Some M is not P; ----------\    /---------> All M is S;
\  /
\/
/\ contrap
/  \
All M is S:       ----------/    \---------> Some p (not-P) is M: 

convert & obvert
.’.  Some S is not P. <------------------------- .’.  Some p (not-P) is S.

In Fig.  IV. the position of the middle term is, in both premises, the reverse of what it is in the First Figure; we may therefore reduce its Moods either by transposing the premises, as with Bramantip, Camenes, and Dimaris; or by converting both premises, the course pursued with Fesapo and Fresison.  It may suffice to illustrate by the case of Bramantip: 

Bramantip.  Barbara.

All P is M;      ----------\  /------>   All M is S;
\/
/\
All M is S:       ----------/  \------>   All P is M: 

convert per acc.
.’.  Some S is P.   <----------------------- .’.  All P is S.

This case shows that a final significant consonant (s, p, or sk) in the name of any Mood refers to the conclusion of the new syllogism in the First Figure; since p in Bramantip cannot refer to that Mood’s own conclusion in I.; which, being already particular, cannot be converted per accidens.

Finally, in Fig.  I., Darii and Ferio differ respectively from Barbara and Celarent only in this, that their minor premises, and consequently their conclusions, are subaltern to the corresponding propositions of the universal Moods; a difference which seems insufficient to give them rank as distinct forms of demonstration.  And as for Barbara and Celarent, they are easily reducible to one another by obverting their major premises and the new conclusions, thus: 

Barbara.  Celarent.
                         obv. 
All M is P; -----------------------> No M is p (not-P);

All S is M:     ----------------------->    All S is M: 

obv.
.’.  All S is P.    <-------------------    .’.  No S is p (not-P).

There is, then, only one fundamental syllogism.

Sec. 7.  A new version of the mnemonic lines was suggested in Mind No. 27, with the object of (1) freeing them from all meaningless letters, (2) showing by the name of each Mood the Figure to which it belongs, (3) giving names to indicate the ostensive reduction of Baroco and Bocardo.  To obtain the first two objects, l is used as the mark of Fig.  I., n of Fig II., r of Fig.  III., t of Fig.  IV.  The verses (to be scanned discreetly) are as follows: 

Balala, Celalel, Dalii, Felioque prioris: 

{Faksnoko}
Cesane, Camenes, Fesinon, { } secundae: 
{ Banoco,}

Tertia, Darapri, Drisamis, Darisi, Ferapro,

Doksamrosk}
          }, Ferisor habet:  Quarta insuper addit. 
Bocaro }

Bamatip, Cametes, Dimatis, Fesapto, Fesistot.

De Morgan praised the old verses as “more full of meaning than any others that ever were made”; and in defence of the above alteration it may be said that they now deserve that praise still more.