Tallage

“ When men and animals carry burdens, or draw or propel loads in certain vehicles, it is difficult, and sometimes impossible, to determine the duty performed in foot-pounds of work, because of the uncertainty of the amount in pounds of the resistance overcome. In this case, for the purpose of comparing performances of the same kind with each other, a unit is employed called a foot-pound of horizontal transport, meaning the conveying of a load of 1 ℔ 1 ft. ”

“ GIVE and TAKE PLATES
—are those where the HORSES carry WEIGHT according to their HEIGHT, by the regulated standard of four inches to a HAND. The fixed rules for a GIVE and TAKE are, that horses measuring FOURTEEN HANDS, are each to carry nine stone; above or below which height, they are to carry seven pounds, more or less, for every inch they are HIGHER or LOWER than the FOURTEEN HANDS fixed as the criterion.—Example: a horse measuring FOURTEEN HANDS, one inch and a half, will carry nine stone, ten pounds, eight ounces ”

“ Nevertheless that which excels in size shows greater powers, since it seizes greater weights and has a wider orbe of virtue. For a loadstone weighing one ounce does not lift a large nail as does one weighing a pound, nor does it rule so widely, nor extend its forces; and if from a loadstone of a pound weight a portion is taken away, something of its power will be seen to go also ”

“ 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. ”

“ Scales and Steelyards.—In the common scale-beam we have a lever, the two arms of which are equal, and therefore equal weights suspended at the ends balance. If they be not exactly equal, a heavier weight will be necessary on the shorter arm than on the longer. The inequality will injure the buyer if the prop be too near the scale in which the weights are placed, and the seller if it be too near that which holds the article to be sold. ”

“ On the principle of the lever are made, scales for weighing different quantities of various kinds of things; the steelyard, which answers the same purpose by a single weight, removed to different distances from the fulcrum on a graduated arm, according as the body to be weighed is more or less in quantity; and the bent lever balance, which, by the revolution of a fixed weight, increasing in power as it ascends in the arc of a circle, indicates the weight of the counterpoise. ”

“ An apparatus for weighing.
μ In its simplest form, a balance consists of a beam or lever supported exactly in the middle, having two scales or basins of equal weight suspended from its extremities. Another form is that of the Roman balance, our steelyard, consisting of a lever or beam, suspended near one of its extremities, on the longer arm of which a counterpoise slides. The name is also given to other forms of apparatus for weighing bodies, as to the combinations of levers making up platform scales; and even to devices for weighing by the elasticity of a spring. ”

“ The weight which suspends itself in the angle will give from it some weight at the sides of this angle which will be between them in the same proportion as is that of the obliquity of their sides. Or: one such weight will distribute itself between its supports in the same proportion as is that of the two angles born of the division of the angle where this weight sustains itself, division of angle which is made by the vertical which descends in the center of the suspended heavy body ”

“ But it is sometimes convenient to use a fixed weight on the long arm, and to infer the amount of the load from the position of the steelyard. The rule for graduation is very simple. The simplest form is that which has a single travelling poise. The more elaborate ones are made either with a heavy travelling poise to measure the bulk of the load with a light traveling poise for the remainder, or else with a knife-edge at the end of the steelyard, on which loose weights are hung to measure the bulk of the load, the remainder being measured with a light travelling poise. ”

“ If now you either pull or push the empty scale downwards, the beam may be brought into the horizontal position again, and the effort required to bring it into the horizontal position will be the greater, the greater the weight of the body in the opposite scale. An ounce in the one scale is easily raised by the pressure of a finger in the other. A pound requires more effort; ten pounds needs putting out the strength of the arm; to raise fifty pounds involves still more exertion; while a couple of hundredweight will not be stirred by the strongest push or pull upon the empty scale. ”

“ Here it may be fairly guessed that man first measured, as he first counted, on his own body. When barbarians tried by finger-breadths how much one spear was longer than another, or when in building huts they saw how to put one foot before the other to get the distance right between two stakes, they had brought mensuration to its first stage. We sometimes use this method still for rough work, as in taking a horse’s height by hands, or stepping out the size of a carpet. If care is taken to choose men of average size as measurers, some approach may be made to fair measurement in this way. ”

“ Most measures of length have been derived from the human form, as foot, span, fathom, nail, &c. To originate a new measure or weight has proved much easier than to preserve their uniformity when established. Here legislation has been resorted to. The arm of Henry I. was measured, and a yard of the same length was deposited in the exchequer as a standard. “Thirty-two (afterwards twenty-four) grains of well dried wheat from the middle of a good ear” were to weigh a penny, twenty pence one ounce, and twelve ounces a pound. ”

“ In order to raise the weight of 14 lbs., it is necessary that the rope to which the power is applied should be pulled downwards by a force of 15 lbs., the extra pound being on account of the friction. To fix our ideas, we shall suppose the 14 lbs. to be raised 1 foot; to lift this load directly, without the intervention of the pulley, 14 foot-pounds would be necessary, but when [Pg 97] it is raised by means of the pulley, 15, foot-pounds are necessary. ”

“ 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. ”

“ My own notion, founded upon my own experience in seeing, is that a block of stone weighing 500 pounds might be in one's parlor twenty years, virtually unseen—but not in an old cultivated field, where it interfered with plowing—not anywhere—if it interfered. ”

“ Do you find a measure or ring through which the stones will pass, a good method of regulating their size?—That is a very good way, but I always make my surveyors carry a pair of scales and a six ounce weight in their pocket, and when they come to a heap of stones, they weigh one or two of the largest, and if they are reasonably about that weight they will do; it is impossible to make them come exactly to it. ”

“ Every stock-raiser should have his own scales. The following is as good a rule as any for estimating the weight of animals by measure: Multiply the girth in inches, taken immediately behind the shoulder blade, by the length in inches from the square of the buttock to the point of the shoulder blade, and divide the product by 144, which gives the number of superficial feet. If the animal has a girth of 3 to 5 feet, multiply the number of superficial feet by 16, and you will have its approximate weight. If the girth is 5 to 7 feet multiply by 23, and if 7 to 9 feet multiply by 31. ”

“ But, being controlled according to the laws of statics, and, by science, reduced to the measure of weight and balance, it bears its burden peaceably (like good horses) , and thus may be of great use to mankind, especially for the raising of water, according to the following table, which indicates the number of pounds which may be raised six inches, 1,800 times an hour, by cylinders half-filled with water, and of the several diameters and depths of said cylinders. ”

“ 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. ”

“ Is it a fact that being one-twelfth the height of a man a Lilliputian should have one-twelfth of a man’s strength? If a man is reduced to one-twelfth of his height what should his weight be?
When they wished to move Gulliver, five hundred carpenters and engineers were set to work to prepare a frame of wood, which was raised three inches from the ground, was about seven feet long, four feet wide, and moved upon twenty-two wheels. ”

“ If one thousand pounds were hung from the end of a suspended timber, so that the direction of the weight coincides with the axis of the timber, then will the tension upon the beam be one thousand pounds. ”

“ A man who raises 5 pounds a height of 5 feet does far more work than a man who raises 5 ounces a height of 5 inches, but the product of force by distance is 25 in each case. There is difficulty because we have not selected an arbitrary unit of work. The unit of work chosen and in use in practical affairs is the foot pound, and is defined as the work done when a force of 1 pound acts through a distance of 1 foot. ”

“ Whence, I believe, a short rod of wood or iron will support a greater weight than if it were long, provided the force be always applied longitudinally and not transversely, and provided also that we take into account the weight of the rope itself which increases with its length. ”

“ A man walking up-hill, or up-stairs, with a pound weight in his hand, to an elevation say of sixteen feet, performs a certain amount of work, over and above the lifting of his own body. If he carries the pound to a height of thirty-two feet, he does twice the work; if to a height of forty-eight feet, he does three times the work ”

“ As the weight of timber varies from 45 to 64 lbs. per cubic foot, the weight of a ship is consequently regulated by her class, as also by her length; and as a ship of ten times her beam must necessarily be built of heavier scantling than one of the same register tonnage, a long and high-class ship will necessarily be of greater weight than a short vessel of inferior description. ”

“ This may be seen from the balances that we call steelyards. When the handle is set as a centre close to the end from which the scale hangs, and the counterpoise is moved along towards the other arm of the beam, shifting from point to point as it goes farther or even reaches the extremity, a small and inferior weight becomes equal to a very heavy object that is being weighed, on account of the equilibrium that is due to the levelling of the beam. ”

“ 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. ”

“ Now, although a knowledge of these relative proportions are of great service both to the artist and the tailor, it has long since been an acknowledged fact that they must not be relied on too implicitly; for example, in measurements taken by one of our best artists, with a view to test the accuracy of "the length extended arms equals the height theory." It was found that out of 84 persons measured, 54 were found to be long armed, 24 short armed, and six only whose extended arms exactly equalled the total height. ”

“ 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. ”

“ If, for example, the balance is attached two inches from the fulcrum and the weight twelve inches, the pull on the balance is found to be six times greater than the weight that is being lifted. If other positions are tried, it is found that the power exerted in each case is as many times greater than the weight as the weight-arm is times longer than the power-arm. ”

“ If the circumference of the body, measured with an inch-tape just below the shoulders, be smaller than the circumference of the hips, the person will rock in walking, and plant his feet heavily upon the ground. If greater, so that the chief weight is above the limbs, the step will be light, as is familiarly seen in corpulent men, whose delicate mode of walking we witness with ever-recurring surprise. ”