Part Ii. P. 246.

Faraday was able to frame some notion of matter in a fourth condition, which should be to gas what gas is to liquid. Such substance, he thought, would not fall far short of *radiant matter*, by which apparently he meant the supposed caloric or matter assumed to constitute heat, according to the corpuscular theory. Even if we could frame the notion, matter in such a state cannot be known to exist, and recent discoveries concerning the continuity of the solid, liquid, and gaseous states remove the basis of the speculation.

*Life of Faraday*, vol. i. p. 216.

From these and many other instances which might be adduced, we learn that analogical reasoning leads us to the conception of many things which, so far as we can ascertain, do not exist. In this way great perplexities have arisen in the use of language and mathematical symbols. All language depends upon analogy; for we join and arrange words so that they may represent the corresponding junctions or arrangements of things and their equalities. But in the use of language we are obviously capable of forming many combinations of words to which no corresponding meaning apparently exists. The same difficulty arises in the use of mathematical signs, and mathematicians have needlessly puzzled themselves about the square root of a negative quantity, which is, in many applications of algebraic calculation, simply a sign without any analogous meaning, there being a failure of analogy.