On this subject, as exhibiting the clearest results arrived at, I transcribe a passage from Mill: 'There is no word which is used more loosely, or in a greater variety of senses, than analogy. It sometimes stands for arguments which may be examples of the most rigid induction. Archbishop Whately, for instance, following Ferguson and other writers, defines analogy conformably to its primitive acceptation, that which was given to it by mathematicians, resemblance of relations. In this sense, when a country which has sent out colonies is termed the mother country, the expression is analogical, signifying that the colonies of a country stand in the same _relation_ to her in which children stand to their parents. And if any inference be drawn from this resemblance of relations, as, for instance, that the same obedience or affection is due from colonies to the mother country which is due from children to a parent, this is called reasoning by analogy. Or if it be argued that a nation is most beneficially governed by an assembly elected by the people, from the admitted fact that other associations for a common purpose, such as joint stock companies, are best managed by a committee chosen by the parties interested; this, too, is an argument from analogy in the preceding sense, because its foundation is, not that a nation is like a joint stock company, or Parliament like a board of directors, but that Parliament stands in the same _relation_ to the nation in which a board of directors stands to a joint stock company. Now, in an argument of this nature, there is no inherent inferiority of conclusiveness like other arguments from resemblance, it may amount to nothing, or it may be a perfect and conclusive induction. The circumstance in which the two cases resemble, may be capable of: being shown to be the _matereal_ circumstance; to be that on which all the consequences, necessary to be taken into account in the particular discussion, depend. In the case in question, the resemblance is one of relation; the _fundamentum relationis_ being the management, by a few persons, of affairs in which a much greater number are interested along with them. Now, some may contend that this circumstance which is common to the two cases, and the various consequences which follow from it, have the chief share in determining all those effects which make up what we term good or bad administration. If they can establish this, their argument has the force of a rigid induction: if they cannot, they are said to have failed in proving the analogy between the two cases, a mode of speech which implies that when the analogy can be proved, the argument founded upon it cannot be resisted.'* * Logic, pp. 97-8, vol. 2.