and even many persons who are not great mathematicians, will tell you that they derive immense pleasure from geometrical reasonings.  Everybody knows mathematicians speak of solutions and problems as “elegant,” and they tell you that a certain mass of mystic symbols is “beautiful, quite lovely.”  Well, you do not see it.  They do see it, because the intellectual process, the process of comprehending the reasons symbolised by these figures and these signs, confers upon them a sort of pleasure, such as an artist has in visual symmetry.  Take a science of which I may speak with more confidence, and which is the most attractive of those I am concerned with.  It is what we call morphology, which consists in tracing out the unity in variety of the infinitely diversified structures of animals and plants.  I cannot give you any example of a thorough aesthetic pleasure more intensely real than a pleasure of this kind—­the pleasure which arises in one’s mind when a whole mass of different structures run into one harmony as the expression of a central law.  That is where the province of art overlays and embraces the province of intellect.  And, if I may venture to express an opinion on such a subject, the great majority of forms of art are not in the sense what I just now defined them to be—­pure art; but they derive much of their quality from simultaneous and even unconscious excitement of the intellect.

When I was a boy, I was very fond of music, and I am so now; and it so happened that I had the opportunity of hearing much good music.  Among other things, I had abundant opportunities of hearing that great old master, Sebastian Bach.  I remember perfectly well—­though I knew nothing about music then, and, I may add, know nothing whatever about it now—­the intense satisfaction and delight which I had in listening, by the hour together, to Bach’s fugues.  It is a pleasure which remains with me, I am glad to think; but, of late years, I have tried to find out the why and wherefore, and it has often occurred to me that the pleasure derived from musical compositions of this kind is essentially of the same nature as that which is derived from pursuits which are commonly regarded as purely intellectual.  I mean, that the source of pleasure is exactly the same as in most of my problems in morphology—­that you have the theme in one of the old master’s works followed out in all its endless variations, always appearing and always reminding you of unity in variety.  So in painting; what is called “truth to nature” is the intellectual element coming in, and truth to nature depends entirely upon the intellectual culture of the person to whom art is addressed.  If you are in Australia, you may get credit for being a good artist—­I mean among the natives—­if you can draw a kangaroo after a fashion.  But, among men of higher civilisation, the intellectual knowledge we possess brings its criticism into our appreciation of works of art, and we are obliged to satisfy it, as well as the mere sense of beauty in colour and in outline.  And so, the higher the culture and information of those whom art addresses, the more exact and precise must be what we call its “truth to nature.”