ASTM E1270-88(2008)

Standard Test Method for Equal Arm Balances

SIGNIFICANCE AND USE
This test method should enable the user of the balance to interpret data determined thereon in terms of accuracy and precision. It should be helpful in using a particular instrument to best advantage. Weaknesses as well as strengths should become apparent. It is not the intention of this test method to compare similar instruments of different manufacture but rather to assist in choosing an instrument which will meet the needs of the user.
SCOPE
1.1 This test method can be used for testing equal-arm balances of any capacity and sensitivity. The testing procedure should enable the user to characterize his instrument sufficiently to determine whether or not it is suitable for the purpose for 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 accessory dampers),
1.2.4 Period of oscillation,
1.2.5 Precision, and
1.2.6 Linearity and calibration of accessory devices that provide on-scale indication of weight.
1.3 This standard does not purport to address all of the safety concerns associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

General Information

• Status: Historical
• Publication Date: 31-Oct-2008
• Technical Committee: E41 - Laboratory Apparatus
• Drafting Committee: E41.06 - Laboratory Instruments and Equipment

Relations

• Replaces: ASTM E1270-88(2003) - Standard Test Method for Equal Arm Balances
• Effective Date: 01-Nov-2008

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E1270 − 88(Reapproved 2008)
Standard Test Method for
Equal Arm Balances
This standard is issued under the fixed designation E1270; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
This 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Although largely superseded by new technologies, equal-arm balances retain a special niche for very
high precision weighing of larger samples (usually greater than 1 kg) as well as objects with large
buoyancy (such as gas bottles). Balances of this type can range from simple instruments of moderate
precision (1:10000) to extremely high precision devices with precision of 1:10000000 or better. A
number of accessory devices may be included for assisting in the weighing process. These devices
may contribute to errors as well as can the basic lever mechanism.This method is designed to test the
entire instrument including the accessories.
1. Scope E617Specification for Laboratory Weights and Precision
Mass Standards
1.1 This test method can be used for testing equal-arm
balances of any capacity and sensitivity. The testing procedure
3. Terminology
should enable the user to characterize his instrument suffi-
3.1 Definitions of Terms Specific to This Standard:
cientlytodeterminewhetherornotitissuitableforthepurpose
3.1.1 capacity—maximumloadrecommendedbythemanu-
for which it is to be used.
facturer. Usually, the capacity refers to the maximum load on
1.2 The characteristics to be examined include:
each pan simultaneously.
1.2.1 Sensitivity at all loads,
3.1.2 readability—value of the smallest unit of weight
1.2.2 Lever arm ratio,
which can be read. This may include the estimation of some
1.2.3 Damping ratio (for instruments without accessory
fraction of a scale division or, in the case of a digital display,
dampers),
will represent the minimum value of the least significant digit.
1.2.4 Period of oscillation,
3.1.3 sensitivity—smallest value of weight which will cause
1.2.5 Precision, and
a change of indication which can be determined by the user.
1.2.6 Linearity and calibration of accessory devices that
This may be independent of the readability because of the
provide on-scale indication of weight.
choice of the reading device used. For example, a magnifying
1.3 This standard does not purport to address all of the
glass may be used in conjunction with a reading scale to
safety concerns associated with its use. It is the responsibility
observe a sensitivity not readily determined without the mag-
of the user of this standard to establish appropriate safety and
nifying glass.
health practices and determine the applicability of regulatory
3.1.4 precision—repeatability of the balance indication with
limitations prior to use.
the same load under essentially the same conditions.The more
2. Referenced Documents
closelythemeasurementsaregrouped,thesmallertheindexof
precision will be. The precision should be measured under
2.1 ASTM Standards:
environmental conditions that represent the conditions under
which the balance is normally used.
This test method is under the jurisdiction of ASTM Committee E41 on
Laboratory Apparatusand is the direct responsibility of Subcommittee E41.06 on 3.1.5 accuracy—degree of agreement of the measurement
Weighing Devices.
with the true value of the magnitude of the quantity measured.
Current edition approved Nov. 1, 2008. Published January 2009. Originally
3.1.6 linearity—characteristicofadirectreadingdevice.Ifa
approved in 1988. Last previous edition approved in 2003 as E1270–88 (2003).
DOI: 10.1520/E1270-88R08.
device is linear, calibration at 2 points (for example, 0 and
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
full-scale) calibrates the device (for example, 2 points deter-
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
mine a straight line); if a device is nonlinear, additional points
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. are needed (perhaps a great many).
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1270 − 88 (2008)
3.1.7 standard weight—any weight whose mass is given. 7.2 Place the standard weights near (or within) the instru-
Since weights are not always available with documented ment.
corrections, weights defined by class (see Specification E617)
7.3 Placethethermometeronthebenchinpositionsothatit
may be used if the class has sufficiently small tolerance limits
may be read without being touched.
and there is an understanding that errors perceived as being
7.4 Makesurethattheinstrumentandtestweightsareclean.
instrumental could be attributed to incorrectly adjusted
weights.
7.5 Allow the instrument and weights to sit undisturbed
sufficiently long to reach temperature equilibrium with the
3.1.8 off-center errors—differences in indicated weight
surrounding area. In the case of a large, high precision
when a sample is shifted to various positions on the weighing
instrument in a controlled environment, it may be necessary to
area of the weighing pan. No separate test is described.
allow 24 h for such equilibrium.
3.1.9 full-scale calibration of an accessory device—
indicatedreadingatequilibriumofanaccessorydevicewhena 7.6 Read the manufacturers instructions carefully. During
standard weight equal to the full-scale range of the device
each step of the test procedure, the instrument should be used
isplaced on the sample pan. Usually, some means is provided
in the manner recommended by the manufacturer.
bythemanufacturertoadjustthefull-scaletomatchtheweight
of the standard.
8. Procedure
8.1 Sensitivity—The sensitivity can be measured at a num-
4. Summary of Test Method
ber of different loads from zero to the capacity to provide a
4.1 Throughout this test method, the instrument is to be
sensitivity versus load curve, or, it can be measured at the load
used in the manner for which it is intended by the manufac-
of particular interest. This test applies to balances which have
turer. All measurements are made with weights whose values
a null position indicator. Balances which are direct reading in
are sufficiently well known for the purpose of the user. The
the on-scale range must be calibrated according to 8.8.4, 8.8.5,
nominal value of the weights used will be determined by the
8.8.6 or 8.8.7.
capacity and rated sensitivity of the balance as well as by the
8.1.1 Place nominally equal weights on each pan for the
resolution and range of the accessory reading devices.
selected load.
8.1.2 Observe the indication. If necessary, place small
5. Significance and Use
weights on the appropriate sample pan to obtain an indication
5.1 Thistestmethodshouldenabletheuserofthebalanceto
near zero.
interpret data determined thereon in terms of accuracy and
8.1.3 Place a small weight on the left pan sufficient to
precision. It should be helpful in using a particular instrument
change the indication about ⁄2 scale of the on-scale range.
to best advantage. Weaknesses as well as strengths should
Record the indication as d .
become apparent. It is not the intention of this test method to
8.1.4 Remove the small weight and place it on the right pan
compare similar instruments of different manufacture but
and record the new indication as d (remember that for
rather to assist in choosing an instrument which will meet the
indicatorscalesgraduatedeithersideofcenterzero,indications
needs of the user.
to the left are recorded as negative values).
8.1.5 Compute the sensitivity as follows:
6. Apparatus
S 5 2 3W/ d 2 d (1)
~ !
1 2
6.1 Standard Weights—Individualorsummationsofweights
1 1 3 where:
equal to approximately ⁄4, ⁄2, ⁄4 and the total capacity.
S = sensitivity in mass units/scale division, and
6.2 Tare Weights—Weights of the same denominations as
W = mass of small test weight.
the standard weights but not necessarily calibrated.
Example:d =5.5 div.
6.3 Calibrating Weights—Balances equipped with acces-
d =−5.3 div.
sory devices such as sliding beam weights, chainweights,
W =10mg
optical scales or electrical transducers require small standard
S =2×10⁄(5.5−(−5.3))=1.85 mg⁄div.
weights equal to the full-scale reading as well as smaller
8.2 Sensitivity as a Function of Load—Balancedesignsvary
weightssuitableforcalibratingintermediatepointsbetweenthe
but in the case of high precision balances, the manufacturer
zero and full-scale points of the devices. Summations of small
usually tries to provide a nearly level sensitivity at all loads.
standards can be used for this purpose.
This is accomplished by the position of the plane determined
6.4 Stop Watch:
by the terminal pivots in relation to the central pivot. If this
6.5 Aroom-temperaturethermometerwitharesolutionofat
plane is lower than the central pivot, the sensitivity will
least 1°C.
decrease with increasing load. Conversely, if the plane is
higher than the central pivot, the sensitivity will increase with
7. Preparation of Apparatus
increasing load and can reach a state of instability if the center
7.1 Place the instrument in the location at which it is to be of gravity goes above the center pivot. Placing all of the pivots
tested. If electrically operated, plug in the line cord to the type in the same plane provides a nearly level sensitivity limited by
of socket recommended by the manufacturer. the elastic properties of the weighbeam. To measure the
E1270 − 88 (2008)
relationship of sensitivity to load, repeat 8.1 at various loads ment is not especially useful since pivot conditions can be
from zero to the capacity and plot sensitivity as a function of better measured as part of a measurement of precision. In the
load. case of a damped balance, this measurement may be useful
insofarasitmaybeusedtocharacterizetheeffectivenessofthe
8.3 Lever Arm Ratio—Equal arm balances are not usually
damping mechanism. Useful damping is that which produces a
used as direct-reading instruments. Rather, they are used as
steady reading in one or two oscillations. Since the damping
comparators using standard weights for reference. For preci-
ratio is usually a function of the load, damper mechanisms are
sion measurements such as weight calibration, the measuring
usually set at some compromise value or are adjusted so that
technique eliminates errors due to the inequality of arm-
they may be optimized for a given load. Release the beam and
lengths. For relative measurements such as quantitative chemi-
observe consecutive indications in the same direction. Com-
cal analysis, if the inequality is considered to be in a constant
pute the damping ratio r as follows:
D
ratio,theresultsofanumberofweighingsonthesamebalance
r 5 d /d (4)
will have a common multiplier (L /L ) and the resulting
D 1 2
1 2
computationsrepresenting,perhaps,fractionalcomponentsofa
where:
compound will be mathematically correct. If there is a need to
d = first turning point, and
determine an absolute mass value from a single direct
d = second turning point in the same direction.
measurement, the lever ratio must be determined.
8.5 Period of Oscillation—The time required to make one
8.3.1 Observe the rest point with empty weigh pans.
full oscillation is an indicator of the time required to make a
8.3.2 Placeapproximatelyequalweightsoneachpanwhose
measurement either for a damped or undamped balance. The
value is near the capacity of the balance.
period is a function of the magnitude of the moving mass and
8.3.3 Observe the new rest point.
of the sensitivity of the balance. For a given arm length,
8.3.4 Transpose the weights to the opposite pans and ob-
balances of high sensitivity have longer periods.
serve the rest point.
8.5.1 For the convenience of the user, high sensitivity
8.3.5 Measure the sensitivity at this load from 8.1.
balances may have means for magnifying the indication thus
8.3.6 Compute the lever ratio as follows:
allowingthesensitivitytobeloweredandtheperiodshortened.
M
However, such an approach must be used with care since such
r 5 (2)
L
M1S ~d 2 ~d 1d !/2!
1 1 2
magnification means smaller angles of deflection are measured
and the balance becomes more sensitive to the tilting which
where:
might occur on a bench or floor of insufficient rigidity.
r = lever ratio,
L
8.5.2 Placeweightsofequalvalueonthepansatornearthe
S = sensitivity in (mass units)/(scale division),
load of interest. Release the beam and start the stop watch as
d = rest point of empty pans in 8.3.1 (scale
the direction of the indicator changes. Count several turning
divisions),
points and stop the watch after n periods of oscillation.
d = rest point from 8.3.3,
d = rest point from 8.3.4, and Calculate the period, p:
M = mass of test weights (the value on each pan).
p 5 t/n (5)
Example: =
M = 100 g (on each pan) where:
S = 1.85 mg/div.=0.00185 g/div.
1 t = total elapsed time, and
d = +1.5 div.
n = number of turning points.
d = +8.5 div.
8.6 Precision—The term ’precision’ in weighing usually
d = −2.5 div.
means repeatability. In quantitative terms, it refers to expected
r =
L
uncertainty of a single reading. The usual method for deter-
10010.00185~1.5 2 ~8.5 2 2.5!/2!
mining the precision is to compare the results of a series of
measurements by some statistical treatment and to compute
r = 1.0000278.
L
some value which gives the user an estimate of the potential
8.3.7 A ratio greater than 1 indicates that the left lever is
uncertainty of a single reading. A common technique is to
longer and if a sample is placed on the left pan and standard
compute the standard deviation (s) of a series of observations.
weights on the right, the “true’’ weight is:
The larger the number of observations the better; but 10 is
W 5 W /r (3) usuallyenough.Assuminganormaldistributionofdata,3swill
T I L
represent with a high degree of certainty the maximum
where:
anticipated error of a single measurement. One convenient
W = indicated weight.
I
measurement model is a series of double substitutions.
8.6.1 Place a weight, ‘A’, considered to be the standard, on
8.4 Damping Ratio—An undamped balance will oscillate
aroundarestpointwithdecreasingamplitudeofoscillationdue the left pan and a tare weight of the same nominal value on the
right pan. Observe the balance indication (A ).
toairdampingontheweightpansandtofrictioninthebearing
system. The ratio of the amplitude of one oscillation to that of 8.6.2 Removethestandardfromtheleftpanandplaceatest
...

This document is not anASTM standard and is intended only to provide the user of anASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation:E1270–88(Reapproved2003) Designation:E1270–88(Reapproved2008)
Standard Test Method for
Equal Arm Balances
This standard is issued under the fixed designation E1270; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
This 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 very
high precision weighing of larger samples (usually greater than 1 kg) as well as objects with large
buoyancy (such as gas bottles). Balances of this type can range from simple instruments of moderate
precision (1:10000) to extremely high precision devices with precision of 1:10000000 or better. A
number of accessory devices may be included for assisting in the weighing process. These devices
may contribute to errors as well as can the basic lever mechanism.This method is designed to test the
entire instrument including the accessories.
1. Scope
1.1 This test method can be used for testing equal-arm balances of any capacity and sensitivity. The testing procedure should
enable the user to characterize his instrument sufficiently to determine whether or not it is suitable for the purpose for 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 accessory dampers),
1.2.4 Period of oscillation,
1.2.5 Precision, and
1.2.6 Linearity and calibration of accessory devices that provide on-scale indication of weight.
1.3 This standard does not purport to address all of the safety concerns associated with its use. It is the responsibility of the
user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations
prior to use.
2. Referenced Documents
2.1 ASTM Standards:
E617 Specification for Laboratory Weights and Precision Mass Standards
3. Terminology
3.1 Definitions of Terms Specific to This Standard:
3.1.1 capacity—maximum load recommended by the manufacturer. Usually, the capacity refers to the maximum load on each
pan simultaneously.
3.1.2 readability—value of the smallest unit of weight which can be read. This may include the estimation of some fraction 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 cause a change of indication which can be determined by the user. This
may be independent of the readability because of the choice of the reading device used. For example, a magnifying glass may be
used in conjunction with a reading scale to observe a sensitivity not readily determined without the magnifying glass.
3.1.4 precision—repeatability of the balance indication with the same load under essentially the same conditions. The more
This test method is under the jurisdiction of ASTM Committee E41 on Laboratory Apparatus and is the direct responsibility of Subcommittee E41.06 on Weighing
Devices.
Current edition approved Sept. 30, 1988. Published November 1988.
Current edition approved Nov. 1, 2008. Published January 2009. Originally approved in 1988. Last previous edition approved in 2003 as E1270–88 (2003).
ForreferencedASTMstandards,visittheASTMwebsite,www.astm.org,[e-mail] Annual Book of ASTM Standards
, Vol 14.02.volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E1270–88 (2008)
closely the measurements are grouped, the smaller the index of precision will be. The precision should be measured under
environmental conditions that represent the conditions under which the balance is normally used.
3.1.5 accuracy—degree of agreement of the measurement with the true value of the magnitude of the quantity measured.
3.1.6 linearity—characteristic of a direct reading device. If a device is linear, calibration at 2 points (for example, 0 and
full-scale) calibrates the device (for example, 2 points determine a straight line); if a device is nonlinear, additional points are
needed (perhaps a great many).
3.1.7 standard weight—any weight whose mass is given. Since weights are not always available with documented corrections,
weights defined by class (see Specification E617) may be used if the class has sufficiently small tolerance limits and there is an
understanding that errors perceived as being instrumental could be attributed to incorrectly adjusted weights.
3.1.8 off-center errors—differences in indicated weight when a sample is shifted to various positions on the weighing area 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 a standard
weightequaltothefull-scalerangeofthedeviceisplacedonthesamplepan.Usually,somemeansisprovidedbythemanufacturer
to adjust the full-scale to match the weight of the standard.
4. Summary of Test Method
4.1 Throughout this test method, the instrument is to be used in the manner for which it is intended by the manufacturer. All
measurements are made with weights whose values are sufficiently well known for the purpose of the user. The nominal value of
the weights used will be determined by the capacity and rated sensitivity of the balance as well as by the resolution and range of
the accessory reading devices.
5. Significance and Use
5.1 This test method should enable the user of the balance to interpret data determined thereon in terms of accuracy and
precision. It should be helpful in using a particular instrument to best advantage. Weaknesses as well as strengths should become
apparent. It is not the intention of this test method to compare similar instruments of different manufacture but rather to assist in
choosing an instrument which will meet the needs of the user.
6. Apparatus
1 1 3
6.1 Standard Weights—Individual or summations of weights equal to approximately ⁄4 , ⁄2 , ⁄4 and the total capacity.
6.2 Tare Weights—Weights of the same denominations as the standard weights but not necessarily calibrated.
6.3 Calibrating Weights—Balancesequippedwithaccessorydevicessuchasslidingbeamweights,chainweights,opticalscales
or electrical transducers require small standard weights equal to the full-scale reading as well as smaller weights suitable for
calibrating intermediate points between the zero and full-scale points of the devices. Summations of small standards can be used
for this purpose.
6.4 Stop Watch:
6.5 A room-temperature thermometer with a resolution of at least 1°C.
7. Preparation of Apparatus
7.1 Place the instrument in the location at which it is to be tested. If electrically operated, plug in the line cord to the type of
socket recommended by the manufacturer.
7.2 Place the standard weights near (or within) the instrument.
7.3 Place the thermometer on the bench in position so that it may be read without being touched.
7.4 Make sure that the instrument and test weights are clean.
7.5 Allowtheinstrumentandweightstositundisturbedsufficientlylongtoreachtemperatureequilibriumwiththesurrounding
area. In the case of a large, high precision instrument in a controlled environment, it may be necessary to allow 24 h for such
equilibrium.
7.6 Read the manufacturers instructions carefully. During each step of the test procedure, the instrument should be used in the
manner recommended by the manufacturer.
8. Procedure
8.1 Sensitivity—Thesensitivitycanbemeasuredatanumberofdifferentloadsfromzerotothecapacitytoprovideasensitivity
versus load curve, or, it can be measured at the load of particular interest. This test applies to balances which have a null position
indicator. Balances which are direct reading in the 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 the selected load.
8.1.2 Observe the indication. If necessary, place small weights on the appropriate sample pan to obtain an indication near zero.
8.1.3 Place a small weight on the left pan sufficient to change the indication about ⁄2 scale of the on-scale range. Record the
indication as d .
8.1.4 Remove the small weight and place it on the right pan and record the new indication as d (remember that for indicator
scales graduated either side of center zero, indications to the left are recorded as negative values).
E1270–88 (2008)
8.1.5 Compute the sensitivity as follows:
S 52 3 W/~d 2 d ! (1)
1 2
where:
S = sensitivity in mass units/scale division, and
W = mass of small test weight.
Example: d =5.5 div.
d =−5.3 div.
W =10mg
S =2 310/(5.5−(−5.3))=1.85 mg/div.
8.2 Sensitivity as a Function of Load— Balance designs vary but in the case of high precision balances, the manufacturer
usually tries to provide a nearly level sensitivity at all loads. This is accomplished by the position of the plane determined by the
terminal pivots in relation to the central pivot. If this plane is lower than the central pivot, the sensitivity will decrease with
increasing load. Conversely, if the plane is higher than the central pivot, the sensitivity will increase with increasing load and can
reach a state of instability if the center of gravity goes above the center pivot. Placing all of the pivots in the same plane provides
a nearly level sensitivity limited by the elastic properties of the weighbeam. To measure the relationship of sensitivity to load,
repeat 8.1 at various loads from zero to the capacity and plot sensitivity as a function of load.
8.3 Lever Arm Ratio—Equal arm balances are not usually used as direct-reading instruments. Rather, they are used as
comparatorsusingstandardweightsforreference.Forprecisionmeasurementssuchasweightcalibration,themeasuringtechnique
eliminates errors due to the inequality of arm-lengths. For relative measurements such as quantitative chemical analysis, if the
inequality is considered to be in a constant ratio, the results of a number of weighings on the same balance will have a common
multiplier (L /L ) and the resulting computations representing, perhaps, fractional components of a compound will be
1 2
mathematically correct. If there is a need to determine an absolute mass value from a single direct measurement, 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 whose value 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 observe the rest point.
8.3.5 Measure the sensitivity at this load from 8.1.
8.3.6 Compute the lever ratio as follows:
M
r 5 (2)
L
M 1 S ~d 2 ~d 1 d !/2!
1 1 2
where:
r = lever ratio,
L
S = sensitivity in (mass units)/(scale division),
d = rest point of empty pans in 8.3.1 (scale divisions),
d = rest point from 8.3.3,
d = rest point from 8.3.4, and
M = mass of test weights (the value on each pan).
Example: =
M = 100 g (on each pan)
S = 1.85 mg/div.=0.00185 g/div.
d = +1.5 div.
d = +8.5 div.
d = −2.5 div.
r =
L
100 10.00185~1.5 2 ~8.5 22.5!/2!
r = 1.0000278.
L
8.3.7 Aratio greater than 1 indicates that the left lever is longer and if a sample is placed on the left pan and standard weights
on the right, the “true’’ weight is:
W 5 W/r (3)
T I L
where:
W = indicated weight.
I
8.4 Damping Ratio—An undamped balance will oscillate around a rest point with decreasing amplitude of oscillation due to
air damping on the weight pans and to friction in the bearing system. The ratio of the amplitude of one oscillation to that of the
next may be a measure of several characteristics of the balance. Since these cannot easily be separated, this measurement is not
E1270–88 (2008)
especially useful since pivot conditions can be better measured as part of a measurement of precision. In the case of a damped
balance, this measurement may be useful insofar as it may be used to characterize the effectiveness of the damping mechanism.
Useful damping is that which produces a steady reading in one or two oscillations. Since the damping ratio is usually a function
of the load, damper mechanisms are usually set at some compromise value or are adjusted so that they may be optimized for a
givenload.Releasethebeamandobserveconsecutiveindicationsinthesamedirection.Computethedampingratio r asfollows:
D
r 5 d /d (4)
D 1 2
where:
d = first turning point, and
d = second turning point in the same direction.
8.5 Period of Oscillation—The time required to make one full oscillation is an indicator of the time required to make a
measurement either for a damped or undamped balance. The period is a function of the magnitude of the moving mass and of 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 sensitivity balances may have means for magnifying the indication thus allowing
thesensitivitytobeloweredandtheperiodshortened.However,suchanapproachmustbeusedwithcaresincesuchmagnification
means smaller angles of deflection are measured and the balance becomes more sensitive to the tilting which might occur on a
bench or floor of insufficient rigidity.
8.5.2 Place weights of equal value on the pans at or near the load of interest. Release the beam and start the stop watch as the
direction of the indicator changes. Count several turning points and stop the watch after n periods of oscillation. Calculate the
period, p:
p 5 t/n (5)
where:
t = total elapsed time, and
n = number of turning points.
8.6 Precision—The term 8precision’ in weighing usually means repeatability. In quantitative terms, it refers to expected
uncertainty of a single reading. The usual method for determining the precision is to compare the results of a series of
measurements by some statistical treatment and to compute some value which gives the user an estimate of the potential
uncertaintyofasinglereading.Acommontechniqueist
...