations of the 

 earth's orbit, and of the theory of the moon, may 

 be regarded as models of simplicity and beauty. 

 The same illustrious mathematician also first in- 

 troduced analysis into the doctrines of the motion 

 of fluids; and by this means threw great light on 

 the hydraulic principles and laws. Mr. ^pinus, 

 of Petersburgh, before mentioned, has made an 

 ingenious attempt to reduce the mysterious pheno- 

 mena of Electricity and Magnetism to the regula- 

 rity of algebraical calculation, M. De Lisle, of 

 France^ has endeavoured, vvith no small degree of 



