the beam; an elevation almost imperceptible in the axis of the beam, destined to compensate for the very slight flexion of the: bar, alone excepted.

2. The apparatus, by the construction of the beam, is ba lanced below its centre of motion; so that when no weight is suspended, the beam naturally remains horizontal, and resumes that position when removed from it, as also when the steel-yard is loaded and the weight is at the division, which ought to shew how much the merchandise weighs. The horizontal situation in this steel-yard, as well as in the others, is known by means of the tongue, which rises vertically above the axis of suspension.

3. It may be discovered that the steel-yard is deranged, if, when not loaded, the beam does not remain horizontal.

4. The advantage of a great and a small side (which in the others augments the extent of their power of weighing) is supplied by a very simple process, which accomplishes the same end with some additional advantages. This process is to employ, on the same division, different weights. The numbers of the divisions on the bar point out the degree of heaviness expressed by the corresponding weights. For example, when the large weight of the large steel-yard weighs 18 pounds each division it passes over on the bar is equivalent to a pound; the small weight, weighing eighteen times less than the large one, will represent, on each of these divisions, the eighteenth part of a pound or ounce; and the opposite face of the bar is marked by pounds at each eighteenth division. In this construction, therefore, we have the advantage of being able, by employing both weights at once, to ascertain, for example, almost within an ounce, the weight of 500 pounds of merchandise. It will be sufficient to add what is indicated by the small weight in ounces, to that of the large one in pounds, after an equilibrium has been obtained by the position of the two weights, viz. the large one placed at the next pound below its real weight, and the small one at the division which determines the number of ounces to be added..

5. As the beam is graduated only on one side, it may have the form of a thin bar, which renders it much less susceptible of being bent by the action of the weight, and affords room for making the figures more visible on both the faces.

6. In these steel-yards the disposition of the axes is not only such that the beam represents a mathematical lever without weight; but in the principle of its division, the interval between every two divisions is a determined and aliquot part of the distance between the two fixed points of suspension; and each of the two weights employed has for its absolute weight the

unity of the weight it represents, multiplied by the number of the divisions contained in the interval between the two constant centres of motion. Thus, supposing the arms of the steel-yard divided in such a manner that ten divisions are exactly contained in the distance between the two constant centres of motion, a weight to express the pounds on each division of the beam must really weigh ten pounds; that to point out the ounces on the same divisions must weigh ten ounces, &c. So that the same steel-yard may be adapted to any system of measures whatever, and in particular to the decimal system, by varying the absolute heaviness of the weights, and their relation with each other. The application of this principle will be seen hereafter in the description of the steel-yard, to which C. Paul, with great propriety, has given the name of universal steel-yard.

But to trace out, in a few words, the advantages of the steel-yards constructed by C. Paul for commercial purposes, we shall only observe, 1. That the buyer and seller are certain of the correctness of the instrument, if the beam remains horizontal when it is unloaded and in its usual position. 2. That these steel-yards have one suspension less than the old ones, and are so much more simple. 3. That by these means we obtain, with the greatest facility, by employing two weights, the exact weight of merchandise, with all the approximation that can be desired, and even with a greater precision than that given by common balances. There are few of these which, when loaded with 500 pounds at each end, give decided indications of an ounce variation; and the steel-yards of C. Paul possess that advantage, and cost one-half less than balances of equal dominion. 4. In the last place we may verify, every moment, the justness of the weights, by the transposition which their ratio to each other will permit; for example, by observing whether, when the weight of one pound is brought back one division, and the weight of one ounce carried forwards eighteen divisions, the equilibrium still remains.

If, instead of ascertaining the weight of the merchandise in pounds, you wished to find it according to the system of decagrammes, hectogrammes, and kilogrammes, it would be sufficient to substitute, for the ordinary weights, an assortment of three weights bearing the above names. These three weights are the decuple one of the other; and the absolute weight of that called kilogramme, is to the absolute weight of that called pound, in the exact ratio of these two quantities. It may be here seen, that, by adapting to the steel-yard a system of three weights, we may arrive at the second decimal, or the centiemes of the unity of the weights employed, and even without adding or changing any thing in the division of the beam.

It is on this simple and advantageous principle that C. Paul has constructed his universal steel-yard. It serves for weighing in the usual manner, and according to any system of weights, all ponderable bodies to the precision of half a grain in the weight of a hundred ounces; that is to say, of a ten-thousandth part. It is employed, besides, for ascertaining the specific gravity of solids, of liquids, and even of the air itself, by processes extremely simple, and which do not require many sub-divisions in the weights.

The beam of this steel-yard when unloaded rests in equilibrio in a horizontal position. The shears are suspended by a screw to a cross horizontal bar of wood supported by two vertical pillars, which rest on the two extremities of a small wooden box furnished with three drawers, and which serves as the stand of the apparatus. This beam is divided into 200 equal parts, beginning at its centre of motion. The division is differently marked on the two faces: on the anterior face the numbers follow each other from 10 to 200, proceeding towards the extremity; and on the other face, the numbers are marked in the opposite direction. We shall soon explain the use of this difference in the order of numeration.

A small vertical frame hangs from the cross-bar nearly at the further extremity of the steel-yard, and is destined to prevent the oscillation of the beam; it is placed at the proper height by means of the nut and screw by which it is suspended. Above the beam is a small cross-bar of brass, suspended by its two extremities from the cross-bar of wood. Different weights are hooked to it, each having marked on it its particular value. And, in the last place, a small mercurial thermometer having the two most usual divisions, viz. Fahrenheit's and Reaumur's, and destined to point out the temperature of the air and the water during the experiments. The axis of suspension of the steel-yard rests upon two beds of very hard well-polished steel. The case is the same, but in a reversed situation, with the axis which supports the hook, that serves for suspending different parts of the apparatus, according to the purpose to which it is to be applied.

When you wish to employ it as a common steel-yard, you suspend from it a brass shell, which is an exact counterbalance for the weight of the beam when unloaded. The latter then assumes of itself a horizontal situation. You then search for the equilibrium of the substance put into this shell, by positing at the proper place, on the beam, the weight and its fractions corresponding with the system of weights adopted; and when you have found the equilibrium, you observe the weight indicated by the divisions on which each of the weights employed

is found, exactly in the same manner as is done in regard to the common steel-yard.

There is also, as part of the apparatus, a glass shell suspended occasionally in a jar filled to a certain height with water. This shell is intended for experiments relative to the specific gravity of solids. It is in equilibrium, if, when immersed into water at 20° of Reaumur, as far as the junction of the three silver wires by which it is supported, it exactly balances the weight of the beam unloaded.

When you wish, then, to try the specific gravity of a solid, you first weigh it in air; but by putting it into the brass shell, and then substituting the glass one, you weigh it in water. It is well known that the difference of these weights, employed as a divisor of the total weight in air, gives for quotient the specific gravity. Care must be taken, as in all experiments of the kind, that no bubble of air adheres to that part of the apparatus immersed in the water, or to the substance, the weight of which is required, and which is immersed also.

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There is likewise a solid glass ball destined for the purpose of ascertaining the specific gravity of liquids, in the following manuer :-This piece is furnished with a hook of fine gold, that it be immersed without inconvenience in acids. When it is suspended to the hook of the steel-yard, and in the air, it is in equilibrium with the beam loaded at its extremity (either at the division marked O (nothing) on the backside of the beam) with weights entitled specific, and T of specific hooked on at the other.

This ball, immersed in distilled water at 12° of Reaumur as far as the end of the straight metal wire which suspends it, is still in equilibrium with these two weights placed in the fol lowing manner, viz. the large one at the division in the middle of the beam marked water on the backside of the beam, and the small one at the division O, that is to say, the extremity. When the apparatus is thus prepared, you fill a jar with the liquid, the specific gravity of which you wish to ascertain; suspend the glass ball to the hook of the steel-yard, and immerse it into the liquid till it rises exactly above the ring from which the ball hangs, observing the temperature, and disengaging carefully all the air-bubbles that may adhere to the ball; then remove the small weight to the division 0 at the end of the beam, and convey the large one as far as that division, preceding that where the weight of the ball would raise the beam; and afterwards move the small weight as far as the division where the equilibrium will be restored, the beam being horizontal. Mark the division at which the large weight is found, and add two cyphers; to this number add the indication imme

diately resulting from the position of the small weight, and the sum of these two numbers gives the specific gravity of the liquid, or its ratio with the weight of distilled water, to a tenthousandth part.

The larger balloon is used in trying the weight of any given kind of gas compared with that of atmospheric air, in the following manner :-The weight entitled air-tare is arranged in such a manner that when placed in a notch, at the further extremity of the beam beyond the divisions, it forms an equilibrium with the balloon exhausted by the air-pump and suspended from the hook of the steel-yard. If the steel-yard is not then in equilibrium, it is an indication that the instrument is deranged, or that the vacuum is not perfect. The air, the relative weight of which in regard to atmospheric air you wish to ascertain, is to be introduced into the balloon, and the weight marked air is to be moved along the beam. The division at which it stands when an equilibrium is produced, will indicate, in hundredth parts of the weight of the volume of atmospheric air that could be contained in the balloon, the weight of the gas actually inclosed in it. This indication is read about the middle of the anterior part of the beam, where the words atmospheric air are marked.

Not satisfied with having procured to philosophers, and those fond of accurate experiments, an instrument extremely convenient for the closet, and of very extensive use, C. Paul has endeavoured to render this apparatus portable, and has constructed various pocket steel-yards, with which the nicest experiments may be made, and the quality of gold coin be ascertained by the trial of its specific gravity. They are constructed exactly on the same principles as the Roman small steel-yard, but are necessarily less extensive in their use. They cannot be employed, for example, in determining the specific gravity of an aëriform fluid, and do not extend beyond 100 deniers of weight; but as they possess all the advantages of a balance, besides those peculiar to themselves, they are extremely convenient for philosophers who are obliged to travel.

A figure of this steel-yard and apparatus may be seen in Tilloch's Philos. Magazine, vol. iii.

STEELYARDS to ascertain animal strength, may readily be attached to almost any kind of machinery in which animals are the first movers: and it is much to be wished that experiments were frequently made with them, in order that our knowledge on this point might be increased.

The following contrivance, falling under this head, has been lately proposed for determining the power of horses drawing in mills. Let AB (fig. 10. pl. XXXII.) be the vertical shaft to