Whoever has the patience to go through the remaining 48 Moods will discover that of the whole 64 only 11 are valid, namely: A.A.A., A.A.I., A.E.E., A.E.O., A.I.I., A.O.O., E.A.E., E.A.O., E.I.O., I.A.I., O.A.O. These 11 Moods have next to be examined in each Figure, and if valid in every Figure there will still be 44 moods in all. We find, however, that in the First Figure, A.E.E., A.E.O., A.O.O. involve illicit process of the major term (3rd Can.); I.A.I., O.A.O. involve undistributed Middle (4th Can.); and A.A.I., E.A.O. are subalterns. In the Second Figure all the affirmative Moods, A.A.A., A.A.I., A.I.I., I.A.I., involve undistributed Middle; O.A.O. gives illicit process of the major term; and A.E.O., E.A.O. are subalterns. In the Third Figure, A.A.A., E.A.E., involve illicit process of the minor term (3rd Can.); A.E.E., A.E.O., A.O.O., illicit process of the major term. In the Fourth Figure, A.A.A. and E.A.E. involve illicit process of the minor term; A.I.I., A.O.O., undistributed Middle; O.A.O. involves illicit process of the major term; and A.E.O. is subaltern. Those moods of each Figure which, when tried by these tests, are not rejected, are valid, namely: Fig. I.--A.A.A., E.A.E., A.I.I., E.I.O. (A.A.I., E.A.O., Subaltern); Fig. II.--E.A.E., A.E.E., E.I.O., A.O.O. (E.A.O., A.E.O., Subaltern); Fig. III.--A.A.I., I.A.I., A.I.I., E.A.O., O.A.O., E.I.O.; Fig. IV.--A.A.I., A.E.E., I.A.I., E.A.O., E.I.O. (A.E.O., Subaltern). Thus, including subaltern Moods, there are six valid in each Figure. In Fig. III. alone there is no subaltern Mood, because in that Figure there can be no universal conclusion. § 5. Special Canons of the several Figures, deduced from the Common Canons, enable us to arrive at the same result by a somewhat different course. They are not, perhaps, necessary to the Science, but afford a very useful means of enabling one to thoroughly appreciate the character of formal syllogistic reasoning. Accordingly, the proof of each rule will be indicated, and its elaboration left to the reader. There is no difficulty, if one bears in mind that Figure is determined by the position of the middle term. Fig. I., Rule (a): _The minor premise must be affirmative_. For, if not, in negative Moods there will be illicit process of the major term. Applying this rule to the eleven possible Moods given in § 4, as remaining after application of the Common Canons, it eliminates A.E.E., A.E.O., A.O.O. (b) _The major premise must be universal_. For, if not, the minor premise being affirmative, the middle term will be undistributed. This rule eliminates I.A.I., O.A.O.; leaving six Moods, including two subalterns. Fig. II. (a) _One premise must be negative._ For else neither premise will distribute the middle term. This rule eliminates A.A.A., A.A.I., A.I.I., I.A.I. (b) _The major premise must be universal._