Scale

“ 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. ”

“ 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. ”

“ 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? ”

“ In it the sky and part of the snow are of the same value, and they match the gray marked High Light in the scale. The distant hill is Low Light; the dark band of trees on the horizon is High Dark, and the tree in the foreground is Dark. In this way you can find in the scale the neutral values used in a picture.
Name the values of the hyacinth, on page 53. What values were used in the moonlight picture on page 10? Make a little scale showing these values and giving their names.
[Pg 81]
Dividing a Space into Large and Small Spaces. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ If we wish the successive divisions of the scale to correspond to equal increments in the density of the corresponding liquids, then the volumes of the instrument, measured up to the successive divisions of the scale, must form a series in harmonical progression, the lengths of the divisions increasing as we go up the stem. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ since, again, they saw that the attributes and the ratios of the musical scales were expressible in numbers; since, then, all other things seemed in their whole nature to be modelled after numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number. ”

“ In the scale of bodies they put in the first and highest place body simply, and in the next place under it less common names, by which it may be more limited and determined, namely animated and inanimated, and so on till they come to individuals. In like manner, in the scale of quantities, they assign the first place to quantity, and the next to line, superficies, and solid, which are names of less latitude ”

“ 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. ”

“ 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. ”

“ The scale at the bottom will enable any mechanic to determine the size of each of these buildings, and their relation to each other. They can, on the same general plan, be made of any dimensions, to suit the wishes of the proprietor. ”

“ 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 ”

“ Each scale is divided into one hundred parts, which are marked from five to five. A slide that can be moved up or down, shows the measure of the qualities therein specified each one possesses, or believes himself to possess. ”

“ He in fact furnished by these tables a scale by which not only the advantages which he proposed of shortening arithmetical and trigonometrical labour were effected, but which enabled men to go infinitely farther, and enabled his successors to weigh the atmosphere and take the altitudes of mountains, compute the lengths and areas of all curves, and to introduce a calculus by which the most unexpected results should be reached. ”

“ 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. ”

“ 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°. ”

“ If this is done accurately, the height to which the new line reaches will measure the size of the figure first drawn; for the taller the figure is, the steeper the hill will be; the longer the figure, the longer the hill; either cause makes both the size of the figure and the height of the hill greater, and in the same proportion; so the one is a measure of the other, and so, moreover, is the height of the hill, which can be measured by scale, a measure of the quantity of electricity that has passed. ”

“ 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. ”

“ 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. ”

“ With a protractor, measure the angle A of the triangle whose sides were just measured, and compare the ratios of the sides or the functional values with those given in the Table, Appendix III, for the same angle. The larger the scale of the drawing, the greater the accuracy. By making use of the hundredths scale of the framing square together with a finely pointed pair of dividers, variation in values should not be great. ”

“ 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. ”

“ In every country the scale is generally expressed by the ratio of some fraction or multiple of the smallest to the largest national units of length, but sometimes by the fraction which indicates the ratio of the length of a line on the paper to that of the correspond- ing line on the ground. ”

“ Fig. 224.
The principles upon which “projection” in drawing is based, are illustrated in the following examples [149] and text: As a real object can be scaled with a foot rule, so a drawing must permit of scaling and measuring. This measuring may take place as with the real object in full size or the drawing may, for the sake of convenience, be reproduced and measured in a reduced scale, as half, or in still smaller sizes. ”

“ On the History of Gunter’s Scale and the Slide Rule during the Seventeenth Century, by Florian Cajori. ”

“ The rough track contained in fourteen sheets, on the scale of half an inch to a mile, will exemplify this. These sheets have been connected, corrected by astronomical observations, and reduced to a small scale. ”

“ 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. ”

“ 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. ”

“ You supplied me with a large scale-map showing the exact spot where each of the previous maimings had taken place. I drew a square to embrace the whole. Lines drawn diagonally from corner to corner gave me the centre of gravity. ”

“ First ascertain the exact height of each piece, as Q, K, B, which represent the queen, king, bishop, &c. Refer these dimensions to the scale, as shown at QKB, which will give us the perspective measurement of each piece according to the square on which it is placed.
[75]
Fig. 83. Chessboard and Men.
76 This is shown in the above drawing (Fig. 83) in the case of the white queen and the black queen, &c. The castle, the knight, and the pawn being about the same height are measured from the fourth line of the scale marked C.
Fig. ”

“ 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. ”