In the first of these figures, the dotted line down the middle expresses the straight lines of which it is composed; which, without the assistance of curve lines, or light and shade, would hardly shew it to have contents.
The same is true of the second, tho' by the bending of the horn, the straight dotted line is changed into the beautiful waving-line.
But in the last, this dotted line, by the twisting as well as the bending of the horn, is changed from the waving into the serpentine-line; which, as it dips out of sight behind the horn in the middle, and returns again at the smaller end, not only gives play to the imagination, and delights the eye, on that account; but informs it likewise of the quantity and variety of the contents.
I have chosen this simple example, as the easiest way of giving a plain and general idea of the peculiar qualities of these serpentine-lines, and the advantages of bringing them into compositions, where the contents you are to express, admit of grace and elegance.
And I beg the same things may be understood of these serpentine-lines, that I have said before of the waving-lines. For as among the vast variety of waving-lines that may be conceiv'd, there is but one that truly deserves the name of the line of beauty, so there is only one precise serpentine-line that I call the line of grace. Yet, even when they are made too bulging, or too tapering, though they certainly lose of their beauty and grace, they do not become so wholly void of it, as not to be of excellent service in compositions, where beauty and grace are not particularly design'd to be express'd in their greatest perfection.
Though I have distinguish'd these lines so particularly as to give them the titles of the lines of beauty and grace, I mean that the use and application of them should still be confined by the principles I have laid down for composition in general; and that they should be judiciously mixt and combined with one another, and even with those I may term plain lines, (in opposition to these) as the subject in hand requires. Thus the cornu-copia, fig. [59 B p. II], is twisted and bent after the same manner, as the last figure of the horn; but more ornamented, and with a greater number of other lines of the same twisted kind, winding round it with as quick returns as those of a screw.
This sort of form may be seen with yet more variations, (and therefore more beautiful) in the goat's horn, from which, in all probability, the ancients originally took the extremely elegant forms they have given their cornu-copias.
There is another way of considering this last figure of the horn I would recommend to my reader, in order to give him a clearer idea of the use both of the waving and serpentine-lines in composition.