With respect to the other notion instituting a comparison betwixt proportion in numbers and proportion in quantity, I urge, that number and quantity are so distinct from each other, as to afford no probability of any natural relation betwixt them. Quantity is a real quality of every substance or body: number is not a real quality, but merely a conception that arises upon viewing a plurality of things in succession. Because an arithmetical proportion is agreeable in numbers, have we any reason to conclude that it must also be agreeable in quantity? At this rate, a geometrical proportion and many others, ought also to be agreeable in both. A certain proportion may coincide in both; and among an endless variety of proportions, it would be wonderful, if there never should be a coincidence. One example is given of this coincidence, in the numbers 16, 24, and 36; but to be convinced that it is merely accidental, we need but reflect, that the same proportions are not applicable to the external figure of a house, and far less to a column.
That we are framed by nature to relish proportion as well as regularity, is indisputable: but that agreeable proportion, like concord in sounds, is confined to certain precise measures, is not warranted by experience: on the contrary, we learn from experience, that various proportions are equally agreeable, that proportion is never tied down to precise measures but admits more and less, and that we are not sensible of disproportion till the difference betwixt the quantities compared become the most striking circumstance. Columns evidently admit different proportions, equally agreeable. The case is the same in houses, rooms, and other parts of a building. And this opens an interesting reflection. The foregoing difference betwixt concord and proportion, is an additional instance of that admirable harmony which subsists among the several branches of the human frame. The ear is an accurate judge of sounds and of their smallest differences; and that concord in sounds should be regulated by accurate measures, is perfectly well suited to this accuracy of perception. The eye is more uncertain about the size of a large object, than of one that is small; and in different situations the same object appears of different sizes. Delicacy of feeling therefore with respect to proportion in quantities, would be an useless quality. It is much better ordered, that there should be such a latitude with respect to agreeable proportions, as to correspond to the uncertainty of the eye with respect to quantity.