ATIVES. 8 V. 1 



Substituting these values in our equations marked A ) we get. b\ a little 1 luci n. 



W 



log([l> ]-[/ ] I 

 log[p]-log[/j- 



log([p] - [/]) 



The same solution would be reached through quite a dillerent road by applying the 

 calculus of finite differences in the usual way. 



\ 



Elementary lu hitives. 



By an elementary relative I mean one which signifies a relation which exists onl 

 between mutually exclusive pairs (or in the case of a oonjugative term, triplet-, or quar- 

 tettes, etc.) of individuals, or else between pairs of classes in such aw v thai • w\\ 

 individual of one class of the pair is in that relation to every individual of the other. 

 If we suppose that in every school, every teacher teaches every pupil 'a imposition 

 which I shall tacitly make whenever in this paper I speak of a school), then ]>vj>'<l 



elementary 



That every relative may he conceived of as a logical sum of 



elementary relatives is plain, from the fact that if a relation is sufficient lv determined 

 it can exist only between two individuals. Thus, a falln -r is either father in the first 

 ten years of the Christian era, or father in the -econd ten ; ars, in the third tea 

 years, in the first ten years, B. C, in the second ten years, or the third ten years, etc 

 Any one of these species of father is father for the first time or father for the s< ood 

 time, etc. Now such a relative a^ "father for the third time in the second decade of 

 our era, of—" signifies a relation which can exist only between mutually exclusive 

 pairs of individuals, and is therefore an elementary relative ; and so the relative foil 

 may be resolved into a logical sum of elementary relatives. 



The conception of a relative as resolvable into elementary relatives ha- the same 

 sort of utility as the conception of a relative as resolvable into infinitesimals or of any 



term as resolvable into individuals. 



Elementary simple relatives are connected together in systems of four. For if 

 A:B be taken to denote the elementary relative which multiplied into 15 gives A, 

 then this relation existing as elementary, we have the four elementary relatives 



A:A A:B B:A B:B . 



a 1*1. 4. ™ \ a nr»llp»<nip • teacher: pupil: schoolmate. In the same 



An example of such a system is — colleague .teacuci . F j 



way, obviously, elementary 



(V 



systems the number of 





