Scales

“ Scales are proportioned rules or mathematical instruments of wood, metal, etc., on which are marked lines and figures for the purpose of measuring sizes and distances. It is usual to make scales in the proportion of parts of an inch equalling a foot; the most generally adopted scale for machine drawing is one and a half inches, equalling one foot ”

“ Arbitrary Scales.—An arbitrary scale can be constructed by selecting any physical property of a substance which varies regularly with the temperature, such as the volume of a liquid, or the pressure or density of a gas, or the electrical resistance of a metal. ”

“ After careful thought and a comparison of different scales, I have come to the conclusion that the scale for standards of size given in the accompanying Table is the one I would recommend to be adopted. I have endeavoured to arrange one which would be easily intelligible to the ordinary workman, and that would in every possible case coincide with the old system, so as not to cause more expense in altering the present sizes than may be absolutely necessary. ”

“ Colour and sound have their Natural Scales, which the eye and ear habitually apply; what science requires is, that those scales should be systematized. We have seen that several conditions are requisite in such scales of qualities: the observer’s skill and ingenuity are mainly shown in devising such scales and methods of applying them. ”

“ Scales of Construction. —Scales of construction are intended to afford means of measuring more minute quantities than scales of distances. Of the former there are two kinds, known respectively as the Diagonal and the Vernier scale. The diagonal is the more frequently employed. Its construction involves no peculiar difficulty, as it consists simply of an ordinary scale of distances, with the addition of a number of parallel lines crossed by other parallel lines drawn diagonally from the smaller points of division. An example will best show the construction and mode of using this scale. ”

“ I saw, methought, a pair of golden scales hanging by a chain in the same metal over the table that stood before me; when, on a sudden, there were great heaps of weights thrown down on each side of them. I found upon examining these weights, they showed the value of everything that is in esteem among men. I made an essay of them, by putting the weight of wisdom in one scale, and that of riches in another, upon which the latter, to show its comparative lightness, immediately "flew up and kicked the beam." ”

“ Weights imply scales, of which we have also mention; and scales involve the primary theorem of mechanics in its least complicated form—involve not a qualitative but a quantitative prevision of mechanical effects. And here we may notice how mechanics, in common with the other exact sciences, took its rise from the simplest application of the idea of equality. For the mechanical proposition which the scales involve, is, that if a lever with equal arms, have equal weights suspended from them, the weights will remain at equal altitudes. ”

“ The consequence is that not one person in a hundred understands to what scale the drawings are made, and not one in a thousand will take the trouble to construct the scales which are indispensably necessary to enable him to study the plates.
14 As a proper punishment for the introduction of so troublesome a novelty as these decimal scales, either the draftsman or lithographer has separated by a dot all the first figures of the decimals in the plate of the restored order (Plate xxii.) . A dimension, therefore, which reads 2·96 or two feet eleven inches and a fraction in plate xxi., reads 2 ft. ”

“ From these, through the medium of the equal-armed lever or scales, we derive our equal units of weight, or gravitative force. And it is by means of these equal units of extension and equal units of weight, that we make those quantitative comparisons by which the truths of exact science are reached. ”

“ Should the scales contain too large or too small units, they may be multiplied or divided, and a new unit found by doubling or halving the units, or by dividing or multiplying them with any number, to gain the desired result. ”

“ Each machine is provided with a number of differing scales, divided suitably for various purposes. When the problem is one of time, the scale represents months and days; for problems of proportion, the zero of the scale is at the center of its length; for problems for the location of center of gravity of a system from a fixed point, the zero is at the extremity of the scale, etc. ”

“ Caroline. But if the scales contained different weights, the centre of gravity would no longer be in the fulcrum of the lever, but remove towards that scale which contained the heaviest weight; and since that point would no longer be supported, the heavy scale would descend, and out-weigh the other.
Mrs. B. True; but tell me, can you imagine any mode by which bodies of different weights can be made to balance each other, either in a pair of scales, or simply suspended to the extremities of the lever? for the scales are not an essential part of the machine ”

“ Much experience and practical skill are required in the designing of the scales, or elaborate balancing of. length, weight, thickness, material, and tension of the strings, to secure uniformity from bass to treble, while conforming to a given length of case, although the design may be planned in accordance with the mathematical theories of stretched strings. ”

“ That which is remarkable concerning the scales is that they stick so close together, by which he is not only kept warm, for no air can pierce him, but kept safe, for no sword can pierce him through those scales. ”

“ "Sometimes I do, sometimes I don't. The scales are balanced so nicely that a feather would turn them." ”

“ If the unit of the scale is some measure of the variability of a defined group, as it is in the majority of our present educational scales, this median point may well be calculated to the nearest tenth of a unit, or, if there are two hundred or more individual measurements in the distribution, it may be found interesting to calculate the median point to the nearest hundredth of a scale unit. Very seldom will anything be gained by carrying the calculation beyond the second decimal place. ”

“ They lie three deep upon the body, every part being covered with 3 scales succesively, tho not above 1/3, part of a scale discover it self to the Eye, the other 2/3 parts being hid by the other scales. As Fig. M. where the part exposed to view is marked 1, 2, 3, 4. the rest is covered by other scales. The point 3 is not always so sharp as I have here made it, but it being like the Original, which seem'd a perfect scale, I would not alter it.
The scales of Fishes also appear but in part, to the Eye, but it is very observable tho fishes never change their scales; yet men do often. ”

“ Extended quantities, such as lines, surfaces and solids, besides what they have in common with all other quantities, have this peculiar, that their parts have a particular place and disposition among themselves: a line may not only bear any assignable proportion to another, in length or magnitude, but lines of the same length may vary in the disposition of their parts; one may be straight, another may be part of a curve of any kind or dimension, of which there is an endless variety. ”

“ Suppose that, instead of pressing down the empty scale, you put something that has weight into it; then, as soon as this weight is equal to that in the other scale, the beam will become horizontal. In fact, one scale has just as much tendency to move towards the centre of the earth as the other has, and as neither can go down without pulling the other up, they neutralise one another. ”

“ A scale might be formed, graduated according to the degrees of a combined ratio of intensity, duration, connexion, periods of recurrence, and utility, which would be the standard, according to which all ideas might be measured, and an uninterrupted chain of nicely shadowed distinctions would be observed, from the faintest impression on the senses, to the most distinct combination of those impressions; from the simplest of those combinations, to that mass of knowledge which, including our own nature, constitutes what we call the universe. ”

“ A geometrical magnitude which has three dimensions, that is, length, breadth, and thickness, is a solid; that which has two dimensions, such as length and breadth, is a surface; and that which has but one dimension is a line. But a point is neither a solid, nor a surface, nor a line ”

“ Any physical quantity whose field can be described by a single numerical value at each point in space. A scalar quantity is distinguished from a VECTOR quantity by the fact that scalar quantity possesses only magnitude, where as, a vector quantity possesses both magnitude and direction.
scale, n. 1. A series of marks or graduations at definite intervals. A linear scale is a scale graduated at uniform intervals; a logarithmic scale is graduated in the logarithms of uniformly-spaced consecutive numbers. 2. The ratio between the linear dimensions of chart, map drawing, etc. ”

“ Draw to scale such parts of the sketch as can be easily measured, and put in the remainder in proportion, and make these sketches at the scale at which you are used to working in the office. They will be of immense advantage in giving you a sense of absolute scale.
"There is such a thing as 'absolute scale,' and scale is not simply proportion. A drawing might be made in good proportion, and the building look well if executed a thousand feet long, and yet lose all its effectiveness if executed but one hundred feet in length, the relative proportions of the parts remaining the same. ”

“ For in homogeneous bodies, it is as weight to weight, so magnitude to magnitude.
If the parts of any ponderant press the beams of the scale every where equally, all the parts cut off, reckoned from centre of the scale, will have their moments in the same proportion with that of the parts of a triangle cut off from the vertex by strait lines parallel to the base. 8. If to the whole length of the beam there be applied a parallelogram, or a parallelopipedum, or a prisma, or a cylinder, or the superficies of a cylinder, or of a sphere, or of any portion of a sphere or prisma ”

“ Diag ́onal Scale, a scale which consists of a set of parallel lines drawn on a ruler, with lines crossing them at right angles and at equal distances. One of these equal divisions, namely, that at the extremity of the ruler, is subdivided into a number of equal parts, and lines are drawn through the points of division obliquely across the parallels. With the help of the compasses such a scale facilitates the laying down of lines of any required length to the 200th part of an inch. ”

“ The confining edge of the design is usually a rectangle, on the printed page. The location of a point of [Pg 25] balance within this rectangle tends to divide it. How shall it be divided in the most interesting way? By applying the ratio of good proportion. So the point of balance may be located usually on a line which divides the page into parts of 2 and 3.
When equal masses are to be balanced it is obvious that they will be equidistant from the point of balance. (Fig. 12.)
Fig. 12. Equal masses balanced at equal distance from the center point. ”

“ It is well known that the same extension at a near distance shall subtend a greater angle, and at a farther distance a lesser angle. And by this principle (we are told) the mind estimates the magnitude of an object, comparing the angle under which it is seen with its distance, and thence inferring the magnitude thereof. What inclines men to this mistake (beside the humour of making one see by geometry) is that the same perceptions or ideas which suggest distance do also suggest magnitude. ”

“ 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. ”

“ It will be seen that if a horizontal line is drawn from the foot of one of these figures, say G, to point O on the edge of the incline, then dropped vertically to o·, then again carried on to o·· where the other figure g is, we find it is the same height and also that the other vanishing scale is the same width at that distance, so that we can work from either one or the other. In the event of the rising ground being uneven we can make use of the scale on the level plane. ”

“ Where we see a body raised in a scale, we are sure that there is in the opposite scale, however concealed from sight, some counterpoising weight equal to it; but it is still allowed to doubt, whether that weight be an aggregate of several distinct bodies, or one uniform united mass. ”

“ The vanishing scale, which we shall find of infinite use in our perspective, is founded on the facts explained in Rule 10. We there find that all horizontals in the same plane, which are drawn to the same point on the horizon, are perspectively parallel to each other, so that if we measure a certain height or width on the picture plane, and then from each extremity draw lines to any convenient point on the horizon, then all the perpendiculars drawn between these lines will be perspectively equal, however much they may appear to vary in length. ”

“ No, you must not define length by means of a rigid scale, and define a rigid scale by means of length.
Phys. I admit I am hazy about strict definitions. There is not time for everything; and there are so many interesting things to find out in physics, which take up my attention. Are you so sure that you are prepared with a logical definition of all the terms you use? ”

“ XXXV How to Form a Vanishing Scale that shall give the Height, Depth, and Distance of any Object in the Picture
If we make our scale to vanish to the point of sight, as in Fig. 89, we can make SB, the lower line thereof, a measuring line for distances. Let us first of all divide the base AB into eight parts, each part representing 5 feet. From each division draw lines to 8th distance; by their intersections with SB we obtain 80 measurements of 40, 80, 120, 160, &c., feet. Now divide the side of the picture BE in the same manner as the base, which gives us the height of 40 feet. ”