54 THE PRINCIPLES OF SCIENCE. [chap. 



a term we substitute its definition, or vice versd. The very 

 purpose of a detiuition is to allow a single noun to be 

 employed in place of a long descriptive phrase. Thus, 

 when we say " A circle is a curve of the second degree," we 

 may substitute a definition of the circle, getting " A curve, 

 all points of which are at equal distances from one point, is 

 a curve of the second degree." The real forms of the pro- 

 positions here given are exactly those shown in the sym- 

 bolic statement, but in this and many other cases it will be 

 sufficient to state them in ordinary elliptical language for 

 sake of brevity. In scientific treatises a term and its 

 definition are often both given in the same sentence, as in 

 " The weight of a body in any given locality, or the force 

 with which the earth attracts it, is proportional to its 

 mass." The conjunction or in this statement gives the 

 force of equivalence to the parenthetic phrase, so that the 

 propositions really are 



Weight of a body = force with which the earth 

 attracts it. 



Weight of a body = weight, &c. proportional to its 

 mass. 

 A slightly different case of inference consists in substitut- 

 ing in a proposition of the form A = AB, a definition of the 

 term B. Thus from A = AB and B = C we get A = AC. 

 For instance, we may say that " Metals are elements" and 

 " Elements are incapable of decomposition." 



Metal = metal element. 



Element = what is incapable of decomposition. 

 Hence 



Metal = metal incapable of decomposition. 

 It is almost needless to point out that the form of these 

 arguments does not suffer any real modification if some 

 of the terms happen to be negative ; indeed in the last 

 example " incapable of decomposition " may be treated as 

 a negative term. Takintc 



A = metal C = capable of decomposition 



B = element c = incapable of decomposition ; 

 the propositions are of the forms 



A = AB 

 V> = c 

 whence, by substitution, 



A = Ac. 



