Tonic. Dominant. Mediant. Plate XXIII. (¹⁄₂) (¹⁄₃) (¹⁄₅) (¹⁄₄) No. VI. So far as I know, there has been only one attempt in modern times, besides my own, to establish a universal system of proportion, based on a law of nature, and applicable to art. This attempt consists of a work of 457 pages, with 166 engraved illustrations, by Dr Zeising, a professor in Leipzic, where it was published in 1854. One of the most learned and talented professors in our Edinburgh University has reviewed that work as follows:— “It has been rather cleverly said that the intellectual distinction between an Englishman and a Scotchman is this—‘Give an Englishman two facts, and he looks out for a third; give a Scotchman two facts, and he looks out for a theory.’ Neither of these tests distinguishes the German; he is as likely to seek for a third fact as for a theory, and as likely to build a theory on two facts as to look abroad for further information. But once let him have a theory in his mind, and he will ransack heaven and earth until he almost buries it under the weight of accumulated facts. This remark applies with more than common force to a treatise published last year by Dr Zeising, a professor in Leipsic, ‘On a law of proportion which rules all nature.’ The ingenious author, after proving from the writings of ancient and modern philosophers that there always existed the belief (whence derived it is difficult to say), that some law does bind into one formula all the visible works of God, proceeds to criticise the opinions of individual writers respecting that connecting law. It is not our purpose to follow him through his lengthy examination. Suffice it to say that he believes he has found the lost treasure in the _Timæus_ of Plato, c. 31. The passage is confessedly an obscure one, and will not bear a literal translation. The interpretation which Dr Zeising puts on it is certainly a little strained, but we are disposed to admit that he does it with considerable reason. Agreeably to him, the passage runs thus:—‘That bond is the most beautiful which binds the things as much as possible into one; and proportion effects this most perfectly when three things are so united that the greater bears to the middle the same ratio that the middle bears to the less.’