_h_ is a line about four feet long, a branch of spruce fir. I have taken this tree because it is commonly supposed to be stiff and ungraceful; its outer sprays are, however, more noble in their sweep than almost any that I know: but this fragment is seen at great disadvantage, because placed upside down, in order that the reader may compare its curvatures with _c d_, _e g_, and _i k_, which are all mountain lines; _e g_, about five hundred feet of the southern edge of the Matterhorn; _i k_, the entire slope of the Aiguille Bouchard, from its summit into the valley of Chamouni, a line some three miles long; _l m_ is the line of the side of a willow leaf traced by laying the leaf on the paper; _n o_, one of the innumerable groups of curves at the lip of a paper Nautilus; _p_, a spiral, traced on the paper round a Serpula; _q r_, the leaf of the Alisma Plantago with its interior ribs, real size; _s t_, the side of a bay-leaf; _u w_, of a salvia leaf; and it is to be carefully noted that these last curves, being never intended by nature to be seen singly, are more heavy and less agreeable than any of the others which would be seen as independent lines. But all agree in their character of changeful curvature, the mountain and glacier lines only excelling the rest in delicacy and richness of transition. § XX. Why lines of this kind are beautiful, I endeavored to show in the "Modern Painters;" but one point, there omitted, may be mentioned here,--that almost all these lines are expressive of action of _force_ of some kind, while the circle is a line of limitation or support. In leafage they mark the forces of its growth and expansion, but some among the most beautiful of them are described by bodies variously in motion, or subjected to force; as by projectiles in the air, by the particles of water in a gentle current, by planets in motion in an orbit, by their satellites, if the actual path of the satellite in space be considered instead of its relation to the planet; by boats, or birds, turning in the water or air, by clouds in various action upon the wind, by sails in the curvatures they assume under its force, and by thousands of other objects moving or bearing force. In the Alisma leaf, _q r_, the lines through its body, which are of peculiar beauty, mark the different expansions of its fibres, and are, I think, exactly the same as those which would be traced by the currents of a river entering a lake of the shape of the leaf, at the end where the stalk is, and passing out at its point. Circular curves, on the contrary, are always, I think, curves of limitation or support; that is to say, curves of perfect rest. The cylindrical curve round the stem of a plant binds its fibres together; while the _ascent_ of the stem is in lines of various curvature: so the curve of the horizon and of the apparent heaven, of the rainbow, etc.: and though the reader might imagine that the circular orbit of any