Roundness

“ At every step you stumble and injure yourself—rocks, rugged stones, sharp points, peaks, angles, and little corners and big corners. The world should be round—quite so, and round it is; roundness is perfection; but it should be an immeasurable sphere of eider-down, so that, if a citizen falls, he may always fall amid softness—thus! (Letting himself fall in the arm-chair, or on one of the cushioned stools at the side of the table.) ”

“ Roundness may therefore be carelessly called an abstraction from the real object “sun”; whereas the peculiar optical and muscular feelings by which the sense of roundness is constituted—probably feelings of gyration and perpetual unbroken movement—are much earlier than any solar observations; they are a self-sufficing element in experience which, by repetition in various accidental contests, has come to be recognised and named, and to be a characteristic by virtue of which more complex objects can be distinguished and defined. ”

“ A curve, a curve is that angle which determines the recognition of the center in relation to the gathering extension, a curve is that result which is disturbing the roundness that is not redder. The center the whole center is a flower and being a flaming flower does not mean that there is a shadow, it means just watering and winking and wading and rearranging, it means just that exactly. ”

“ Whereas the case is the very reverse: all that is known is grasped not conformably to its own efficacy, but rather conformably to the faculty of the knower. An example will make this clear: the roundness of a body is recognised in one way by sight, in another by touch. Sight looks upon it from a distance as a whole by a simultaneous reflection of rays; touch grasps the roundness piecemeal, by contact and attachment to the surface, and by actual movement round the periphery itself. ”

“ One may therefore say that the truth which is the square shape is not only above, but even against, the witness of our feeble sight.' It must be admitted that this observation is correct, and although it be true that the appearance of roundness comes simply from the effacement of the angles, which distance causes to disappear, it is true, notwithstanding, that the round and the square are opposites. ”

“ Again, it will be found that among amateur students there is almost universal deficiency in the power of expressing the roundness of a surface. They frequently draw with224 considerable dexterity and vigour, but never attain the slightest sense of those modulations in form which can only be expressed by gradations in shade. ”

“ And it is on this side that the balance would seem to be in the finest art. Even the finest curves are those that approach the straight line rather than the circle, that err on the side of flatnesses rather than roundnesses. ”

“ By having all lasts, diagrams, and patterns, made by the scale, and all proportions of fulness of lasts regularly graded, making the children’s much the fullest in width, owing to the greater degree of roundness of the foot, and wider in proportion, on account of rapid growth. ”

“ It was therefore good reason the most beautifull body should haue the most perfect and exquisite shape. Exact roundnesse then is not found in any body, but the Heauens; the earth is round as was showed before, but not precisely, with out all roughnes and inæquality of its surface. There are hills like warts and vallies like wrinkels in a mans body; and that both for ornament and vse. ”

“ We all know the earth is round—I demonstrated that to my own satisfaction by travelling steadily west until I reached home—and so many persons have done likewise since the days of Sir Francis Drake, the first circumnavigator, that the rotundity of the earth is everywhere accepted and understood Now if the whole earth is round, it follows naturally that any part of it is curved in proportion to its extent. ”

“ The curve is known to designers as the Curve of Force and is most valuable in all forms of enrichment. Designers even in early ages used it in some form as will be noted from the fragment of Greek sculpture in Figure 72. Its beauty rests in its variety. A circle has little interest due to its rather monotonous curvature. The eye desires variety and the curve of force administers to this need and gives a sense of satisfaction. As designers on wood, how are we to utilize this curve for purposes of outline enrichment? ”

“ We get it when we pass from a short vertical line to a long horizontal one, from a small square to a large circle, as well as when we pass between those figures whose shapes are congruous. But when the shapes are congruous our consciousness of the relation is a good deal more distinct, and it is most distinct of all when, in the exercise of our analytic attention, we notice, first, a part, and then the whole, of a single line or shape. ”

“ Why a curve is more pleasing to the eye than a straight line may be too deep a question; but none the less may one safely appeal to the universal experience that there are certain lines, certain forms, certain colors, certain sounds which give us pleasure. ”

“ They amicably laid it down, that there was a just and geometrical arrangement and proportion of the several parts of the human frame to its several destinations, offices, and functions, which could not be transgressed but within certain limits—that nature, though she sported——she sported within a certain circle;—and they could not agree about the diameter of it. ”

“ A circle may be described with any given point as a center and any given line as a radius. This involves the use of the second of the two geometric instruments, the compasses.
5. Any figure may be moved from one place to another without altering the size or shape. This is the postulate of the homogeneity of space, and asserts that space is such that we may move a figure as we please without deformation of any kind. It is the basis of all cases of superposition. ”

“ All curvature, however, is not equally agreeable; but 264 the examination of the laws which render one curve more beautiful than another, would, if carried out to any completeness, alone require a volume. ”

“ But there are other modes in which infinity may be represented, which are confused by no associations of the kind, and which would, as being in mere matter, appear trivial and mean, but for their incalculable influence on the forms of all that we feel to be beautiful. The first of these is the curvature of lines and surfaces, wherein it at first appears futile to insist upon any resemblance or § 14. The beauty of curvature.suggestion of infinity, since there is certainly in our ordinary contemplation of it, no sensation of the kind. ”

“ The different positions of the several parts of the body with regard to the eye, when put together, make a real figure, which is truly extended in the length and breadth, and which represents a figure that is extended in length, breadth, and thickness. In like manner, a projection of the sphere is a real figure, and hath length and breadth, but represents the sphere, which hath three dimensions. ”

“ The feeling of longitudinal forms is one of continued movement, forward or upward as the case may be; when the distance is very great, the feeling is of infinity, either of vista, as in an aisle, or of height, as in a tower, for even when the point at the end is clearly seen and known, we continue it in the imagination. The radial forms, on the other hand, even when the axes are very long, express completeness and security, for no matter how far we go in any one direction, we have to proceed along a line which brings us back to our starting point ”

“ Fig. 34.
Well, as curves are more beautiful than straight lines, it is necessary to a good composition that its continuities of object, mass, or colour should be, if possible, in curves, rather than straight lines or angular ones. Perhaps one of the simplest and prettiest examples of a graceful continuity of this kind is in the line traced at any moment by the corks of a net as it [Pg 370] is being drawn: nearly every person is more or less attracted by the beauty of the dotted line. ”

“ We start with a Definition which is simply ridiculous! Now for the distinction between 'right Line' and 'curve'—
Nie. Here my client's meaning is not very clear. The first Definition I can find is that of a curve. He says (p. 6) 'a point may be moved, and then it will describe a path. This path of a moving point is a curve.'
Min. Surely he does not mean that a point can never move straight? He must mean that there are two kinds of curves, 'curved curves,' and 'straight curves'—as the Irish talk of 'tay-tay' and 'coffee-tay.' But, if so, he makes 'Line' and 'curve' synonymous. ”

“ Here we have a perfect balance between variety and unity. The curvature is varied to an infinite degree, at no point is its curving at the same ratio as at any 139other point; perhaps the maximum amount of variety that can be got in a symmetrical figure, preserving, as it does, its almost perfect continuity, for it approaches the circle in the even flow of its curvature. ”

“ A perfectly straight line has obviously no variety at all, while a circle, by curving at exactly the same ratio all along, has no variation of curvature, it is of all curves the one with the least possible variety. These two lines are, therefore, two of the dullest, and are seldom used in pictures except to enhance the beauty and variety of others. And even then, subtle variations, some amount of play, is introduced to relieve their baldness. ”

“ Why, the height of a man, in nine cases out of ten, can be told from the length of his stride. It is a simple calculation enough, though there is no use my boring you with figures. I had this fellow's stride both on the clay outside and on the dust within. Then I had a way of checking my calculation. When a man writes on a wall, his instinct leads him to write about the level of his own eyes. Now that writing was just over six feet from the ground. ”

“ When a circle is made, and from its centre a number of lines are drawn to the circumference, all these lines, though ever so distant in the circumference, meet together in the point, which is in the middle. ”

“ The angle of a segment is that which is contained by the straight line and the circumference.
8. An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment.
9. And an angle is said to insist or stand on the circumference Intercepted between the straight lines which contain the angle.
10. A sector of a circle is the figure contained by two straight lines drawn from the centre, and the circumference between them. ”

“ So seen, then, all objects appear to the human eye simply as masses of colour of variable depth, texture, and outline. The outline of any object is the limit of its mass, as relieved against another mass. ”

“ So then a 'Line' must be bent, though a 'curve' need not be so? Your client has clearly one merit—great originality of style!
Nie. Here is another definition of 'curve,' which may be more to your taste, 'A curve is a one-way spread, with points as elements.' (p. 10.)
Min. Too much like a dinner à la Russe. I don't like 'spread' at all.
Nie. He illustrates his use of 'spread' by applying it to other subjects. For instance, 'a musical tone allows of variations which form a two-way spread, with different degrees of intensity and of pitch as elements.' (p. 12.) ”

“ Similarly, the distance a boy can run may be considered as depending on the time. Or, we may say that the area of a square is a function of the length of a side, and the volume of a sphere is a function of its diameter. ”

“ Just in the same way straightness mingled with curvature, that is to say, the close approximation of part of any curve to a straight line, gives to such curve all its spring, power, and nobleness: and even perfect straightness, limiting curves, or opposing them, is often pleasurable: yet, in the abstract, straightness is always ugly, and curvature always beautiful. ”

“ The width of the line may increase or diminish gradually, in which case we may have, not only accents in the line, but movements due to gradations of dimension, to convergences, or to an increase or gradual crowding together of attractions in a series of visual angles. ”

“ In such a country, you will perceive at once that it is impossible that there should be anything of what you call a "solid" kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them. ”

“ The perpendicularity of the one line, and the horizontality of the other, must not in any way be interfered with; in the sketch they should, in fact, meet and form a right angle, which should just be rounded off. ”

“ For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square. ”

“ This will lead the pupil to conclude, that objects of the same size appear the smaller the farther they are from the eye, and the larger the nearer they are to it, though the real size of the object is unchanged. ”

“ Leading lines of Villa-composition.
244. Take a flat line of beauty, a d, fig. 14, for the length of the edifice. Strike a b horizontally from a, c d from d; let fall the verticals, make c f equal m n, the maximum; and draw h f. The curve should be so far continued as that h f shall be to c d as c d to a b. Then we are sure of a beautifully proportioned form. Much variety may be introduced by using different curves; joining parabolas with cycloids, etc.; but the use of curves is always the best mode of obtaining good forms. ”

“ The results showed that lines of greater length, or figures of greater area must be put nearer the center than shorter or smaller ones—'A short line must be farther than a long one, a narrow farther than a wide, a line farther than a square; an empty interval must be larger than one filled, and so on.' And for colors, "blue, maroon and green, the dark colors, are the farthest out; white, red and orange, the bright colors, are nearest the center. This means that a dark color must be farther out than a bright one to compensate for a form on the other side. ”