this point, it were well to examine what proportion is; since several who make use of that word do not always seem to understand very clearly the force of the term, nor to have very distinct ideas concerning the thing itself.  Proportion is the measure of relative quantity.  Since all quantity is divisible, it is evident that every distinct part into which any quantity is divided must bear some relation to the other parts, or to the whole.  These relations give an origin to the idea of proportion.  They are discovered by mensuration, and they are the objects of mathematical inquiry.  But whether any part of any determinate quantity be a fourth, or a fifth, or a sixth, or a moiety of the whole; or whether it be of equal length with any other part, or double its length, or but one half, is a matter merely indifferent to the mind; it stands neuter in the question:  and it is from this absolute indifference and tranquillity of the mind, that mathematical speculations derive some of their most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiassed to examine the point.  All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater, from lesser, from equality and inequality.  But surely beauty is no idea belonging to mensuration; nor has it anything to do with calculation and geometry.  If it had, we might then point out some certain measures which we could demonstrate to be beautiful, either as simply considered, or as related to others; and we could call in those natural objects, for whose beauty we have no voucher but the sense, to this happy standard, and confirm the voice of our passions by the determination of our reason.  But since we have not this help, let us see whether proportion can in any sense be considered as the cause of beauty, as hath been so generally, and, by some, so confidently affirmed.  If proportion be one of the constituents of beauty, it must derive that power either from some natural properties inherent in certain measures, which operate mechanically; from the operation of custom; or from the fitness which some measures have to answer some particular ends of conveniency.  Our business therefore is to inquire, whether the parts of those objects, which are found beautiful in the vegetable or animal kingdoms, are constantly so formed according to such certain measures, as may serve to satisfy us that their beauty results from those measures, on the principle of a natural mechanical cause; or from custom; or, in fine, from their fitness for any determinate purposes.  I intend to examine this point under each of these heads in their order.  But before I proceed further, I hope it will not be thought amiss, if I lay down the rules which governed me in this inquiry, and which have misled me in it, if I have gone astray. 1.  If two bodies produce the same or a similar effect on the mind, and on examination they are found to