Weighing and measuring

“ All units must be assumed to be equal in that other respect; and this is never accurately true, for one actual pound weight is not exactly equal to another, nor one measured mile's length to another; a nicer balance, or more accurate measuring instruments, would always detect some difference. ”

“ It is not correct to define mass by the introduction of the idea of weight, because the mass of a body is something independent of the existence of the earth, whereas weight is produced by the attraction of the earth. It is true that weight is a convenient means of measuring mass, but this is only a consequence of the property of gravity which the experiment proves, namely, that the attraction of gravity for a body is proportional to its mass. ”

“ Masses are compared by the Balance (q.v.) , which may be made to indicate a 100,000,000th of the mass. They may also be estimated, not by their attractive force being balanced by an equal mass, but by the elasticity of a spring; this, which is the only true weighing-machine showing weight and not mass, is useful for rough purposes, owing to its quick indication ”

“ One reason of the great accuracy of weighing with a good balance is the fact, that weights placed in the same scale are naturally added together without the slightest error. There is no difficulty in the precise juxtaposition of two grams, but the juxtaposition of two metre measures can only be effected with tolerable accuracy, by the use of microscopes and many precautions. ”

“ The object to be weighed should be placed on the left-hand balance pan and the weights upon the right-hand pan. Every substance which could attack the metal of the balance pan should be weighed upon a watch-glass, and all objects must be dry and cold. A warm body gives rise to air currents which vitiate the accuracy of the weighing. ”

“ We are in the habit of estimating mass by its weight, and we do so rightly, for at any place on the earth, as London, the weights of masses are always proportioned to the masses, and if you want to find out what mass of tea you have got, you weigh it, and you know for certain. Hence in our minds we confuse mass with weight. ”

“ And similarly with mechanical forces, the unhesitating assumption is that if one unit of force acting in a given direction produces a certain result, two units will produce twice the result. Every process of measurement in a physical experiment takes this for granted; as we see in one of the simplest of them—the process of weighing. If a measured quantity of metal, gravitating towards the Earth, counterbalances a quantity of some other substance, the truth postulated in every act {301} of weighing is, that any multiple of such weight will counterbalance an equi-multiple of such substance. ”

“ The common balance for testing equality of mass or weight is so delicate and so easily tested that the process of calibration may frequently with advantage be reduced to a series of weighings, as for instance in the calibration of a burette or measure-glass by weighing the quantities of mercury required to fill it to different marks. The balance may, however, be regarded more broadly as the type of a general method capable of the widest application in accurate testing. ”

“ This weight will exceed w in consequence of the water displaced by the solid, and the weight of the water thus displaced will be W1−w, which is therefore the weight of a volume of water equal to that of the solid. Hence, since the weight of the solid itself is W−w, its density must be (W−w) / (w1−w) .
The above example illustrates how Nicholson’s or Fahrenheit’s hydrometer may be employed as a weighing machine for small weights. ”

“ Though the lump of metal will have different weights at different parts of the earth’s surface, it has been found (by experiment) that the weights of bodies at any one place are proportional to their masses. Therefore the same numbers that express the weights of bodies might also express their masses; but for certain good reasons these quantities are referred to different units. In England a piece of metal weighing 32 lbs. ”

“ Weight has been defined as the measure of the earth's attraction. A body weighing one pound attracts the earth and is attracted by it with a force of one pound, but the same body at the sun's surface would attract the mass of the sun with a force of twenty-seven pounds, since its weight has been increased twenty-seven times by the sun's attraction. ”

“ Nothing is perhaps more practical than the verification of the standards of weight by which commodities are bought and sold. Even the weights of the mint are tested at the Bureau of Standards. Accordingly in a basement room mounted upon heavy brick piers, which are a prominent feature in every physical laboratory in order to secure freedom from vibration, we find extremely accurate balances, some of which are capable of weighing a body with an accuracy of one part in fifteen or twenty millions. ”

“ If, therefore, we increase the weight of a body three hundred and fifty-four thousand times, in consequence of the greater amount of matter in the sun, and diminish it twelve thousand five hundred and forty-four times, in consequence of the force acting at a greater distance from the body, we shall find that the body would weigh about twenty-eight times more on the sun than on the earth. Hence, a man weighing three hundred pounds would, if conveyed to the surface of the sun, weigh eight thousand four hundred pounds, or nearly three tons and three quarters. ”

“ The origin of the Ounce, the foot, the 57cubic foot or wine-bushel is explained. That of Troy weight has been seen, and its predecessor, Tower weight, came from another ounce of the Arabic cantar. The origin of every measure and weight used in the civilised world will be found in the stories of the ancient cubits and talents.
10. Quadrantal, the Roman standard of capacity, a cubic vessel measuring one foot on each of its inside panels.
11. The French word pan has the same meaning, while Fr. empan, a span, is a corruption of espan.
58 CHAPTER V
ENGLISH LINEAR MEASURES 1. ”

“ For instance, if a 67-inch roll, 7,000 yards long, weighs 1,200 pounds exclusive of core, and measures 32 inches in diameter, these figures when worked out into reams show that that paper averages .30.7 pounds to the 500 sheets, measuring 24 by 36 inches, and that the paper has been well calendered. ”

“ Generally the specific gravity is observed by weighing in air and dividing the weight in grams by the volume in cubic centimetres, the latter being found from the weight of water displaced, divided by its density at the temperature at which the experiment is carried out. ”

“ The nature of measurement is well understood except in so far as it relates to psychological phenomena; in this realm metaphysicians seem wholly to misconceive its nature. I cannot measure the number of the ultimate particles of a body by counting them, but I may measure the relative number of its atoms by weighing it. I do not determine its force, but its mass only, when I weigh the body, for the total force in the body is the sum of its motion in all its incorporations. A pound of powder has much more force than that which is measured as a pound. ”

“ There are many reliable kinds of weighing machines, but the ordinary shop scales and weights still remain the most popular, and the price of a set of weights and scales, with weights sufficient to weigh from 1⁄4 oz. ”

“ A pair of ordinary weighing scales also exemplifies the first order of levers. The knife edge on which the beam is balanced serves as a fulcrum; it is placed exactly in the middle of the beam, which we shall suppose to be 10 inches long. If we place a 1-lb. weight in one scale to represent the resistance to be overcome, the weight will be lifted the moment that a pound of sugar has been placed in the opposite scale—the sugar thus representing the power. ”

“ Thus, suppose a globe, weighing a million of pounds, were suspended from the ceiling by a string, and we should apply to it the snap of a finger,—it is granted that the motion would be quite insensible. Let us then divide the body into a million equal parts, each weighing one pound ”

“ The mass of bodies varies according to their size; if you have the same nature of material, then for a double size you have a double mass. Some bodies are more concentrated than others, that is to say, more dense; it is as though they were more tightly squeezed together. Thus a ball of lead of an inch in diameter contains forty-eight times as much mass as a ball of cork an inch in diameter. In order to know the weight of a certain mass of matter, we should have to multiply the mass by a figure representing the attractive force or pull of the earth. ”

“ For weighing four balances are provided, each with mechanism for the transposition of the weights, and the lowering of the balance into play on its bearings, so that weighings can be performed at 13 feet distance from the balance, thus avoiding the disturbance caused by the warmth of the observer. ”

“ What kind of a quantity is that which now weighs more, and now weighs less, so to speak? But this apparent deviation from the method of determination commonly used in practical life, that by weight, is, closely considered, an agreement. On a high mountain a heavy mass also is less powerfully attracted to the earth than at the level of the sea, and if it is permitted us in our determinations to neglect the consideration of level, it is only because the comparison of a body with fixed conventional weights is invariably effected at the same level. ”

“ Moreover, a few thousand drops would fill the tumbler, and if a thousand drops weigh something, each drop must have a thousandth of that weight. The fact is that our feeling of effort is a very rough measure of weight, and does not enable us to compare small weights, or even to perceive them if they are very small. To know anything accurately about weight we must have recourse to an instrument which is contrived for the purpose of measuring weights with precision. ”

“ 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 ”

“ When there is no weight on the spring, the place to which the indicator points is marked zero. When these scales are manufactured, a pound weight is placed so that it pulls on the spring and the indicator is pulled down to another place, and this is marked one. Scales are thus marked for the number of pounds they are to weigh. The spaces between the pounds marked are divided into equal divisions, such as sixteenths which indicates ounces. These scales cannot be relied on for accuracy, for springs stretch or become weaker as they are used. ”

“ In the case of solids we may determine the volume in some cases by direct measurement—this gives at the best a very rough and ready value; a better method is to immerse the body in a fluid (in which it must sink and be insoluble) contained in a graduated glass, and to deduce its volume from the height to which the liquid rises. The weight may be directly determined by the balance. The ratio “weight to volume” is the absolute density. ”

“ The weight of objects is not the same all over the world; a thing which weighs thirty pounds in New York would weigh an ounce more than thirty pounds in a spring-balance in Greenland, and nearly an ounce less at the equator. ”

“ The extreme delicacy and exactness of the measurement work done upon the standards was illustrated by saying that when two of the standard kilogrammes were balanced against two similar masses, if one of the masses on one side of the balance was placed on top of the other mass, the balance would be destroyed. In other words, raising the mass of one kilogramme through less than two inches made a difference in the attraction of the earth readily observed. ”

“ The best way of precisely ascertaining the weight of any particular substance is to weigh it twice, once with the decimal divisions of the pound, and another time with the common subdivisions or vulgar fractions, and, by comparing these, we attain the utmost accuracy. ”

“ And 1000 ounces of water at the original weight of the averdepois ounce, of Roman standard = 437 grains, would weigh 999·5 of such ounces, at 62° in air.
Practically measures of capacity need only approximate coincidence with standards; they are used for 143convenience in order to avoid weighing, especially in retail trade. Corn and many other kinds of produce are more conveniently measured than weighed, the average weight being ascertained, if desired, by a sample bushel. ”

“ As the moon is much smaller than the earth, what weighs a pound with us would weigh much less than a pound in the moon. And as the sun is much larger than the earth, what is a pound with us would be much more than a pound there. If we knew the exact densities of the sun and the moon and the earth, as well as their size, we could estimate exactly the difference in the weights which any body would have in them; for the attraction which causes the pressure that we call weight is as the quantity of matter, and the quantity of matter depends on both density and size. ”

“ A pound of iron attracts a small body near by; two pounds of iron attract it precisely twice as much; in other words, the greater the weight of an object, the greater the power of attraction it exercises on the objects near by. Hence, if we know the attractive power of a body, we also know its weight. Nay, we would be able to do without scales of any kind in the world, if we were only able to measure accurately the attractive power of every object. ”