This is really a syllogism of the mood Darapti in the third figure, except that we obtain a conclusion of a more exact character than the old syllogism gives. From the premises “Potassium is a metal” and “Potassium floats on water,” Aristotle would have inferred that “Some metals float on water.” But if inquiry were made what the “some metals” are, the answer would certainly be “Metal which is potassium.” Hence Aristotle’s conclusion simply leaves out some of the information afforded in the premises. It even leaves us open to interpret the *some metals* in a wider sense than we are warranted in doing. From these distinct defects of the old syllogism the process of substitution is free, and the new process only incurs the possible objection of being tediously minute and accurate. *Miscellaneous Forms of Deductive Inference.* The more common forms of deductive reasoning having been exhibited and demonstrated on the principle of substitution, there still remain many, in fact an indefinite number, which may be explained with nearly equal ease. Such as involve the use of disjunctive propositions will be described in a later chapter, and several of the syllogistic moods which include negative terms will be more conveniently treated after we have introduced the symbolic use of the second and third laws of thought. We sometimes meet with a chain of propositions which allow of repeated substitution, and form an argument called in the old logic a Sorites. Take, for instance, the premises Iron is a metal, (1) Metals are good conductors of electricity, (2) Good conductors of electricity are useful for telegraphic purposes. (3) It obviously follows that Iron is useful for telegraphic purposes. (4) Now if we take our letters thus, A = Iron, B = metal, C = good conductor of electricity, D = useful for telegraphic purposes, the premises will assume the forms A = AB, (1) B = BC, (2) C = CD. (3) For B in (1) we can substitute its equivalent in (2) obtaining, as before, A = ABC. Substituting for C in this intermediate result its equivalent as given in (3), we obtain the complete conclusion A = ABCD. (4) The full interpretation is that *Iron is iron, metal, good conductor of electricity, useful for telegraphic purposes*, which is abridged in common language by the ellipsis of the circumstances which are not of immediate importance. Instead of all the propositions being exactly of the same kind as in the last example, we may have a series of premises of various character; for instance, Common salt is sodium chloride, (1) Sodium chloride crystallizes in a cubical form, (2) What crystallizes in a cubical form does not possess the power of double refraction; (3) it will follow that