RELATIVES. 



8: 



appears to denote the giver of a horse to an owner of a horse. But let the individual 

 horses be H, H', H", etc. Then 



h 



II-fe-H'-fcir' + ete. 



goh 



5 o(H -^ H' -fc- II" -fc etc.) = 5 .oH -fc 5 oII' ,- 5 oII" -fc et, 



Now this last member must be interpreted as a giver of a horse to the owner of that 

 horse, and this, therefore, must be the interpretation of 5 oh. This is alw.iyi vci 

 important. A term multiplied by two relatives shows that the me HDIViduai is in 

 the two relations. If we attempt to express the giver of a horse to a lover of a 

 woman, and for that purpose write 



5^wh, 



2 written giver of a woman to a lover of her, and if we add brackets, thin 



hav 



g.(lm)h, 



abandon the associative principle of multiplication 



A 



reflect 



that the associative principle must in some form or other be 



1 will hov 

 ed at this 



point 



But while 



principle is sometimes falsified, it oftener 



must be adopted which will show of itself 



We ah tdy 



we cannot express multiplication by writing the multiplicand directly 

 tiplier; let us then affix subjacent numbers after 



after 



lates are to be found. The first number 



denote how many factors must b< 



counted from left 

 must be counted 



•ht to reach the first correlate, the second how many more 



each the second, and 



Then, the giver of 



to 



lover of a woman may be written 



£ 12 / lW h =5iifehw =52-ih/iW. 



Of course a negative number indicates that the former correlate foil 

 by the corresponding positive number. A subjacent zero makes the 



term it> If the 



correlate. Thus, 



I 







denotes the lover of that lover or the lover of hto.-clf, just » 9 «>' *•«*» *•* *• 



horse is given to the owner of itself, for to make a term doubly a correlate -, by 

 the distributive principle, to make each individual doubly a correlate, so that 



l = U -t Li 4r K -fc etc. 



