than both, could we see the internal constitution of the small parts of the bread, from whence its smell, and taste, and wholesomeness, are all derived. Thus, again, all the arguments of induction for the manner of extracting the square root in numbers vanish into the single demonstrative proof, as soon as this is produced. And the great business in all branches of knowledge is thus to reduce, unite, and simplify our evidences; so as that the one resulting proof, by being of a higher order, shall be more than equal in force to all the concurrent ones of the inferior orders.
Having now considered in what manner the doctrine of chances, and the Newtonian differential method, may serve to shew in general the value of dependent and independent or concurrent evidences, and the probability of general conclusions formed by induction and analogy; let us next inquire by what means we are to form these general conclusions, and discover their evidences. Now the different methods of doing this may be said to resemble respectively the rule of false in common arithmetic; the algebraic methods of bringing the unknown quantity into an equation, under a form capable of all the algebraic operations, addition, subtraction, &c.; the algebraic methods of finding the roots of equations of the higher orders by approximation; and the art of decyphering: all which four methods bear also a considerable resemblance to each other. I will consider them in order, and endeavour to shew how analogous methods may be introduced into the sciences in general to advantage.
First, then, As according to the rule of false, the arithmetician supposes a certain number to be that which is sought for; treats it as if it was that; and finding the deficiency or overplus in the conclusion, rectifies the error of his first position by a proportional addition or subtraction, and thus solves the problem; so it is useful in inquiries of all kinds to try all such suppositions as occur with any appearance of probability, to endeavour to deduce the real phænomena from them; and if they do not answer in some tolerable measure, to reject them at once; or if they do, to add, expunge, correct, and improve, till we have brought the hypothesis as near as we can to an agreement with nature. After this it must be left to be farther corrected and improved, or entirely disproved, by the light and evidence reflected upon it from the contiguous, and even, in some measure, from the remote branches of other sciences.
Were this method commonly used, we might soon expect a great advancement in the sciences. It would much abate that unreasonable fondness, which those who make few or no distinct hypotheses, have for such confused ones as occur accidentally to their imaginations, and recur afterwards by association. For the ideas, words, and reasonings, belonging to the favourite hypothesis, by recurring, and being much agitated in the brain, heat
