306 PROCEEDINGS OP THE AMERICAN ACADEMY 



Read positively, the conclusion is, 



A B C-\-aB C-\-ab C-\-abc=l; 



or, more briefly, 



B C^ab— 1. 



Ordinarily, the conclusion called for is part only of the total con- 

 clusion. Thus, syllogism with the above premises asks for a conclu- 

 sion involving only A and O. An inspection of the dial-plate will 

 show us the conclusion A -< C, and also other conclusions involving 

 relations between other terms than A and C ; thus, 



c {A-\- B) -<^ 0; b-< a-\- c, etc. 



Nor is it necessary that our conclusions should be limited to relations 

 between terms given in the premises, as may be seen in the solution 

 of the following problems. 



Problem I. 



Let us suppose that there are four girls at school, Anna, Bertha, 

 Cora, and Dora, and that some one had observed that 



(1.) Whenever either Anna or Bertha (or both) remained at home, 

 Cora was at home ; and 



(2.) When Bertha was out, Anna was out ; and 



(3.) Whenever Cora was at home, Anna was at home. 



What information is here conveyed concerning Dora ? 



Indicating by the capital letters the fact of remaining at home, and 

 by the small letters that of going out, our premises are 



b -< a =b A -< 



C-< A = Ca^ 



and, impressing them upon the machine, there will result the state 

 of things indicated by Fig. 1. From this we may read off the con- 

 clusion, 



D-<AB C-\-abc. 



d -< A B 0-\- abc. 



Or, if Dora remain at home, her three sisters will be all at home or 

 all out ; and the same will be true if Dora goes out. 



