Scale (device)

“ 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 ”

“ In other cases I may have read off the scale wrong, for however simple it seems to read off an instrument, those practically acquainted with their use know well how some errors almost become chronic, how with a certain familiar instrument the chance of error is very great at one particular part of the scale, and how confusing it is to read off through steam alternately from several instruments whose scales are of different dimensions, are differently divided, and differently lettered ”

“ Use of the binary scale.—The binary scale seems particularly well suited for electronic computation because of its simplicity and the fact that valve equipment can very easily produce and distinguish two sizes of pulse. ”

“ In this way the scale can be viewed by a microscope of much higher magnifying power than can be employed for the photographed spectrum. Indeed, if the scale were subdivided to 1/10 mm. the power employed might only be limited by the sharpness of the division-lines. But for refined work this would imply the investigation of too many divisions of the scale; it is therefore more usual to divide the scale into single millimetres or half-millimetres and to provide a micrometer which subdivides the millimetre into 1000 or, by estimation, into 10,000 parts. ”

“ At 1000 miles a second the contraction is not large enough to be appreciable in ordinary affairs; but it is quite large enough to be appreciable in measurements of scientific or even of engineering accuracy. One of the most fundamental procedures in physics is to measure lengths with a scale moved about in any way. Imagine the consternation of the physicists on this planet when they learn that they have made a mistake in supposing that their scale is a constant measure of length. ”

“ 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. ”

“ When the sizes of the fitting parts of machines are determined by sight from the lines on a scale or a two-foot rule, such nicety of measurement is out of the question; and as long as they are made on that system, the progress of improvement will be retarded. My experience has satisfied me that no system of measurement depending on the power of sight is suitable for obtaining the size of the working parts of machines. Where exact size or good fitting is required, the sense of touch is far more to be depended upon. ”

“ 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 ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ Heliometer observations of distance in their most refined sense cannot be considered absolute measures of angles. Essentially the scale-value of the instrument depends on the relation of the focal length of the object-glass to the length of the unit of the scale. But the eye is tolerant of small changes in the focal adjustment which sensibly affect the scale-value. These changes may and do arise from the following causes: (i.) The focal length of the object-glass and the length of the tube are affected by temperature. ”

“ It is the 'Metroscope,' 'an instrument for measuring inaccessible heights and distances, and for levelling.' To be able to measure the width of a river, or the height of a tower to the very top of the weathercock, is a manifest advantage, which is further increased by the instrument being provided with a scale, on which the measure can be read off in feet and inches, or feet and decimals. ”

“ 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. ”

“ 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. ”

“ The placing of objects of a known size near, to give scale, is a useless expedient in such a case. At times it may be successful, often of use; but if the scale of the main object is false, the other object of known size, instead of giving size to the main one, as it is intended to do, will be itself dwarfed by it. ”

“ For example, if there are ten space-types and 1/10 of an inch of space remains to be filled, each space-type must be increased in thickness just 1/100 of an inch completely to fill the line. It is not necessary, however, for the operator to make this calculation, for he has only to consult the scale provided for this purpose, and is referred at once to the proper keys to punch the justifying perforations in the strip. ”

“ I.—THE HORIZONTAL DIAL. A very useful and instructive pastime for boys will be found in the construction of a sundial, full directions for making which I give in this chapter.
Fig. 1.
Fig. 1 enlarged (112 kB)
The first thing to be done is to make what is called the dialing scale (Fig. 1) . It is constructed as follows: With a pair of compasses describe the circle A B C D with any radius, say four inches. Draw the two diameters A C and B D, cutting each other at right angles in the point 0. Join D C for the scale of chords and B C for the scale of latitudes. ”

“ If there are 1, 4, 7, 10, etc., zeros,
then use the middle third of the K scale. If there are no zeros or 3, 6,
9, 12, etc., zeros, then use the right-hand third of the K scale. For
example:
Example 41: cube_root ( 185 ) = 5.70
Since there are 3 digits in the given number, we set the indicator on
185 in the right-hand third of the K scale, and read the result 570 on
the D scale. We can place the decimal point by thinking of the nearest
perfect cube, which is 125. Therefore, the decimal point must be placed
so as to give 5.70, which is nearest to 5, the cube root of 125. ”

“ This chart drum or computing cylinder extends vertically within external casing and it is arranged to rotate on a vertical axis within the external casing. This casing is appropriately connected to the spring balancing mechanism and to the scale pan so that when the spring balancing mechanism moves up and down on the placing or removing of a load on the scale pan, the chart drum will be rotated in one direction or the other within the external casing or frame. ”

“ The horizontal scale is fixed to the upper horizontal plate of the theodolite. The vertical scale is on the vertical edge of a right-angled triangle, which can be slid along on the top of the horizontal scale. The inclined scale carries a slide which is provided with two verniers. One of these is parallel to the inclined scale, and is for the purpose of setting off on the scale (in terms of the divisions on the scale) the inclined distance of the staff from the axis of rotation of the telescope. ”

“ The mapping out is accomplished by means of a photographic scale fixed as a standard spectrum (Fig. 198) , in the position of A A, illuminated by 254 the small mirror at R, and focussed by a small lens at C, so that on looking into the instrument one can see the spectrum accurately divided into one hundred equal parts, and scale readings can be made at once; the only precaution needed is to be sure the D (or the sodium line, if D cannot be got) always stands at the same number on the scale. ”

“ When we come to astronomical phenomena, the physical operations with meter sticks can no longer be carried out, and it is meaningless to ascribe to beams of light on an astronomical scale the same geometrical properties that we do on a small scale. ”

“ 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. ”

“ This is not an inappropriate place to say that when we adopted the Centigrade scale for our work, we thought that a special thermometer, decimal throughout and consequently more handy, might be arranged for science alone, leaving every man the free use of whatever scale he liked best ”

“ Good, even illumination of the field may also very simply be secured by reflecting light into the instrument from a sheet23 of white paper laid on a table. On looking down the eyepiece we see a scale (Fig. 18) , the eyepiece being, if necessary, focused until the divisions of the scale are clearly and distinctly seen. Suppose, for experiment, we smear a little vaseline or similar fatty substance on the plane surface of the dense glass, which just projects beyond the level of the brass plate embracing it. ”

“ Set the iron punch on the end upon the floor, in such a place as that the scales may pass over it in making their circle: then electrify one scale, by applying the wire of a charged phial to it. As they move round, you see that scale draw nigher to the floor, and dip more when it comes over the punch; and if that be placed at a proper distance, the scale will snap and discharge its fire into it. ”

“ We may measure with the scale moving in any way we choose, and if results for different motions disagree, there is no criterion for selecting the true one. Further, if the particles are sliding past the scale, it makes all the difference what instants we choose for making the two readings. ”

“ 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. ”

“ For since the apparent diameter is reciprocally as the distance of the eye, when the distance of the eye is nothing or when the eye is close to the object at C, the apparent diameter will be the reciprocal of nothing, or infinite. ”