DESCRIPTION 



ES 



30 



VI 



dual 



Such relatives I term infinitesimal on account of the vanishing of their 



higher powers. Every relative has a converse, and since this converse is conceivable 

 as divisible into individual terms, the relative itself is conceivable as divisible into in- 

 finitesimal terms. To indicate this we may write 



(122.) 



If z> 



x 



*, + X "tr X. -t «*»■ 



As a term .which vanishes is not an individual, nor is it composed of individuals, so 

 it is neither an infinitesimal nor composed of infinitesimals. 



As we write 

 so we may write 

 (123.) 



IS', IS", IS'", tit 



I s , 



L s, Z j, L n/ s, etc 



i 



s 



But as the first formula is affected by the circumstance that 



that I s w does 



vanish on account of no woman having the particular kind of 



denoted by S", I s w denoting merely every lover of whatever servant th 



of any woman 



the second formula is affected 



way, bo that the 





vanishing of L t s does not make k to vanish, but this is to be interpreted as denot- 

 ing everything which is a lover, in whatever way it is a lover at all, of a servant 

 Then just as we have by (112), that 



(124.) 

 so we have 



(125.) 



Mr. De Morg 



* 



1 



i 



s 



1 



1(1 



o an denotes » and k by LS' and L,S respectively, and he has traced 



the manner°of forming the converse and negative of such functions in detail 



Tl 



following table contains most of his results in my 

 I write ut : and for that of n, u. 



For the converse of 





Jix 



6 



urn 



ui) 



(1 



m) n 



m(l 



JLQ 



W 



1 



I shall term the operation by which w is changed 



/ 



backward 



All 



the laws of this but one are the same as 



for ordinary involution, and the one exccp 



of that kind which is said to prove the 



It is that whereas with ordinary 



