[Illustration: XXI. Diagram of a variation on the Form of the Portland Vase. _D. R. Hay delᵗ._ _G. Aikman sc._] [Illustration: XXII. Diagram of a second variation on the Form of the Portland Vase. _D. R. Hay delᵗ._ _G. Aikman sc._] [Illustration: XXIII. Diagram of a third variation on the Form of the Portland Vase. _D. R. Hay delᵗ._ _G. Aikman sc._] INTRODUCTION. Twelve years ago, one of our most eminent philosophers,[1] through the medium of the _Edinburgh Review_,[2] gave the following account of what was then the state of the fine arts as connected with science:—“The disposition to introduce into the intellectual community the principles of free intercourse, is by no means general; but we are confident that Art will not sufficiently develop her powers, nor Science attain her most commanding position, till the practical knowledge of the one is taken in return for the sound deductions of the other.... It is in the fine arts, principally, and in the speculations with which they are associated, that the controlling power of scientific truth has not exercised its legitimate influence. In discussing the principles of painting, sculpture, architecture, and landscape gardening, philosophers have renounced science as a guide, and even as an auxiliary; and a school has arisen whose speculations will brook no restraint, and whose decisions stand in opposition to the strongest convictions of our senses. That the external world, in its gay colours and lovely forms, is exhibited to the mind only as a tinted mass, neither within nor without the eye, neither touching it nor distant from it—an ubiquitous chaos, which experience only can analyse and transform into the realities which compose it; that the beautiful and sublime in nature and in art derive their power over the mind from association alone, are among the philosophical doctrines of the present day, which, if it be safe, it is scarcely prudent to question. Nor are these opinions the emanations of poetical or ill-trained minds, which ingenuity has elaborated, and which fashion sustains. They are conclusions at which most of our distinguished philosophers have arrived. They have been given to the world with all the authority of demonstrated truth; and in proportion to the hold which they have taken of the public mind, have they operated as a check upon the progress of knowledge.”