266 On Definitions. 



a , b K COS. (nt-\-e) 

 hence we have by (6) u= - sin. nt— - cos. nt 7— — 



K^sin. {nt-\-e) . . .,. t, rr • 



g- > [e), in a similar way if P=Ksin. (ni + e) we shall 



a h Ksin. (nf + e) Kfcos. (n^ + e) 

 get «= -sin. n^- - cos. nt - ^, + ^^ , (/); 



since the third terms of m in {«}) and (/), when developed are of the 

 same forms as the first two, they may be comprehended in those 

 terms by changing a and h accordingly ; see Mec. Cel., Vol. 1, p. 241 . 



Note. — When in the course of this article, it is said that quantities of the order 

 of the squares, &c. of the disturbing masses m', in", &c. are rejected ; the meaning 

 is, that quantities which depend on tlie squares, products, &c. of the masses are 

 rejected. 



Art. V. — On Definitions ; by Rev. D. Wilkie, of Quebec. 



No. II. 



Having proceeded thus far to trace analytically, to the best of my 

 ability, the natural process of the mind, in settling the terms neces- 

 sarily required for carrying on social intercourse, I shall next pro- 

 ceed, as well as I can, to illustrate synthetically, the use that is made 

 of definitions, by the greatest improvers of human knowledge, in lay- 

 ing the foundations of the various sciences of which they treat. The 

 fiction of the two persons meeting in ignorance of each other's lan- 

 guage, may now be laid aside. We proceed to consider the general 

 practice of philosophical inquirers. 



The use, then, of a definition, is to give such a verbal description 

 of the object or objects, implied in any term, as shall enable us to 

 distinguish it from every other term, so that there can no longer ex- 

 ist any doubt, or ambiguity, or uncertainty, as to its meaning. The 

 definition further enables us to ascertain and enumerate all the indi- 

 vidual objects which this class comprehends ; and, further, to trace 

 the various and sometimes very numerous consequences, to which 

 the property thus ascribed to ihe object may lead. The definition, 

 as I observed, is effected by a verbal description, and not by the in- 

 spection of the object, as in the former case, nor by reasoning from 

 causes to effects, or from effects to cause, as in another case already 

 alluded to. - 



