Consecutive IV eighings.—To eliminate any effect due to slight inequality in the lengths of the two arms of the balance, at the same time to minimise the effect of any small residual drift of zero due to a gradual change in temperature conditions and to obtain a determination of the sensitivity of the balance at the time of weighing, consecutive weighings should be made to the following order :— Here A and B are the two masses being compared, and x a small known weight which serves to determine the sensitivity. Each mass is weighed an equal number of times on each pan of the balance, and the mean time of all the weighings of each mass on each pan is the same, so that the effect of any steady temperature drift is eliminated. In weighing, the balance is not brought to rest, but the pointer, or spot of light, is observed while swinging, and the extreme positions of several successive swings to right and left are noted. From these the mean readings or rest points corresponding to each arrangement of weights on the scale pans are calculated. If, for example, four successive readings are q2, q3, q4, then, allowing for the effect of the gradual reduction in the amplitude of the swing, due to damping, the corresponding rest point, p, is if If p be the rest point when two equal masses of value nominally equal to A and B are on the pans, then we have Usually of course several masses will be compared each with each in turn, and the best values for the differences between them finally computed by the method of least squares from all the observed differences obtained in the above manner.
The construction of the balance must be such as to ensure that after each successive arrestment of the beam and pans, the knife edges are brought into exactly the same relationship with the planes, and to secure this it is necessary to support the pans by means of a series of crossed knife edges below each terminal knife edge on the beam. If the weighings are not conducted in vacuo, the air density must be calculated for each weighing from observations of temperature, pressure and hygroscopic state of the air, and each observed reading corrected for air buoyancy, allowing for the effect of temperature on the volumes of the weights.
The volumes, and hence the densities, of the weights are deter mined by weighing them, first in air, and then immersed in distilled water, against other weights always in air. The density of the air must be calculated as usual from its temperature, barometric pressure and humidity, and that of the distilled water is known from its temperature. The difference between the two weighings, due allowance being made for the air buoyancy corrections on all the weights involved, is equal to the difference in weight between the quantities of water and air at the observed densities of each, which would fill a volume equal to that of the weight being ex amined. If for any reason it is considered objectionable to immerse a standard weight in water, it is possible to determine its volume, though somewhat less accurately, by means of a volumenometer, which is an apparatus for observing the change of pressure of the air enclosed within a given space, when a definite change is made in its volume, firstly when it is filled with air alone, and secondly when the weight is enclosed within it.
The calibration of a set of fractional or multiple weights in terms of the original unit can be effected by weighing together in groups of nominally equal sum by a process precisely analogous to that described above for a set of fractional end standards.
Ordinary brass weights usually exhibit a certain variability of mass, which is probably attributable to variations of surface con dition depending on the degree of humidity of the surrounding atmosphere. Care should, of course, be taken to see that the metal of which weights are made is free from porosity, and weights intended for precision work should be made solid, without screwed-in tops covering holes containing adjusting material. The surfaces of high class weights are frequently electroplated with gold or platinum, with the object of minimising the effects of oxidation and hygroscopic action on the surface. Of the two, platinising is the preferable process, but weights coated with either gold or platinum have been found to exhibit instability to a certain degree, though usually less than in the case of unplated weights. The success of gilding or platinising depends upon the care exer cised to obtain a firm and hard deposit.
To minimise the effects of temperature upon the action of a balance, a beam of invar may be used. But it must be remembered that invar is to a certain extent magnetic, and if results of high precision are required, care must be taken with such a beam as to ensure that it is completely screened from any possible magnetic influence. The balance should preferably be entirely enclosed within a sheet iron case.
For weighing very small quantities, and in particular for com paring the densities of small quantities of gases, micro-balances constructed entirely of fused quartz have been used. Such balances have been made both with knife edges, and preferably, with the beam torsionally supported on a thin horizontal quartz fibre at right angles to its length, and the pans supported from its ends by means of other fibres fused directly to it. The weighings are usually made by arranging a small bulb or similar contrivance at one end of the beam, counter-balanced by solid quartz at the other end. The two ends of the beam are therefore differently affected by the buoyancy of the air, and weighings are made by adjusting the pressure of the air in the balance case until the buoyancy just restores the beam to balance. The air pressure is read by means of a suitable manometer, and serves to measure the weight of the object under examination. With such balances loads as small as gramme have been weighed to an accuracy of i part in