tives. 333 



The application of involution to conjugative terms presents little difficulty after 

 the explanations which have been given under the head of multiplication. It is ob- 

 vious that betrayer to every enemy should be written 



tf, 



just as lover of every woman 



/> 



jj ut £ _ £ n an d therefore, in counting forward as the subjacent numbers direct, 

 we should count the exponents, as well as the factor of the letter to which the 

 subjacent numbers are attached. Then we shall have, in the case of a relative of 

 two correlates, six different ways of affixing the correlat- to it, tin. 



km betrayer of a man to an enemy of him; 



a) m betrayer of every man to some enemy of him ; 



iia m betrayer of each man to an enemy of every man; 



£a m betrayer of a man to all enemies of all men ; 



k a m betrayer of a man to every enemy of him ; 



k am betrayer of every man to every enemy of him. 



If both correlates are absolute terms, the cases are 



&mW betrayer of a woman to a man; 



(&m) w betrayer of each woman to some man; 



&m w betrayer of all women to a man; 



lt m " betrayer of a woman to every man ; 



k m w betrayer of a woman to all men; 



£mw betrayer of every woman to every man. 

 These interpretations are by no means obvious, but I shall show thai they *• correct 



further 



It will be perceived that the rule still holds here 



that 



m s— iiQ 



that is to say, that those individuals each of which stand to every man in there,. 

 tion of betrayer to every enemy of his are identical wtft those md.v.duals each of 

 which is a betrayer to every enemy of a man of that mar 



of other 



If the proportion of lovers of .**-. "JJ^i Z whole universe have 



the average number of lovers which angle individuals 



then 



p.] = pw,] p*"J P**J etc - = M W • 



Thus arithmetical involution appears as a special case of logical involution 



VOL. IX. 



46 



