Scale (balance)

“ 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 ”

“ Whenever cheating is practiced by the "false balance," it is of course done in a small way, to avoid any observation by the eye of the inequality of the two arms of the scale-beam, and the weight of the scale hanging from the shorter arm is made a little greater than that of the other, so that they may balance. Scales may be rendered very accurate by making the fulcrum or pivot of hardened steel, and of a wedge shape, with a sharp edge, in order to avoid friction as much as possible. ”

“ Why are we so interested in the type of scale that measures a dependent variable? The crux of the matter is the relationship between the variable's level of measurement and the statistics that can be meaningfully computed with that variable. ”

“ 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. ”

“ It is said in the Bible that God has ordered all things according to weight, number and measure. Omnia in pondere et numero et mensura disposuit Deus. Weight is equilibrium, number is quantity, measure is proportion—these three, and these are the eternal or divine basis of the science of Nature. Here now is the formula of equilibrium: Harmony results from the analogy of contraries. Number is the scale of analogies, the proportion of which is measure. The entire occult philosophy of the Zohar might be termed the science of equilibrium. ”

“ Of mechanical ones the most familiar is that of the scales. If accurately made and not clogged by dirt or rust, a pair of scales cannot be perfectly balanced: eventually one scale will descend and the other ascend—they will assume a heterogeneous relation. ”

“ 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." ”

“ The unit of the scale must constantly be the same, although realized in the metals, or the whole operation fails in the most essential part. This realizing the unit is like adjusting a pair of compasses to a geometrical scale, where the smallest deviation from the exact opening once given must occasion an incorrect measure. The metals, therefore, are to money what a pair of compasses is to a geometrical scale. ”

“ The median point of any distribution of measures is that point on the scale which divides the distribution into two exactly equal parts, one half of the measures being greater than this point on the scale, and the other half being smaller. When the scales are very crude, or when small numbers of measurements are being considered, it is not worth while to locate this median point any more accurately than by indicating on what step of the scale it falls. ”

“ 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. ”

“ 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. ”

“ When reducing by scales, it is obviously not essential to use the same scale as that to which the original is made; the dimensions on one scale may be readily transferred to any other, and the student will do well to make himself familiar with the operation. ”

“ 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. ”

“ When the masses are unequal the point is at unequal distances from the centers of the masses. These unequal distances have the same ratio as the masses themselves, but the larger mass is always the shorter distance from the point. If 1 pound is to balance 4 [Pg 26] pounds it is obvious that the 1-pound mass must be 4 times as far from the point of balance as the 4-pound mass.
Fig. 13. Mass of 4 units balanced by 1 unit.
Hence, to balance two masses in a rectangle, the point of balance will be found by proportion, placing it [Pg 27] on a line which divides the rectangle into parts of 2 to 3. ”

“ In almost every case a measuring instrument serves, and should serve only as a means of comparison between two or more magnitudes. As a general rule, we should not attempt to make the divisions of the measuring scale exact multiples or submultiples of the unit, but, regarding them as arbitrary marks, should determine their values by comparison with the standard itself. ”

“ This effect of scale is simply due to the fact that, of the physical forces, some act either directly at the surface of a body, or otherwise in proportion to the area of surface; and others, such as gravity, act on all particles, internal and external alike, and exert a force which is proportional to the mass, and so usually to the volume, of the body.
The strength of an iron girder obviously varies with the cross-section of its members, and each cross-section varies as the square of a linear dimension; but the weight of the whole structure varies as the cube of its linear dimensions. ”

“ When you do not wish to write the real height, you make two divisions, of which one proceeds upwards, the other downwards. You do not, in this case, double the value of each division, but in observations made with such a barometer scale you add the degree marked by the two surfaces, in order to find the real height. ”

“ A scale might be formed, graduated according to the decrees 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. ”

“ Gunter’s scale, which Wingate calls the “rule of proportion,” contained, as described in the French edition of 1624, four lines: (1) A single line of numbers; (2) a line of tangents; (3) a line of sines; (4) a line, one foot in length, divided into 12 inches and tenths of inches, also a line, one foot in length, divided into tenths and hundredths. ”

“ These graphs represent the normal form of distribution usually expected when any fundamental ability is measured in a random group. If the number of cases at each unit of measurement are plotted by a point placed relatively as far above the scale, used as a base line, as the number of cases found at that unit of the scale, it will be discovered that these points arrange themselves in the form of a symmetrical curve high at the middle and flaring out 257along the base-line scale. ”

“ 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. ”

“ When in an imperfect balance, we reverse the weights to eliminate error, the true weight will be the geometric mean of the two apparent weights. In almost all the calculations of statistics and commerce the geometric mean ought, strictly speaking, to be used. If a commodity rises in price 100 per cent. and another remains unaltered, the mean rise of a price is not 50 per cent. because the ratio 150 : 200 is not the same as 100 : 150. The mean ratio is as unity to √1·00 × 2·00 or 1 to 1·41. ”

“ The ratio of any element of area in the volume-pressure or the entropy-temperature diagram, or in any other in which the scale of work and heat is unity, to the corresponding element in the volume-entropy diagram is represented by or The cases in which this ratio is 0, or changes its sign, demand especial attention, as in such cases the diagrams of constant scale fail to give a satisfactory representation of the properties of the body, while no difficulty or inconvenience arises in the use of the volume-entropy diagram. ”

“ When you go a journey and your luggage is weighed, it is not put on scales, but on a spring; the weight depresses the spring a certain amount, and the result is indicated by a needle on a dial. The same principle is used in automatic machines for finding your weight. The spring balance shows weight, but scales show mass. So long as you stay in one part of the world, the difference does not matter ”

“ 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. ”

“ 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. ”

“ Though the improvements in agriculture had stood still at 1 in the arithmetical scale this would not lessen or alter the height to which the geometrical scale would have mounted in the interval. ‘It keeps on its way unslacked of motion.’ By advancing in the arithmetical scale or increasing the means of subsistence, you do not advance the geometrical scale, much less by increasing the disproportion between the two, do you increase the waste population of the world, which must be greater in proportion as less of it had been provided for. ”

“ Hence h = c, or the mean height of the figure is equal to the mean distance between the dents. The quantity in the brackets is too great to be neglected, however. If we were always dealing with circles, the ratio (R/2p) 2 would be a constant, and numerically equal to 1/16 or 6.25 per cent. Then all we should have to do would be to use a scale 6.25 per cent. longer than the true scale. But with a long narrow figure such as an indicator diagram, this ratio is much smaller. The measurement of a large number of diagrams gave a mean value of 1/60 for diagrams 4 in. ”

“ If, however, the form of distribution remains uniform, it would first be necessary for those advocating the use of any of the other quantitative definitions to show that the units of their scales are equal under some reasonable hypothesis. A ratio or a deviation statable only in scale units which are not demonstrably equal is a hazard, with the chances badly weighted against its reliability. So far as both the Binet and the Point scales are concerned we have found that the units are not equal. ”

“ And we may further notice how, in this first step of rational mechanics, we see illustrated the truth awhile since named, that as magnitudes of linear extension are the only ones of which the equality is exactly ascertainable, the equalities of other magnitudes have at the outset to be determined by means of them. For the equality of the weights which balance each other in scales, depends on the equality of the arms: we can know that the weights are equal only by proving that the arms are equal. ”

“ 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. ”