Sodium is a metal (1) Metals conduct electricity, (2) we may conclude that Sodium conducts electricity. (3) Taking A, B, C to represent the three terms respectively, the premises are of the forms A = AB (1) B = BC. (2) Now for B in (1) we can substitute its expression as given in (2), obtaining A = ABC, (3) or, in words, from Sodium = sodium metal, (1) Metal = metal conducting electricity, (2) we infer Sodium = sodium metal conducting electricity, (3) which, in the elliptical language of common life, becomes “Sodium conducts electricity.” The above is a syllogism in the mood called Barbara[60] in the truly barbarous language of ancient logicians; and the first figure of the syllogism contained Barbara and three other moods which were esteemed distinct forms of argument. But it is worthy of notice that, without any real change in our form of inference, we readily include these three other moods under Barbara. The negative mood Celarent will be represented by the example [60] An explanation of this and other technical terms of the old logic will be found in my *Elementary Lessons in Logic*, Sixth Edition, 1876; Macmillan. Neptune is a planet, (1) No planet has retrograde motion; (2) Hence Neptune has not retrograde motion. (3) If we put A for Neptune, B for planet, and C for “having retrograde motion,” then by the corresponding negative term c, we denote “not having retrograde motion.” The premises now fall into the forms A = AB (1) B = B*c*, (2) and by substitution for B, exactly as before, we obtain A = AB*c*. (3) What is called in the old logic a particular conclusion may be deduced without any real variation in the symbols. Particular quantity is indicated, as before mentioned (p. 41), by joining to the term an indefinite adjective of quantity, such as *some*, *a part of*, *certain*, &c., meaning that an unknown part of the term enters into the proposition as subject. Considerable doubt and ambiguity arise out of the question whether the part may not in some cases be the whole, and in the syllogism at least it must be understood in this sense.[61] Now, if we take a letter to represent this indefinite part, we need make no change in our formulæ to express the syllogisms Darii and Ferio. Consider the example-- [61] *Elementary Lessons in Logic*, pp. 67, 79. Some metals are of less density than water, (1) All bodies of less density than water will float upon the surface of water; hence (2) Some metals will float upon the surface of water. (3) Let A = some metals, B = body of less density than water, C = floating on the surface of water then the propositions are evidently as before,