CHAP. VIII.] OF REDUCTION. 129 



nearly all disappear, and we have only left 



xyz + xyz = ; (5) 



whence 



0_ 



Qxy + - xy + - xy + Qxy 



0_ 



furnishing the interpretation. Wherever the property C is found, 

 either the property A or the property B will be found with it, but 

 not both of them together. 



From the equation (5) we may readily deduce the result ar- 

 rived at in the previous investigation by the method of arbitrary 

 constant multipliers, as well as any other proposed forms of the 

 relation between x, y, and z ; e. g. If the property B is absent, 

 either A and C will be jointly present, or Cwill be absent. And 

 conversely, If A and C are jointly present, B will be absent. 

 The converse part of this conclusion is founded on the presence 

 of a term xz with unity for its coefficient in the developed value 



