Ellery Williams Davis 



Multiplication is here supposed performed from left to right, 

 multiplicands being' taken from the upper border, while multi- 

 pliers are taken from the left border. We have marked by * 

 in the table 



scs, (sc) 2 , and c=scs (sc) 2 . 



In words, the equation just written is 



supplement-of-complement-of-supplement 



of 



supplement-of-complement-of supplement-of-complement-of 



is the same as 



complement-pi. 



It will be noted that every operation occurs in every line of the 

 table and that the square of every operation except sc and cs is 

 unity, while the product of each of these by the other is unity. 

 That is to say — 



i. The product of all the operations of the group into or by 

 any one of them is again all the operations of the group. 



2. The group is composed of operations that are either self- 

 reciprocal or reciprocal in pairs. 



These are properties of all groups. 



232 



