Weight and measurement

“ 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. ”

“ 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. ”

“ So in like manner we must choose our unit of work, but in order to do so we must first of all choose our units of weight and of length, and for these we will take the kilogramme and the metre, these being the units of the metrical system. ”

“ The kilogramme is now, like our pound, a certain metal standard, and the litre is a measure containing, more or less exactly, a kilogramme of water. A perfect litre standard contains 1000 grammes of water at 39·2°; but 1·1 gramme less at 62°, 2 grammes less at 70°, and 3·3 grammes less at 80°, a very frequent summer temperature. For exact correspondence of measure with weight, corrections are always required whether on the imperial or on the metric system. ”

“ In determinations of volume which do not admit of a high degree of accuracy the cubic decimetre can be taken as equivalent to the litre; and in these determinations expressions of volumes based on the cube of the unit of linear measure can be substituted for expressions based on the litre as defined above.
(c) The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. [1]
(d ) The term “weight” denotes a magnitude of the same nature as a force; the weight of a body is the product of the mass of the body by the acceleration of gravity ”

“ 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. ”

“ 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. ”

“ Divide its weight in grains by the number expressing its specific gravity; extract the cube root of this quotient, and multiply it by 1·9612 for the diameter.
WEIGHT OF A CUBIC FOOT OF THE FOLLOWING MATERIALS,
in pounds.
By means of the foregoing table, the weight of any quantity of the materials specified (in cubic feet) may readily be found.
MOTION, FORCES, &c.
Body is the mass or quantity of matter in any material substance, and it is always proportional to its weight, or gravity, whatever its figure may be. ”

“ No purchaser is bound to accept goods by weight or measure other than those of the Imperial standard, but bargains entered into upon the basis of the weights or measures of the metric system are valid, according to a fixed scale of equivalent Imperial weights and measures. ”

“ It is only because a yard-stick has a fixed and definite length of its own that we are enabled to measure the length of other things by it. It is only because a pound weight has a fixed and definite weight of its own that we are enabled to measure weight of other things by it. ”

“ To express mechanical force or power, the foot pound is the unit employed—that is, the mechanical energy necessary to raise a weight of one pound to a height of one foot. On the Continent, where the units of length and weight are the metre and the gramme, the unit of mechanical energy is the metre gramme. ”

“ One pound of tea taken to the sun would be as heavy as twenty-eight pounds of it at the earth’s surface; and weight varies at different parts of the earth. Hence the true measure of quantity of matter is mass, not weight. ”

“ This consequence is seen more clearly and exactly by the following table. The mean weight of man when the organization is complete being sixty-three kilogrammes sixty-seven decimetres, at the time of birth he has yet to gain sixty kilogrammes forty-seven decimetres. ”

“ 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. ”

“ It will help to avoid confusion if we reserve the simple terms "gram" and "pound" to denote exclusively an amount of matter, that is, a mass, and to use the full expression "gram of force" or "pound of force" whenever we have in mind the pull of the earth upon these masses. Or, one may speak of a pound-weight meaning the amount of attraction exerted by the earth upon the object. The same is true of gram-mass and gram-weight. The mass of a body does not change when the body is transferred to another place. ”

“ There are also measures of weight, ounces, pounds and tons. Now these different measures are the same all over the United States. A pound of butter in New York is the same as a pound of butter in California. There are other countries that do not have measures like ours. France, for example, has the metric system. Should you go into a dry goods store in Paris you would not ask for a yard of cloth, but for a meter.
God's measures are the same. God has a measure for girls and boys, and that measure is the same in Ohio, Mexico, England or Spain. ”

“ The thousands upon many thousands who in some way or other have recourse to weights and measures in the pursuance of their avocations, would not only have to face new methods of working, and fresh forms of calculations, but would have to do so with implements of unfamiliar dimensions. It would be impossible to catalogue them—the engineer’s gauge, the carpenter’s rule, and the milkman’s pint, the butcher’s lb., the tailor’s tape, the warehouseman’s appliances for determining weight, qualities and values, all would have to be swept away ”

“ When the weights which are to be compared are of different metals further complications arise, for the volumes of equal weights of different metals will be different, and therefore the quantity of air displaced by them will be different, and the difference of the weights of air displaced by the two weights must be allowed for. And the weight of air displaced depends upon the density of the air at the time of weighing, and therefore the barometer reading must be taken. ”

“ When the scholars have learnt to distinguish the pound, ounce, &c., they may come out in turn and weigh various objects.
It would be well to explain that solid objects occupy less room than lighter substances—that a pound of feathers, e.g., would take up a large space, while a pound of lead would go into a very small compass.
Guessing Game.—When the object to be weighed has been chosen, a number of children are allowed to come out and hold it in turn, and say what they think is its weight. ”

“ A weight W is to be raised by means of a lever with the force F at one end and the point of support at the other. If the weight is suspended from a point at a distance a from the point of support, and the weight of the beam is w pounds per linear foot, what should be the length of the lever in order that the force required to lift it shall be a minimum? ”

“ 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. ”

“ 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. ”

“ For instance, Mr. Mee measured six stacks of hay 1681⁄2 loads, 250 feet to the load; and Mr. Harding measured the same stacks at 256 loads, 216 feet to the load.
We have already disposed of this question, in page 52, where the principle of weight for weight is clearly defined; and upon this plain principle, it is submitted, Mr. ”

“ 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. ”

“ In the weighing of large masses of coarse material, such as grain, coal, cotton seed, and the like, machines have been constructed which automatically weigh such materials and at the same time register the weight. ”

“ 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 ”

“ 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. ”

“ This metre (m.) is the only unit of metric—extension by which all other metric measures of extension—whether linear, superficial or solid—are ascertained.
The kilogram (kg.) is represented by an iridio-platinum standard weight, of cylindrical form, by which all other metric weights, and all measures having reference to metric weight, are ascertained in the United Kingdom.
From the above four units are derived all other heights and measures (W. and M.) of the two systems.
The gallon is the standard measure of capacity in the imperial system as well for liquids as for dry goods. ”

“ 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. ”

“ 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. ”

“ The whole load borne by the knife-edge is of course 8 lbs., being the sum of the weights. If we multiply 2, the number of pounds at one end, by 36, the distance of that end from the knife-edge, we obtain the product 72; and we find precisely the same product by multiplying 6, the number of pounds in the other weight, by 12, its distance from the knife-edge. To express this result concisely we shall introduce the word moment, a term of frequent use in mechanics. The 2 lb. weight produces a force tending to pull its end of the bar downwards by making the bar turn round the knife-edge. ”

“ Volumes are always most accurately defined by their weight of water, as weighing can be more accurately done than measuring. If the volume is hollow, it may be filled with water and closed with a sheet of plate glass, or if solid the body may be weighed in water and out, the difference giving the weight of its volume of water. ”

“ If the weight be equal, whether they are carrying the ark of the temple or a calf, a nugget of gold or a stone, they will be subject to the law of the weight and their expression can indicate nothing but that weight. ”

“ 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. ”