Calchas

“ Does it appear to be a strange proposition that money should be measured? Why should not a dollar be just as absolute as a dollar as a pound is as a pound; or as a foot is as a foot; or as a gallon is as a gallon? A cord of wood contains one hundred and twenty-eight solid feet, or eight cord feet. It must always be eight feet in length, four feet in height and four feet in width, or some other multiples of one hundred and twenty-eight. A cord can never be any more, never any less than just that measurement. ”

“ For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centred at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square. ”

“ 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 ”

“ 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. ”

“ I was told that the surface of the body, or the skin of a large man, measured sixteen feet square, which is equal to the surface of a table four feet long and four broad. Now, you know that in four feet there are forty-eight inches, and on the surface of the table are forty-eight rows, with forty-eight inches in each, or 2,304 square inches; so that a man's surface is 2,304 square inches, and the weight his body supports is 34,560 lbs., or upwards of fifteen tons—always at the rate of fifteen pounds to every square inch, you understand. ”

“ A man of correct proportions will, in general, be about the same height as the length of the arms from tip to tip of the long fingers, when extended. I have frequently seen cases of factory deformities, in which the length of the arms thus, was six inches more than the altitude of the body; in my own case, this difference is eight inches. I have observed, that, so far from the ratio of these cripples being in proportion to the weight of the work to be done, it is directly the contrary ”

“ If the build is to be successful, we have to measure and calculate all the curves, and the other dimensions, with rule and compass with the utmost accuracy. Geometers and arithmeticians we must be, that we may compute the proportions and the capacities of our casks. Ah, good sir, I can tell you my very heart laughs within my body when I see a fair, well-proportioned cask laid on to the end-stool, the staves all beautifully finished off with the riving knife and the broad-axe, and the men set to with the mallets, and 'clipp, clapp' ring; the strokes of the driver. Ha! ha! that is merry music. ”

“ 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. ”

“ Yes; everything on which there is a duty when it is taken off the boats has to be weighed, and to do this there are big scales, and for each one a scale house. When a scale is being used there are two men in the scale house. One of these is the Government weigher, who sets the scale to a balance and notes down the weight in a book. The other man, who is an employee of the company, writes the weight also in a book of his own; and he is called the company’s checker. But though there are half a dozen scales, almost everything, when it is possible, is unloaded in front of Scale No. ”

“ Weight for Inches.—It may prove a matter of intelligence to those persons unconnected with the movements and terms of the sporting world, to understand that the graduated scale for a match, when made for two or more horses to run and carry weight for inches, is thus: that horses measuring fourteen hands high are 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. ”

“ 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. ”

“ Calculi.—In reviewing the statistics of vesical calculi, the strangest anomalies in their size and weight have been noticed. Among the older writers the largest weights have been found. Le Cat speaks of a calculus weighing over three pounds, and Morand is accredited with having seen a calculus which weighed six pounds. In his statistics in 1883 Cross collected reports on 704 stones, and remarked that only nine of these weighed above four ounces, and only two above six, and that with the last two the patient succumbed. ”

“ The calculation however proved inexact, so that the metre is now really a standard measure of the old sort, but so great is the convenience of using the same measures, that the metre and its fractions are coming more and more into use for scientific work all over the world. The use of scales and weights, and of wet and dry measures, had already begun among the civilized nations in the earliest known times. Our modern standards can even to some extent be traced back to those of the old world, as for instance the pound and ounce, gallon and pint, come from the ancient Roman weights and measures. ”

“ A very high calkin is not only objectionable, it is unnecessary. Not much prominence is required to afford a catch or stop. Excessive height is usually given to meet wear, and this can be obtained equally well by increasing the width and breadth. I, therefore, recommend that when calkins are used they should be low, square and broad. The further under a foot the calkin is placed, the greater is the raising of the heel, therefore calkins should always be accompanied by a long shoe. ”

“ Scales.—There are sixty scales on the lateral line, and twenty-two in a vertical row between the first dorsal and centre of the belly. The scales are rather small, their bases truncated and furrowed to near the middle (striées en éventail) by six grooves corresponding to eight minute lobes of the margin. A narrow border of the outer rounded edge is very minutely streaked, producing teeth on the margin, visible under a lens. The length and breadth of a scale, taken from the side, are about equal, being two and a half lines. ”

“ 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. ”

“ Besides the weight of an ounce or two ‘telling sadly before the end of a day’s work,’ there remains the evil that it tells permanently upon the horse’s legs. There is, perhaps, no modern authority that has not been explicit thereon; yet heavy shoes are still most generally in use, in spite, also, of the old proverb, ‘An ounce at the heels tells more than a pound on the back.’ Mr. ”

“ Many, if not most, of the feet that have broken-down arches also tread over inward along the whole side. In such cases the weight of the body, as already stated, falls upon the arch in a wrong direction. The arch, instead of standing upright and receiving the weight directly over itself, supports the body while itself leaning over to one side. Any other kind of arch, in a similar condition, would quickly fall over or settle down; and it is no wonder the foot settles down to a level in the shank. ”

“ 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? ”

“ Taking these proportions, and granting that 1/6000 of a foot is the actual ascertained amount of loss from the whole surface, we ascertain by a simple arithmetical process that 1/12 of an inch is carried away from the plains and table-lands in seventy-five years, while the same amount is worn out of the valleys in eight and a half years. One foot must be removed from the former in 10,800 years, and from the latter in 1,200 years. ”

“ With a square and a compass it is a comparatively easy matter accurately to step off 45 degrees, as it is the line C, midway between A and B, and the other degrees may be calculated from the line C and the cardinal lines A or B.
Degrees Without a Compass.—But in the absence of a compass and when you do not wish to step off a circle, you will in such case lay down the square, and mark off at the outer margin of the limbs two equal dimensions. Suppose we take 2 inches on each limb of the square. The angle thus formed by the angle square blade is 45 degrees. ”

“ In falling down, the calcaneum is pushed backward making the long-heeled foot, while the bones forward of the astragalus must advance more or less in their direction, thus adding to the foot’s length at both ends, and making the leg appear to be set far toward the middle. The ends must necessarily be separated before the middle of the arch can sink, and this is why its flattening is accompanied by the long heel. ”

“ If an husbandman therefore shall lend unto his neighbour a sacke full or corne, and the base of the sacke be 4 foote over. And the neighbour afterward for that one sacke, shall pay him 4 sacke fulls, every sacke being as long as that was, yet but one foote over in the diameter, he may be thought peradventure to have repayed that which he borrowed in equall measure, to wit in heighth and base. ”

“ 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. ”

“ 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. ”

“ 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 ”

“ It consists in simply supporting the back part of the arch as nature does in her own way; that is, in supporting the whole under-surface of the calcaneum, or heel-bone, as is done when the bare foot is pressed upon the ground. A long heel—one extending under the sole far enough for its front edge to support the front part of the bone—is the thing required. ”

“ Into one cask I poured a quart of water and wetted the interior thoroughly, to make the wood swell and secure tight joints. Then into it I introduced the Jew, in a sitting posture, and was gratified to find that the specimen occupied the space comfortably. But here a slight difficulty presented itself. The center of gravity of a cask filled with homogeneous matter coincides with the geometrical center. ”