(1) All Devonshire men are Englishmen. All Bideford men are Devonshire men. .'. All Bideford men are Englishmen. (2) All Englishmen are Teutons. All Bideford men are Englishmen. .'. All Bideford men are Teutons. (3) All Teutons are Aryans. All Bideford men are Teutons. .'. All Bideford men are Aryans. _Regressive Sorites._ All Teutons are Aryans. All Englishmen are Teutons. All Devonshiremen are Englishmen. All Bideford men are Devonshiremen. .'. All Bideford men are Aryans. (1) All Teutons are Aryans. All Englishmen are Teutons. .'. All Englishmen are Aryans. (2) All Englishmen are Aryans. All Devonshiremen are Englishmen. .'. All Devonshiremen are Aryans. (3) All Devonshiremen are Aryans. All Bideford men are Devonshiremen. .'. All Bideford men are Aryans. § 816. When expanded, the sorites is found to contain as many syllogisms as there are propositions intermediate between the first and the last. This is evident also on inspection by counting the number of middle terms. § 817. In expanding the progressive form we have to commence with the second proposition of the sorites as the major premiss of the first syllogism. In the progressive form the subject of the conclusion is the same in all the syllogisms; in the regressive form the predicate is the same. In both the same series of means, or middle terms, is employed, the difference lying in the extremes that are compared with one another through them. [Illustration] § 818. It is apparent from the figure that in the progressive form we work from within outwards, in the regressive form from without inwards. In the former we first employ the term 'Devonshiremen' as a mean to connect 'Bideford men' with 'Englishmen'; next we employ 'Englishmen' as a mean to connect the same subject 'Bideford men' with the wider term 'Teutons'; and, lastly, we employ 'Teutons' as a mean to connect the original subject 'Bideford men' with the ultimate predicate 'Ayrans.' § 819. Reversely, in the regressive form we first use 'Teutons' as a mean whereby to bring 'Englishmen' under 'Aryans'; next we use 'Englishmen' as a mean whereby to bring 'Devonshiremen' under the dame predicate 'Aryans'; and, lastly, we use 'Devonshiremen' as a mean whereby to bring the ultimate subject 'Bideford men' under the original predicate 'Aryans.' § 820. A sorites may be either Regular or Irregular. § 821. In the regular form the terms which connect each proposition in the series with its predecessor, that is to say, the middle terms, maintain a fixed relative position; so that, if the middle term be subject in one, it will always be predicate in the other, and vice versâ. In the irregular form this symmetrical arrangement is violated. § 822. The syllogisms which compose a regular sorites, whether progressive or regressive, will always be in the first figure.