# ASTM E1270-88 (Reapproved 2014)

Designation: E1270 − 88 (Reapproved 2014)Standard Test Method forEqual Arm Balances1This standard is issued under the fixed designation E1270; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThis test method is designed to test balances whose lever-arm ratio is substantially equal to unity.Although largely superseded by new technologies, equal-arm balances retain a special niche for veryhigh precision weighing of larger samples (usually greater than 1 kg) as well as objects with largebuoyancy (such as gas bottles). Balances of this type can range from simple instruments of moderateprecision (1:10 000) to extremely high precision devices with precision of 1:10 000 000 or better. Anumber of accessory devices may be included for assisting in the weighing process. These devicesmay contribute to errors as well as can the basic lever mechanism. This method is designed to test theentire instrument including the accessories.1. Scope1.1 This test method can be used for testing equal-armbalances of any capacity and sensitivity. The testing procedureshould enable the user to characterize his instrument suffi-ciently to determine whether or not it is suitable for the purposefor which it is to be used.1.2 The characteristics to be examined include:1.2.1 Sensitivity at all loads,1.2.2 Lever arm ratio,1.2.3 Damping ratio (for instruments without accessorydampers),1.2.4 Period of oscillation,1.2.5 Precision, and1.2.6 Linearity and calibration of accessory devices thatprovide on-scale indication of weight.1.3 This standard does not purport to address all of thesafety concerns associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety andhealth practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E617 Specification for Laboratory Weights and PrecisionMass Standards3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 capacity—maximum load recommended by the manu-facturer. Usually, the capacity refers to the maximum load oneach pan simultaneously.3.1.2 readability—value of the smallest unit of weightwhich can be read. This may include the estimation of somefraction of a scale division or, in the case of a digital display,will represent the minimum value of the least significant digit.3.1.3 sensitivity—smallest value of weight which will causea change of indication which can be determined by the user.This may be independent of the readability because of thechoice of the reading device used. For example, a magnifyingglass may be used in conjunction with a reading scale toobserve a sensitivity not readily determined without the mag-nifying glass.3.1.4 precision—repeatability of the balance indication withthe same load under essentially the same conditions. The moreclosely the measurements are grouped, the smaller the index ofprecision will be. The precision should be measured underenvironmental conditions that represent the conditions underwhich the balance is normally used.3.1.5 accuracy—degree of agreement of the measurementwith the true value of the magnitude of the quantity measured.3.1.6 linearity—characteristic of a direct reading device. If adevice is linear, calibration at 2 points (for example, 0 andfull-scale) calibrates the device (for example, 2 points deter-mine a straight line); if a device is nonlinear, additional pointsare needed (perhaps a great many).1This test method is under the jurisdiction of ASTM Committee E41 onLaboratory Apparatus and is the direct responsibility of Subcommittee E41.06 onWeighing Devices.Current edition approved Nov. 1, 2014. Published November 2014. Originallyapproved in 1988. Last previous edition approved in 2008 as E1270–88 (2008).DOI: 10.1520/E1270-88R14.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.7 standard weight—any weight whose mass is given.Since weights are not always available with documentedcorrections, weights defined by class (see Specification E617)may be used if the class has sufficiently small tolerance limitsand there is an understanding that errors perceived as beinginstrumental could be attributed to incorrectly adjustedweights.3.1.8 off-center errors—differences in indicated weightwhen a sample is shifted to various positions on the weighingarea of the weighing pan. No separate test is described.3.1.9 full-scale calibration of an accessory device—indicated reading at equilibrium of an accessory device when astandard weight equal to the full-scale range of the deviceisplaced on the sample pan. Usually, some means is providedby the manufacturer to adjust the full-scale to match the weightof the standard.4. Summary of Test Method4.1 Throughout this test method, the instrument is to beused in the manner for which it is intended by the manufac-turer. All measurements are made with weights whose valuesare sufficiently well known for the purpose of the user. Thenominal value of the weights used will be determined by thecapacity and rated sensitivity of the balance as well as by theresolution and range of the accessory reading devices.5. Significance and Use5.1 This test method should enable the user of the balance tointerpret data determined thereon in terms of accuracy andprecision. It should be helpful in using a particular instrumentto best advantage. Weaknesses as well as strengths shouldbecome apparent. It is not the intention of this test method tocompare similar instruments of different manufacture butrather to assist in choosing an instrument which will meet theneeds of the user.6. Apparatus6.1 Standard Weights—Individual or summations of weightsequal to approximately1⁄4,1⁄2,3⁄4 and the total capacity.6.2 Tare Weights—Weights of the same denominations asthe standard weights but not necessarily calibrated.6.3 Calibrating Weights—Balances equipped with acces-sory devices such as sliding beam weights, chainweights,optical scales or electrical transducers require small standardweights equal to the full-scale reading as well as smallerweights suitable for calibrating intermediate points between thezero and full-scale points of the devices. Summations of smallstandards can be used for this purpose.6.4 Stop Watch:6.5 Aroom-temperature thermometer with a resolution of atleast 1°C.7. Preparation of Apparatus7.1 Place the instrument in the location at which it is to betested. If electrically operated, plug in the line cord to the typeof socket recommended by the manufacturer.7.2 Place the standard weights near (or within) the instru-ment.7.3 Place the thermometer on the bench in position so that itmay be read without being touched.7.4 Make sure that the instrument and test weights are clean.7.5 Allow the instrument and weights to sit undisturbedsufficiently long to reach temperature equilibrium with thesurrounding area. In the case of a large, high precisioninstrument in a controlled environment, it may be necessary toallow 24 h for such equilibrium.7.6 Read the manufacturers instructions carefully. Duringeach step of the test procedure, the instrument should be usedin the manner recommended by the manufacturer.8. Procedure8.1 Sensitivity—The sensitivity can be measured at a num-ber of different loads from zero to the capacity to provide asensitivity versus load curve, or, it can be measured at the loadof particular interest. This test applies to balances which havea null position indicator. Balances which are direct reading inthe on-scale range must be calibrated according to 8.8.4, 8.8.5,8.8.6 or 8.8.7.8.1.1 Place nominally equal weights on each pan for theselected load.8.1.2 Observe the indication. If necessary, place smallweights on the appropriate sample pan to obtain an indicationnear zero.8.1.3 Place a small weight on the left pan sufficient tochange the indication about1⁄2 scale of the on-scale range.Record the indication as d1.8.1.4 Remove the small weight and place it on the right panand record the new indication as d2(remember that forindicator scales graduated either side of center zero, indicationsto the left are recorded as negative values).8.1.5 Compute the sensitivity as follows:S 5 2 3W/~d12 d2! (1)where:S = sensitivity in mass units/scale division, andW = mass of small test weight.Example:d1= 5.5 div.d2= −5.3 div.W =10mgS =2×10⁄(5.5 − (−5.3)) = 1.85 mg⁄div.8.2 Sensitivity as a Function of Load—Balance designs varybut in the case of high precision balances, the manufacturerusually tries to provide a nearly level sensitivity at all loads.This is accomplished by the position of the plane determinedby the terminal pivots in relation to the central pivot. If thisplane is lower than the central pivot, the sensitivity willdecrease with increasing load. Conversely, if the plane ishigher than the central pivot, the sensitivity will increase withincreasing load and can reach a state of instability if the centerof gravity goes above the center pivot. Placing all of the pivotsin the same plane provides a nearly level sensitivity limited bythe elastic properties of the weighbeam. To measure theE1270 − 88 (2014)2relationship of sensitivity to load, repeat 8.1 at various loadsfrom zero to the capacity and plot sensitivity as a function ofload.8.3 Lever Arm Ratio—Equal arm balances are not usuallyused as direct-reading instruments. Rather, they are used ascomparators using standard weights for reference. For preci-sion measurements such as weight calibration, the measuringtechnique eliminates errors due to the inequality of arm-lengths. For relative measurements such as quantitative chemi-cal analysis, if the inequality is considered to be in a constantratio, the results of a number of weighings on the same balancewill have a common multiplier (L1/L2) and the resultingcomputations representing, perhaps, fractional components of acompound will be mathematically correct. If there is a need todetermine an absolute mass value from a single directmeasurement, the lever ratio must be determined.8.3.1 Observe the rest point with empty weigh pans.8.3.2 Place approximately equal weights on each pan whosevalue is near the capacity of the balance.8.3.3 Observe the new rest point.8.3.4 Transpose the weights to the opposite pans and ob-serve the rest point.8.3.5 Measure the sensitivity at this load from 8.1.8.3.6 Compute the lever ratio as follows:rL5MM1S1~d 2 ~d11d2!/2!(2)where:rL= lever ratio,S1= sensitivity in (mass units)/(scale division),d = rest point of empty pans in 8.3.1 (scaledivisions),d1= rest point from 8.3.3,d2= rest point from 8.3.4, andM = mass of test weights (the value on each pan).Example: =M = 100 g (on each pan)S1= 1.85 mg/div. = 0.00185 g/div.d = + 1.5 div.d1= + 8.5 div.d2= −2.5 div.rL=10010010.00185~1.5 2 ~8.5 2 2.5!/2!rL= 1.0000278.8.3.7 A ratio greater than 1 indicates that the left lever islonger and if a sample is placed on the left pan and standardweights on the right, the “true’’ weight is:WT5 WI/rL(3)where:WI= indicated weight.8.4 Damping Ratio—An undamped balance will oscillatearound a rest point with decreasing amplitude of oscillation dueto air damping on the weight pans and to friction in the bearingsystem. The ratio of the amplitude of one oscillation to that ofthe next may be a measure of several characteristics of thebalance. Since these cannot easily be separated, this measure-ment is not especially useful since pivot conditions can bebetter measured as part of a measurement of precision. In thecase of a damped balance, this measurement may be usefulinsofar as it may be used to characterize the effectiveness of thedamping mechanism. Useful damping is that which produces asteady reading in one or two oscillations. Since the dampingratio is usually a function of the load, damper mechanisms areusually set at some compromise value or are adjusted so thatthey may be optimized for a given load. Release the beam andobserve consecutive indications in the same direction. Com-pute the damping ratio rDas follows:rD5 d1/d2(4)where:d1= first turning point, andd2= second turning point in the same direction.8.5 Period of Oscillation—The time required to make onefull oscillation is an indicator of the time required to make ameasurement either for a damped or undamped balance. Theperiod is a function of the magnitude of the moving mass andof the sensitivity of the balance. For a given arm length,balances of high sensitivity have longer periods.8.5.1 For the convenience of the user, high sensitivitybalances may have means for magnifying the indication thusallowing the sensitivity to be lowered and the period shortened.However, such an approach must be used with care since suchmagnification means smaller angles of deflection are measuredand the balance becomes more sensitive to the tilting whichmight occur on a bench or floor of insufficient rigidity.8.5.2 Place weights of equal value on the pans at or near theload of interest. Release the beam and start the stop watch asthe direction of the indicator changes. Count several turningpoints and stop the watch after n periods of oscillation.Calculate the period, p:p 5 t/n (5)where:t = total elapsed time, andn = number of turning points.8.6 Precision—The term ’precision’ in weighing usuallymeans repeatability. In quantitative terms, it refers to expecteduncertainty of a single reading. The usual method for deter-mining the precision is to compare the results of a series ofmeasurements by some statistical treatment and to computesome value which gives the user an estimate of the potentialuncertainty of a single reading. A common technique is tocompute the standard deviation (s) of a series of observations.The larger the number of observations the better; but 10 isusually enough.Assuming a normal distribution of data, 3s willrepresent with a high degree of certainty the maximumanticipated error of a single measurement. One convenientmeasurement model is a series of double substitutions.8.6.1 Place a weight, ‘A’, considered to be the standard, onthe left pan and a tare weight of the same nominal value on theright pan. Observe the balance indication (A1).8.6.2 Remove the standard from the left pan and place a testweight ‘B’on the left pan. The tare weight remains on the rightpan. Observe the balance indication (B1).E1270 − 88 (2014)38.6.3 Add a small weight (S) to the left pan chosen so thatthe change in indication will be approximately equal to thedifference between the indications A1and B1. Observe theindication with this