_The Form of Statement not invariable._--As there are different kinds of syllogism, so also there are different forms in which any kind of syllogism may be stated. These forms are not essential, pertaining to the nature of the syllogism itself, but accidental, pertaining merely to the order of announcing the several propositions. It has already been remarked, in speaking of the general structure of the syllogism, that the order of propositions is not essential. Either premiss may precede, either follow. Nay, we may state _first the conclusion_, and _then the reasons_, _or grounds_. This latter method, as Hamilton has shown in his _New Analytic of Logical forms_, is perfectly valid, though usually neglected by writers on logic. It is not only valid, but the more natural of the two methods. When asked if Socrates is mortal, it is more natural to say, He is mortal, for he is a man, and all men are mortal, than to say, All men are mortal, he is a man, and therefore, he is mortal. In fact, most of our reasoning takes the first of these forms. The two are designated by Hamilton, respectively, as the _analytic_ and _synthetic_ syllogism. _Order of Premises may vary._--As to the order of the premises, which shall precede the other, this, too, is quite unessential and accidental. The earlier method, practised by Greek, Arabian, Jewish and Latin schools, was to state first the minor premiss, precisely the reverse of our modern custom. _Order of Terms not essential._--The order of the _terms_, in the several propositions, is also accidental rather than essential. There are several possible and allowable arrangements of these terms with reference to the order of precedence and succession, giving rise to what are called _figures_ of the syllogism. These arrangements and figures have usually been reckoned as four; three only are admitted by Hamilton, the fourth being abolished. The first figure occurs when the middle term is the subject of one premiss and the predicate of the other. The second figure gives the middle term the place of predicate in both premises. The third makes it the subject of both. _A further Variation._--There is still another form of statement, in which the terms compared are not, as above, severally subject and predicate, but, in the same proposition, are both subject, or both predicate, as when we say, A and B are equal; B and C are equal; therefore, A and C are equal. This is a valid synthetic syllogism, though not recognized by logicians previously to the _New Analytic_ of Hamilton. It is termed by him the unfigured syllogism.