are gradually compelled into the right road, even from wrong suppositions fairly compared with the phænomena. This would habituate the mind to a right method, and beget the factitious sagacity above-mentioned.
The second of the four methods proposed is, that of bringing the unknown quantity to an equation, and putting it into a form susceptible of all the algebraic operations. Now to this answers, in philosophy, the art of giving names, expressing nothing definite, as to manner, quantity, &c. and then inserting these names, or indefinite terms, in all the enunciations of the phænomena, to see whether, from a comparison of these enunciations with each other, where the terms are used in the greatest latitude, some restrictions, something definite in manner, degree, or mutual relation, will not result. Things that are quite unknown have often fixed relations to one another, and sometimes relations to things known, which, though not determinable with certainty and precision, may yet be determined in some probable manner, or within certain limits. Now as in algebra it is impossible to express the relation of the unknown quantity to other quantities known or unknown, till it has a symbol assigned to it of the same kind with those that denote the others; so in philosophy we must give names to unknown quantities, qualities, causes, &c. not in order to rest in them, as the Aristotelians did, but to have a fixed expression, under which to treasure up all that can be known of the unknown cause, &c. in the imagination and memory, or in writing for future inquirers.
But then it is necessary, for the same reasons, that these terms should have no more of secondary ideas from prior associations, than the terms x and y in algebra.—Whence, if we use old terms excluding the old associations, the reader should be made aware of this at first, and incidentally reminded of it afterwards. Sir Isaac Newton has used the words æther, attraction, and some others, in this way, not resting in them, but enumerating a great variety of phænomena; from the due comparison of which with each other, and with such as farther observation and experiments shall suggest, their laws and action will, perhaps, be discovered hereafter; so that we may be able to predict the phænomena. There is also an instance of the proper manner of reasoning concerning the knowable relations of unknown things in Mr. Mede’s Clavis Apocalyptica.
The third method is that of approximating to the roots of equations. Here a first position is obtained, which, though not accurate, approaches, however, to the truth. From this, applied to the equations, a second position is deduced, which approaches nearer to the truth than the first; from the second, a third, &c. till the analyst obtains the true root, or such an approximation as is practically equivalent, every preceding discovery being made the foundation for a subsequent one, and the equation resolving itself, as it were, gradually. Now this is indeed the way, in
