MB 



are the same as the things which are related to all women as lovers of nothin 

 but their servants. 



It is worth while to mention, in passing, a singular proposition derivable from ( 1 1! S ). 



Since, by (124) and (125) 



and since 



'?/ = (1 — z )0-y) , 



1 _ ( u -j- f) = 6-<« + == 6-«,6~f = (1 — u),(l - f) . 



(128) gives us, 



f )(i-»),(i -0 = (1 - /)0-«) -t 2,(1 - p-^-'Ml - /' '- j 



This is, of course, as true for u and / as for (1 — it) and ( 1 — /). Miking those sub- 



stitutions, and taking the negative of both sides, we have, by (1 



(131.) J(u,f) = (toW P ((l - P> -k pO>W > 



or, the lovers of French violinists are those persons who, in reference to every mode 

 of loving whatever, either in that way love some violinists or in me other wmj love 

 some Frenchmen. This logical proposition is certainly not sclf-evin nt, and its prac- 

 tical importance is considerable. In a similar way, from (12) we obtain 



(132.) ' Mf=nv(^-?)+v)i 



that is, to say that a person is both emperor and conqueror of the Nine French*.:... is 

 the same as to say that, taking any class of Frenchmen whatever, this person ,s otter 

 an emperor of some one of this class, or conqueror of some one among the remam.ng 

 Frenchmen. , . L . ., 



The properties of zero and unity, with reference to backward mvolut.on, are easily 



derived from (125). I give them here in comparison with the correspond.ng formal* 

 for forward involution. 



(133.) 



(134.) *0=0 0^ = 0, 



where q is the converse of an unlimited relative, and r is greater than zero. 



o*=l * 



0=1. 



■fx — z 



(135.) 



(136.) '*=* 



x? = x . 



y 



z 



where y is infinitesimal, and . is individual. Otherwise, both vanish 



