Probably the simplest of all forms of inference is that which has been called *Immediate Inference*, because it can be performed upon a single proposition. It consists in joining an adjective, or other qualifying clause of the same nature, to both sides of an identity, and asserting the equivalence of the terms thus produced. For instance, since Conductors of electricity = Non-electrics, it follows that Liquid conductors of electricity = Liquid non-electrics. If we suppose that Plants = Bodies decomposing carbonic acid, it follows that Microscopic plants = Microscopic bodies decomposing carbonic acid. In general terms, from the identity A = B we can infer the identity AC = BC. This is but a case of plain substitution; for by the first Law of Thought it must be admitted that AC = AC, and if, in the second side of this identity, we substitute for A its equivalent B, we obtain AC = BC. In like manner from the partial identity A = AB we may obtain AC = ABC by an exactly similar act of substitution; and in every other case the rule will be found capable of verification by the principle of inference. The process when performed as here described will be quite free from the liability to error which I have shown[55] to exist in “Immediate Inference by added Determinants,” as described by Dr. Thomson.[56] [55] *Elementary Lessons in Logic*, p. 86. [56] *Outline of the Laws of Thought*, § 87. *Inference with Two Simple Identities.* One of the most common forms of inference, and one to which I shall especially direct attention, is practised with two simple identities. From the two statements that “London is the capital of England” and “London is the most populous city in the world,” we instantaneously draw the conclusion that “The capital of England is the most populous city in the world.” Similarly, from the identities Hydrogen = Substance of least density, Hydrogen = Substance of least atomic weight, we infer Substance of least density = Substance of least atomic weight. The general form of the argument is exhibited in the symbols B = A (1) B = C (2) hence A = C. (3)