222 EXAMPLE OF ANALYSIS. [CHAP. XIV. 



This, indeed, is only the fifth premiss reproduced, but it 

 shows that there is no other relation connecting the two elements 

 which it involves. 



If we seek the whole relation connecting the elements x, w, 

 and y, we find, on developing (1) with reference to those sym- 

 bols, and proceeding as before, 



xy + xwy = 0. 



Suppose it required to determine hence the consequences of the 

 hypothesis, " Motion does not exist," relatively to the questions 

 of the necessity of matter, and the necessary presence of gravita- 

 tion. We find 



xy 

 1 0_ 



or, 1 - w = xy + - x, with xy = 0. 



The direct interpretation of the first equation is, If motion does 

 not exist, either matter is a necessary being., and gravitation is not 

 necessarily present, or matter is not a necessary being. 



The reverse interpretation is, If matter is a necessary being, 

 and gravitation not necessary, motion does not exist. 



In exactly the same mode, if we sought the full relation be- 

 tween x, z, and w, we should find 



xzw + xz = 0. 

 From this we may deduce 



z = xw + - x, with xw = 0. 



Therefore, If the world is merely material, and not subject to 

 any presiding intelligence, either matter is a necessary being, and 

 motion does not exist, or matter is not a necessary being. 



Also, reversely, If matter is a necessary being, and there is no 

 such thing as motion, the world is merely material. 



3. We might, of course, extend the same method to the de- 



