Rules and canons of proportion designed to reduce to a mathematical formula the things that move us in beautiful objects, have not been a great success; the beautiful will always defy such clumsy analysis. But however true it is that beauty of proportion must ever be the result of the finer senses of the artist, it is possible that canons of proportion, such as those of the human body, may be of service to the artist by offering some standard from which he can depart at the dictates of his artistic instinct. There appears to be no doubt that the ancient sculptors used some such system. And many of the renaissance painters were interested in the subject, Leonardo da Vinci having much to say about it in his book.

Like all scientific knowledge in art, it fails to trap the elusive something that is the vital essence of the whole matter, but such scientific knowledge does help to bring one's work up to a high point of mechanical perfection, from which one's artistic instinct can soar with a better chance of success than if no scientific scaffolding had been used in the initial building up. Yet, however perfect your system, don't forget that the life, the "dither," will still have to be accounted for, and no science will help you here.

The idea that certain mathematical proportions or relationships underlie the phenomena we call beauty is very ancient, and too abstruse to trouble us here. But undoubtedly proportion, the quantitative relation of the parts to each other and to the whole, forms a very important part in the impression works of art and objects give us, and should be a subject of the greatest consideration in planning your work. The mathematical relationship of these quantities is a subject that has always fascinated scholars, who have measured the antique statues accurately and painstakingly to find the secret of their charm. Science, by showing that different sounds and different colours are produced by waves of different lengths, and that therefore different colours and sounds can be expressed in terms of numbers, has certainly opened the door to a new consideration of this subject of beauty in relation to mathematics. And the result of such an inquiry, if it is being or has been carried on, will be of much interest.

But there is something chilling to the artist in an array of dead figures, for he has a consciousness that the life of the whole matter will never be captured by such mechanical means.

The question we are interested to ask here is: are there particular sentiments connected with the different relations of quantities, their proportions, as we found there were in connection with different arrangements of lines and masses? Have abstract proportions any significance in art, as we found abstract line and mass arrangements had? It is a difficult thing to be definite about, and I can only give my own feeling on the matter; but I think in some degree they have.

Proportion can be considered from our two points of view of unity and variety. In so far as the proportions of any picture or object resolve themselves into a simple, easily grasped unity of relationship, a sense of repose and sublimity is produced. In so far as the variety of proportion in the different parts is assertive and prevents the eye grasping the arrangement as a simple whole, a sense of the lively restlessness of life and activity is produced. In other words, as we found in line arrangements, unity makes for sublimity, while variety makes for the expression of life. Of course the scale of the object will have something to do with this. That is to say, the most sublimely proportioned dog-kennel could never give us the impression of sublimity produced by a great temple. In pictures the scale of the work is not of so great importance, a painting or drawing having the power of giving the impression of great size on a small scale.