68 THE PRINCIPLES OF SCIENCE. 



our formulae to express either of the syllogisms Darii or 

 Ferio. Consider the example 



Some metals are of less density than water (i) 

 All bodies of less density than water will float 



upon its surface (2) 



Some metals will float upon its surface. (3) 



Let A = some metals 



B = body of less density than water 

 C = floating on the surface of water ; 

 then the propositions are evidently as before, 



A = AB (i) 



B = BC; (2) 



hence A = ABC. (3) 



Thus the syllogism Darii does not really differ from Bar- 

 bara. If the reader prefer it, we can readily employ a 

 distinct symbol for the indefinite sign of quantity. 

 Let P = some 



Q = metal, 



B and C having the same meanings as before. Then the 

 premises become 



PQ = PQB (i) 



B = BC ; (2) 



hence, by substitution, as before, 



PQ = PQBC. (3) 



Except that the formulae look a little more complicated 

 there is no difference whatever. 



The mood Ferio is of exactly the same character as 

 Darii or Barbara, except that it involves the use of a 

 negative term. Take the example 



Bodies which are equally elastic in all directions do 



not doubly refract light, 

 Some crystals are bodies equally elastic in all direc- 

 tions; therefore some crystals do not doubly 

 refract light. 

 Assigning the letters as follows 



