BALANCE, a generic term designating machines for com paring the weights of two bodies. This article deals chiefly with the equi-arm type treated mainly as instruments of precision. (See also WEIGHING MACHINES.) Of all the instruments used in making precise measurements, the familiar equi-arm balance is one of the most productive of high accuracy. The average type of balance is illustrated in fig. I.
Essentially the balance is an equi-arm lever consisting of a beam, usually of metal, which turns about a horizontal central knife-edge as fulcrum, while the objects weighed are supported on pans suspended at the extremities of the beam from terminal knife-edges which are equidistant from the fulcrum. Normally when the balance is not in use the three knife-edges are relieved of their loads. The balance reading is made by noting the angular swing of the beam about its fulcrum, and is ordinarily indicated by the position, relative to a small fixed scale, of a metal pointer attached to the beam.
Some typical shapes of beams in general use are shown in figs. 2 and 3.
Balance beams are usually made of brass or bronze suitably covered with a protective coating, but in recent years aluminium alloy has also been employed on account of its low density while the use of invar steel has also been advocated owing to the low thermal expansibility of this material. The magnetic properties of invar however constitute a disadvantage.
In the working condition of the balance the centre of mass of the beam lies slightly below the fulcrum knife-edge. Instability will of course occur if the centre of mass lies above the fulcrum. The smaller the distance of the centre of mass below the fulcrum, the more sensitive is the balance, but the longer its period of swing. Adjustability of working conditions of sensitiveness and period of swing is obtainable by raising or lowering the "gravity bob" on the beam of the balance.
A separate adjustment for poise is also provided so as to enable the reading of the balance, when not loaded, to be brought to a convenient zero or reference mark on the scale.
Hard alloys, e.g., stellite, are occasionally used for this purpose.
Fig. 4 shows a sectional view of an agate knife mounted after the usual man ner in a triangular brass block for conve nient attachment to the beam. The knife edge is formed by two facets inclined to each other at an obtuse angle. This type of knife-edge has been found to withstand many years' regular usage.
The precision obtainable from the balance depends especially on the accuracy with which the knives are mounted on the beam and adjusted to their correct relative positions. These fundamental adjustments demand much patience. As the central knife is usually first mounted square with the beam, the terminal knife edges have to be set parallel to, equidistant from and coplanar with the central one. These conditions are realized, to a moderate degree of accuracy in balances in general. In many balances made for low-precision work, all three knives are fixed to the beam without means of re-adjustment. In the more familiar types of balances used for chemical and technical purposes, the agate plane which bears on a terminal knife-edge is mounted in a metal stirrup which has at its lower end a hook, or an eye-hole, from which the balance pan hangs. This method of suspension has been found sufficiently good for most purposes. Improved meth ods of suspension have been used for special weighings of the highest precision.
As to the mechanical gear for operating the arrestment, a cam controlled by a milled wheel outside the balance case raises or lowers a vertical frame which carries the arresting stops or points. The same motion raises or lowers the pan-supports, which are in good adjustment when they just touch the under surfaces of the pans as the arrestment is completed. It is preferable to design the arrestment so that, on releasing the balance for swinging, the load is transmitted to the terminal knives before the central knife is finally lowered on to its bearing plane. This is achieved in some makes of balance, but is by no means generally found.
The square of the period of swing of the balance is therefore proportional to The conditions of performance of a balance may now be summed up by an inspection of the above formulae : The ideal conditions of use of a balance are those in which the three knife-edges are coplanar for all loads placed on the balance pans, since the balance is then equally sensitive at all loads. This condition is not fully realized in practice. Even if the three knives were coplanar when relieved of their load, the slight bend ing of the beam under load would modify this relation at other loads. The period of swing of the balance will inevitably become slower as the load is increased.
\\Then the balance is first set up, if the component parts, includ ing the arrestment, appear to be in good working order, the oper ator should test its performance thoroughly before putting it into general use. In some cases the method of weighing adopted will depend on the performance of the balance and its limitations. The sensitiveness and period of swing of the balance should be deter mined for a number of different loads and different positions of the gravity bob. The position finally chosen for the latter should be that which gives a sensitiveness compatible with the accuracy sought for, together with a suitably short period. Sometimes it may even be desirable to sacrifice sensitiveness in order to obtain a quicker swing. If facilities permit, an optical method of reading the balance may be used to obtain improved precision of observa tion while retaining a quick period of swing. The degree of equal ity of the arms of the balance should also be ascertained in order to decide to what extent the method of "single weighing" will suffice to give the required accuracy in certain operations in weighing.
The term "single weighing" implies that the body to be weighed is suspended only from one arm of the balance and poised against known weights operating on the other arm of the instrument, and clearly involves an assumption that the arms are equal. This assumption can always be tested easily by making a "double weighing"; i.e., by seeing how the apparent weight of the body varies according to the arm from which it is weighed. It has been found that the effective lengths of the arms of a good analytical or chemical balance are usually equal to within r part in roo,000.
The constancy of the rest point of the balance should also be tested at several loads over a considerable period of time espe cially at the maximum load taken by the balance. Most balances exhibit small variations in rest point, even at no load, which may be caused by changes in temperature or by fatigue resulting from previous loading. Some observations should also be made on the use of a rider weight with the balance. Usually the graduated bar which holds the rider when in use is arranged to be in the plane through the terminal knives. This is not always the case, but unless it is so, the apparent weight of the rider when placed on the rider bar will depend on the inclination of the beam to the horizontal. The accuracy of graduation of the rider bar should also be tested, especially if it is intended to use relatively large rider weights. In work of the highest precision, it may be neces sary to restrict the size of rider employed.
In all work with knife-edge balances, it will be found that the instrument is relatively slow to use. In general, the practice of weighing by the "null" method is followed ; i.e., the weights on one pan of the balance are arranged so as to obtain zero deflection of the beam. which is usually taken as corresponding to the posi tion of the pointer opposite the central line of the scale. The reali zation of the equilibrium position is, of course, facilitated by a prior knowledge of the sensitiveness of the balance in terms of one division of the scale. Alternatively, and often preferably, if the operator has obtained balance with the pointer reading a few divisions away from the centre of the scale, he may calculate from the sensitiveness of the balance the extra loading on one pan nec essary to make the pointer read zero.
In cases where the residual errors of inequality of the arms of the balance prohibit the use of the method of "single weighing," the choice lies between "counterpoise weighing" and "double weighing." In the former case, a constant mass is kept on one pan of the balance, and known weights are used on the other pan in addition to that which has to be determined. Weighing is thus made by substitution, and is independent of the length of the arm of the balance, provided that this length remains constant during the series of weighings. In "double weighing," the ordinary single weighing is repeated with the loads interchanged in the pans, the object being to minimize the combined errors due to inequality of the arms of the beam and unevenness of tempera ture distribution within the balance case. The double weighings may be repeated in the reverse order if for special reasons it is desired to eliminate errors due to changes in rest-point of the balance during the course of the weighings.
The period of the balance should be regulated, in consideration of the above table, according to the nature of the weighings to be made, and the accuracy required. The least stable position is often not very useful as, owing to great sensitiveness, the balance cannot be poised unless the loads to be compared have very nearly the same weight.
It is somewhat difficult to give a fair impression of the accuracy attainable in the use of the balance, since in many cases the balance is not used under conditions suitable for maximum accuracy. Under ordinary conditions of use, it may be said that a roogrm. balance weighs to an accuracy of o•000i gram Similarly larger balances will weigh to an accuracy representing one part in a million of the maximum load weighed. Small bal ances, of the type used in assay work, are capable of weighing to o.0000igrm. in general. These estimates, however, will not hold good unless the weights used in the process of weighing are accurate, and correct allowance is made for the buoyant force of the atmosphere on the objects weighed.
Brass weights are sometimes coated with a metal-plating or a lacquer in order to prevent tarnishing. Lacquered weights, how ever, absorb moisture from the atmosphere and consequently may vary to the extent of o•000 i grm. for the denominations ordinarily used by chemists. For metal-plated weights, platiniz ing should be preferred to gilding owing to the softer nature of the latter. The stability of a plated weight depends considerably on the method and care of plating. In general, however, platinized brass weights are preferable to non-coated polished ones, and are often used in work of a high accuracy. In some cases where special precision is required even platinized-brass weights may not be sufficiently reliable, and it may be necessary to consider other materials such as nickel-chromium (8o% nickel, 2o% chromium) which has been used with success for the construction of some laboratory reference standards of mass. Weights of this material are not ordinarily obtainable on the market. Platinum is still regarded as the most stable and suitable metal for use in the con struction of the fundamental standards of mass, but its cost limits its use to the construction of relatively small weights.