Gradient

“ If we regard the potential gradient near the ground as representing a negative charge on the earth, then if the source of supply of that charge is unaffected the gradient will rise and become high when the operations by which discharge is promoted slacken their activity. ”

“ The gradient is calculated using the tangent of the angle concerned, although in practice it makes little difference whether the sine or the tangent is used. The gradient on new signs must be expressed as a percentage; old signs showing a ratio may remain in place until life-expired.
DESCENT
May be used with diagram 511, 525, 526, 527, 570, 572, 573 or 817.2. The numerals may be varied (see Appendix C)
May be used with diagram 511, 525, 526, 527, 570, 572 or 573. ”

“ Our road was a road of steep gradients, leading us through gorges of a grandeur which would have been called appalling when the world was a little younger, and more in awe of savage Nature. If a midge could be provided with a proportionately tiny motor car, and sent coasting at full tilt down a greased corkscrew, from the handle to the sharp end of the screw, the effect would have been somewhat that of our Mercédès leaping down the steep defiles. ”

“ 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. ”

“ In drawing these curves great exactitude is required to properly find their centres; nothing looks worse in a drawing than an unfair or uneven junction between curves and straight lines. To find the location for these centres, set the compasses to the required radius for the curve, and from the point or corner A draw the arcs b and c, from c mark the arc e, and from b the arc d, and where d and e cross is the centre for the curve f. ”

“ 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? ”

“ The increment of length divided by the increment of time gives the absolute rate of growth at any part of the curve. As long as the growth is uniform, so long the slope of the curve remains constant. If a stimulating agency enhances the rate of growth, there is an immediate upward flexure in the curve; a depressing agent, on the other hand, lessens the slope of the curve.
I shall now give a few typical examples of the employment of the Crescograph for in­ves­ti­ga­tions on growth: the first example I shall take is the demonstration of the influence of variation of temperature. ”

“ 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. ”

“ Draw a Scheme of Variates on the blackboard, and show that it consists of two parts; the median which represents a constant, and the curve which represents the variations from it. Draw a horizontal line from limit to limit, through the top of the Median to serve as Axis to the Curve. Divide the Axis centesimally, and wipe out everything except Curve, Axis, and Limits. This forms a Scheme of Distribution of Deviates. Draw ordinates from the axis to the curve at the 25th and 75th divisions. ”

“ It becomes necessary therefore to study the phenomenon of growth in successive small portions; to study, that is to say, the successive lengths, or the successive small differences, or increments, of length (or of weight, etc.) , attained in successive short increments of time. This we do in the first instance in the usual way, by the “graphic method” of plotting length against time, and so constructing our “curve of growth.” Our curve of growth, whether of weight or length (Fig. 3) , has always a certain char­ac­ter­is­tic form, or char­ac­ter­is­tic curvature. ”

“ The factors which lend themselves most readily to this method of representation are the variable ones, water-content, humidity, light, temperature, and wind, and corresponding curves are distinguished. Altitude and slope may likewise be shown by means of curves, but the use of cross section or contour lines serves the same purpose and is more natural. With regard to time and position, curves are distinguished as level, station, and point curves. A level curve is one based upon readings made at the same level through a series of stations or of habitats, e. ”

“ When all the observations are arranged in this way the outer contour of the figure may be so compacted that the projecting corners of the separate squares are transformed into a symmetrical curve. If now the separate measures are of such a sort that their central value may be considered as a constant as conceived by physical science, the form of the resulting curve is of the kind marked a and b in Fig. 1. If the middle value is a statistical constant, the curve may have any sort of a form. ”

“ In sketching hills endeavour to project as many horizontal curves as possible, which should be lightly put in, and then the shading lines may be drawn over them. The degree of slope should be frequently written down in numbers upon the sketch. The names of localities, streams, hills, farms, &c., should also be entered.
Thus far we have supposed a measured line upon the ground, to which the situation and dimensions of objects might be referred. It is much more difficult to embody the relative positions and dimensions, where all is left to the eye. ”

“ Follow with your eye any two adjacent lines, and you will see that where they are close to each other the surface has an abrupt change of level; where they are further apart the surface is nearly horizontal. Where the surface approaches the perpendicular, as on the sides, the dark line showing the separation of the strata is thin, because it has been cut through nearly at right angles. Where the surface is more horizontal the dark line is broader, because it has been cut through obliquely, the breadth varying steadily with the angle of inclination. ”

“ The static features of physiography, altitude, etc., lend themselves readily to determination by means of precise instruments. These factors, though by no means negligible, are remote, and consequently their mere measurement is insufficient to indicate the nature or extent of their influence upon the plant. It is necessary to determine also the manner and degree in which they affect other factors, a task yet to be done. Readings of altitude, slope, and exposure are so easily made that the student must carefully avoid the tendency to let them stand at their own value, which is slight. ”

“ In such a structure, then, we have certain primary phenomena of growth manifested in their original simplicity, undisturbed by secondary and conflicting phenomena. What actually grows is merely the lip of an orifice, where there is produced a ring of solid material, whose form we have treated of under the name of the generating curve; and this generating curve grows in magnitude without alteration of its form. ”

“ Consequently, Nature herself supplies us with an ascending scale or Alphabet of angles for half a degree up to 60°, specimens of which are placed in every Elementary School throughout the land. Owing to occasional retrogressions, to still more frequent moral and intellectual stagnation, and to the extraordinary fecundity of the Criminal and Vagabond Classes, there is always a vast superfluity of individuals of the half degree and single degree class, and a fair abundance of Specimens up to 10°. ”

“ When a plant organ is subjected to the continued action of unilateral stimulus of light, it exhibits increasing tropic curvature, which in certain cases reaches a limit; in other instances a reversal takes place, seen in neutralisation, or in the conversion of the positive into negative curvature. I shall in this chapter enter into a detailed study of the phototropic curve, and determine its characteristics. ”

“ Arcs having the same length but varying in both radius and angle may be felt to be in Measure-Harmony. It is doubtful, however, whether lines of the same length but of very different curvatures will be felt to correspond. If the correspondence of lengths is not felt, visually, it has no interest or value from the point of view of Pure Design.
68. Any line may be continued in a repetition or repetitions of its shape, whatever the shape is, producing what I call a Linear Progression. In the repetitions we have Shape-Harmony.
Fig. 77
This is an example of Linear Progression. ”

“ A spiral curve is a [45] harmonious line, says the designer: repeat it, reversed, and you prolong the harmony; repeat it again, with variations, and you complete the harmony. Or, harmonious effect is produced by recurring form and line. Here is a circular form; here is a meandering line: combine and repeat them, and you get a logical and harmonious border motive. ”

“ Draw a Base line and a perpendicular thereto, and from O in the Base line prick the negative resolvends downwards, and the affirmative ones upwards, and raise their roots upon them as ordinates, a Curve passing through the same is one Moity of the Curve or Locus on the right hand for affirmative roots, and the other moity on the left hand is described in the same manner by assuming a rank of negative roots, and raising resolvends thereunto. ”

“ A little experimenting will show unsuspected possibilities in strong, forceful curves, and the young student is advised to make many experiments in the effort to discover such possibilities. An example of profiles to be avoided is given in Problem II, on page 309. That these are vase forms and not bowl contours is immaterial. A is commonplace because the two parts of the curve are too much alike. ”

“ Find the equation of the evolute in parametric form, plot the curve and the evolute, find the radius of curvature at the point where , and draw the corresponding circle of curvature.
Substituting in above formulas (A) and then in (50) , §117, gives the parametric equations of the evolute. Assuming values of the parameter , we calculate from (B) and (C) ; and tabulate the results as follows: Now plot the curve and its evolute. The point is common to the given curve and its evolute. The given curve (semi cubical parabola) lies entirely to the right and the evolute entirely to the left of . ”

“ 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. ”

“ The very curves demonstrate the theorem that a curve is made up of little straight lines, the arches are stiff and unbending, and wherever a public building demands an ornament, a fir-shaped cone of straight lines rises in stoic severity. ”

“ The dead weight of a locomotive forms a large proportion of the whole travelling load, and thus inherently involves a proportionate waste of power—a waste which is enhanced by the steepness of the gradients and the speed of the trains. ”

“ The method adopted consists in employing lines varying in their thickness and in their intervals apart according to the slope of the ground to be represented. This method is based upon the principle of the horizontal contours, which is to give to the same vertical interval the same absolute amount of shade, whatever the inclination of the ground may be. The shading lines are used, as we have said, to fill in the features of the ground between contours already fixed; and to ensure accuracy and uniformity in the representation, a “scale of shade” is employed. The accompanying Fig. ”

“ You might, at first, imagine that, given what we may call our scale of solidity, or scale of depth, the diminution from nature would be in regular proportion, as, for instance, if the real depth of your subject be, suppose, a foot, and the depth of your bas-relief an inch, then the parts of the real subject which were six inches round the side of it would be carved, you might imagine, at the depth of half an inch, and so the whole thing mechanically reduced to scale. ”

“ Our earliest ideas of form are probably derived through the different colours of objects around us, by which they are thrown into relief upon the background, or against other objects; and, as I mentioned in the first chapter, we reach outline by observing the edges of different masses relieved as dark or light upon light or dark grounds, so now, in my last, we come again to the consideration of the definition of line and form by colour, and their relief and expression upon different planes or fields of colour. ”

“ The fundamental form-elements may be reduced to the six proposed by Professor Penck as the basis of his double system of classification by form and origin. [32] These may be looked upon as being all derived by various modifications or arrangements of the single form-unit, the slope or inclinedThe six elementary land forms. plane surface. No one form occurs alone, but always grouped together with others in various ways to make up districts, regions and lands of distinctive characters. The form-elements are:
1. ”