We do not yet quite understand the process of reasoning by which the Greeks arrived at the laws which guided their practice in this respect; but they evidently attached the utmost importance to it, and when the ratio was determined upon, they set it out with such accuracy, that even now the calculated and the measured dimensions seldom vary beyond such minute fractions as can only be expressed in hundredths of an inch. Though the existence of such a system of ratios has long been suspected, it is only recently that any measurements of Greek temples have been made with sufficient accuracy to enable the matter to be properly investigated and their existence proved.[139] The ratios are in some instances so recondite, and the correlation of the parts at first sight so apparently remote, that many would be inclined to believe they were more fanciful than real.[140] It would, however, be as reasonable in a person with no ear, or no musical education, to object to the enjoyment of a complicated concerted piece of music experienced by those differently situated, or to declare that the pain musicians feel from a false note was mere affectation. The eyes of the Greeks were as perfectly educated as our ears. They could appreciate harmonies which are lost in us, and were offended at false quantities which our duller senses fail to perceive. But in spite of ourselves, we do feel the beauty of these harmonic relations, though we hardly know why; and if educated to them, we might acquire what might almost be considered a new sense. But be this as it may, there can be no doubt but that a great deal of the beauty which all feel in contemplating the architectural productions of the Greeks, arises from causes such as these, which we are only now beginning to appreciate. [Illustration: 139. The Parthenon. Scale 50 ft. to 1 in.] To understand, however, the Doric order, we must not regard it as a merely masonic form. Sculpture was always used, or intended to be used, with it. The Metopes between the triglyphs, the pediments of the porticoes, and the acroteria or pedestals on the roof, are all unmeaning and useless unless filled or surmounted with sculptured figures. Sculpture is, indeed, as essential a part of this order as the acanthus-leaves and ornaments of the cornice are to the capitals and entablature of the Corinthian order; and without it, or without its place being supplied by painting, we are merely looking at the dead skeleton, the mere framework of the order, without the flesh and blood that gave it life and purpose. It is when all these parts are combined together, as in the portico of the Parthenon (Woodcut No. 139), that we can understand this order in all its perfection; for though each part was beautiful in itself, their full value can be appreciated only as parts of a great whole.