CHAP. XII. WEIGHING MACHINES. ANTIQUITY OF THE BALANCE. — PRINCIPLE OF THE EQUAL-ARMED CONTRIVANCES for ascertaining the relative amount of ponderable substances generally, by poising an unknown against a known weight, are of great antiquity, and in their approaches towards perfection have exhibited those varieties of form and that diversity of principle, which we might naturally enough have looked for in articles of such universal use and importance in every civilised community. The most ancient, as well as the most obvious, and, it may be added, for ordinary purposes the most perfect, weighing machine with which we are acquainted, appears to have been the balance or scales, constructed very much in the manner of those in common use among our shopkeepers at the present day, for the purpose of weighing articles by avoirdupois. To this description of scales there are frequent allusions in the Bible; and the idea of the zodiacal Libra shows that the knowledge of a contrivance of this kind was familiar to astronomers so early as the time when the celestial constellations received their present names. Although the principle of the balance is perhaps the least adapted for weighing false of any other in common use, without subjecting the fraud to detection, it is neverthe less certain, that false weights and false balances are as old as the art of weighing itself. The manufacture of weighing machines is carried on in this country to an extent and perfection commensurate with the amount and precision of our dealings with foreigners, as well as with one another, and likewise in consistency with those perfect methods of operation which characterise our workmanship in metals, and our knowledge of the calculation and application of mechanical forces. The equal-armed balance, so commonly seen in this country, is an exemplification of what writers on mechanics usually denominate a lever of the first kind, the point of suspension in the middle of the beam being the fulcrum; consequently equal weights act with equal momenta at both ends. The subjoined cut exhibits the figure of a rude pair of scales, copied from the margin of an Anglo-Saxon MS. by Mr. Strutt. Suppose A B a stick or rod of metal twelve inches in length, and C D two basins of copper suspended from the opposite ends of the rod by chains or strings; while E is another string, tied so exactly in the middle of the rod or beam, that when the whole is poised, the said rod A B and the scales C and D hang in horizontal lines, and, of course, parallel to each other. Now, if two pieces of lead, or any other substance perfectly equal in size and density, be placed one in each scale, the equipoise will remain just the same as it was before; or if one of these pieces be removed,—say that from C,—and its place supplied by equal weight of any other substance of greater or less specific gravity, the bulk will, by this means, be materially diminished or increased in relation to the size of the weight in D, but the equiponderance of the scales may remain unaffected. The scales being in the position described, it will be obvious, that if any portion of ponderable matter be taken from or added to the contents of scale C, such alteration should be indicated by the proportionate rising or falling of the opposite scale; but then the degree of nicety with which such variation will be indicated will depend upon the delicacy with which the balance is constructed, especially in those parts upon which the movement depends. Suspended by a string, as we have supposed the beam in this case to be, particularly if that string should be of considerable thickness, it is evident that a palpable alteration might be made in the contents of either scale, before that alteration would be indicated by any corresponding inclination of the beam; because, before any such effect could take place, the cause thereof must not only be sufficient to overcome the vis inertia of the beam in a state of rest, and even the friction of so much of the string as passed underneath, but likewise of the contact of the string with both sides of the beam, which, in proportion to its thickness, would cause the suspend→→ ing cord to act with a certain leverage against sensible oscillation. It is an easy matter, however, in the manufacture of scales for ordinary uses, so to suspend the beam upon an axis, and the chains which support the basins upon the extremities of the beam, that the friction shall be very trifling as compared with the amount of the article weighed. All these points, however, may be carefully attended to, and still the weighing may be deceitful, For instance, Balances used in commerce are sometimes constructed, either fraudulently or by inaccurate workmanship, so as to make unequal weights produce equilibrium. This effect is produced by making the arms of the balance, though apparently equal, really unequal. In this case, the weight suspended from the longer arm will balance a greater weight suspended from the shorter arm, and the proportion of the weights which will thus balance each other will always be the same as the proportional length of the arms of the balance. Suppose the longer arm is expressed by the number 51, and the shorter by the number 50; then a weight of fifty ounces suspended from the longer arm will exactly balance a weight of fifty-one ounces suspended from the shorter arm. When such a balance is used in commerce for the purposes of fraud by the seller, he will put the article to be weighed in the scale attached to the longer arm, and the weights or counterpoise in the scale attached to the shorter arm : the weight indicated will then be one ounce in every fifty-one ounces greater than the true weight of the commodity: but if it be used by a fraudulent buyer, he will, on the contrary, suspend the commodity which he is about to buy from the shorter arm, and the counterpoising weights from the longer arm; in which case fifty-one ounces of the commodity bought will appear to weigh only fifty ounces. It will be readily perceived that the more unequal the arms of the balance are, the more unequal will be the real and apparent weight of the commodity, and therefore the greater the extent of the fraud. The detection of a fraudulent balance of this description, than which nothing is more easy, depends on the fact, that if two weights produce equilibrium when placed in the dishes, the equilibrium will be destroyed if they are transposed. Thus, when the commodity to be weighed, placed in one dish, is balanced by weights placed in the other, let the commodity be removed to the dish in which the weights are placed, and the weights to the dish in which the commodity is placed. If the balance be fraudulent, the equilibrium will be no longer maintained; and on the other hand, if the equilibrium continue, it may be inferred that the balance is a just one. When a common balance is purchased for domestic purposes, it should always be tested in this way :- Let a weight be put in one dish, and balanced by other weights in the other dish; let the weights be then transposed, and if the equilibrium be not preserved, the balance is incorrect and useless. In the formation of a good balance there are three things to be especially attended to the fulcrum or prop which sustains the beam; the points of suspension on which the dishes or scales rest; and the centre of gravity of the beam. In a well constructed balance, two triangular prisms of hardened steel are attached to the centre of the beam, so that when the beam is placed in the horizontal position these pieces present an acute angle downwards: these knife-edges, as they are called, rest on plates of hard steel or agate, which are inserted in the stand which sustains the balance. Now, suppose a line drawn in the horizontal direction through the point of this knife-edge: this line must pass through two other knife-edges formed of hardened steel presented upwards. On these edges the scales or cups are suspended, so that in a strict sense the arms of the balance are the distances from the centre knife-edge to the edges which form the points of suspension: these distances should therefore be made accurately equal; and a provision is accordingly made in some balances, by which one of the points of suspension may be moved towards or from the centre, so as to render the arms equal, if they should happen to be unequal. The centre of gravity of the beam, when unloaded and in the horizontal position, should be perpendicularly below the knife-edge on which the beam rests. If it were above that edge, the beam would evidently have a |
