The Absolute Calibration of Weights and Balance for Direct Precision Weighing WILLIAM MARSHALL MncNEVIN
Ohio State University, Columbus, Ohio
T
HIS paper describes a method of calibrating weights and balance so that the absolute weight of an object may be obtained by direct weighing. The limitations of the Richards (1)and modified Richards (2) methods are discussed, and it is suggested that students be taught a method that will be useful in all circumstances. Most students of chemistry learn the method of calibrating weights in which relative values are obtained. It is pointed out by numerous textbook writers that relative values are suficlent for the larger Part of chemical measurements in which ratios are obtained, as, for example, in andysls or in the determination of atomic weights. Widely recommended for this purpose is the calibration procedure of Richards based on the Borda method of weighing by substitution. Eventually the chemist meets the situation where he needs to know the absolute* weight of an object and he must change the method learned earlier. Hopkins, et al. (2),have modified the Richards method by introducing four standard weights, whose absolute among the weights to be 'Omare pared. In this way the absolute values of the weights are obtained. Several textbook writers recommend the use of a single standard weight but as was Pointed out by Hopkins, et al., the tendency for the errors of the Richards method to become additive still remains unless several standard weights of maximum, minimum, and intermediate values are used. Even though the absolute values of the weights are determmed i t is necessary to weigh by substitution in order to obtain the absolute weight of an ohject. Of course, the absolute weight of an object might be obtained by direct weighing with weights calibrated in absolute terms provided one determined the ratio of the anns of the beam and applied the proper correction. W'iiams (3) has Suggested that one determine the actual weight difference corresponding to the deviation of the arm length ratio from unity and simply add or subtract the correction in milligrams. His method does not allow for the possibility that the arm length ratio may change with load although it could be easily modified to do so.
CALIBRATION OF WEIGHTS TO m I G H THE TRUE OR ABSOLUTE WEIGHT OF AN OBJECT
A third method, described below, which seems to have bee,, overlooked by textbook is to brate the weights to wagh directly the true or absolute of an object, one of has been ~ ~ ~ t~ h ~(*)d ~but ~ ,it ,~is not ~ j found in u nor illustrated with the detail that has been frequently in describing the ~ i ~ method, h ~ ~ d ~ The calibration of a working set of weights includes of the rider, since most modern balc~proving~ ances have notched beams, it is necessary for precision to determine the of moving the =ider from one notch to the next in terms of the absolute weight balanced on the left pan. As will be seen, the proposed method for calibrating the weights is a continuation of the procedure used to determine the of rider, The followingmethod of Calibration of rider, notches, and weights assumes the possession of a primary or secondary standard set of weights whose values are known in terms of the absolute standard of mass. It is described for a balance marked with 100 notches from the center to end knife edge and intended to cany a 10-mg. rider. Usually calibrations need be made .dY for the milligram notches and linearity can be for the intermediate markings. ~h~ method of swings is used and the sensitivity of the balance a t different loads be known. CARE OF PRIMARY AND SECONDARY STANDARDS
Since the possession and care of a set of standard weights is a prerequisite, i t is interesting to note the practice instituted and followed for many years by Professor C . W. Foulk and colleagues of the Department of Chemistry a t The Ohio State University. The set of weights calibrated by the Bureau is the primary standard of the laboratory and consists of onepiece gold-plated, whole-gram and fractional weights conforming to class M specifications (with the exception of the 2-mg. weight). The box containing the primary set is kept in a tight cardboard box, sealed and stored in a safe. The com"Absolute" is used here in mntrast to "rplative" weight, but bination of this safe is known only to members of the it does not mean vacuum weight. It means the value given to a st&. The rule is followed that the weights are used weight so that on applying the proper buoyancy correction, the by One of the staff, and they are never Out vacuum weight in terms of the International Kilogram is obtained. of the sight of this person when out of the safe. A 406
~
careful record is kept of the day and hour of removing the weightsirom the safe, of the individual weights that are handled, and the date and hour of returning them to the safe. In addition, the outer box surrounding the weights is sealed with paper seals which are signed and dated. The primary set is used only for the calibration of two secondary standard sets, used in turn for the calibration of the numerous working sets of the laboratory. It is important to note that the secondary standards are compared with the primary standards by the method of substitution rather than by the method described below for the calibration of a working set. Calibration of Rider and Notches. Place the rider on the zero notch and determine the rest point of the empty balance. Place the 1'-mg. weight of the standard set on the left pan, move the rider to the 1.0 notch, and redetermine the rest point. Calculate
first 10-mg. weight of the set to be calibrated on the right pan, move the rider if necessary and redetermine the rest point. As before, calculate 1. The absolute effect of the 10-mg.weight. 2. The correction to be applied to the nominal value of the weight to give the absolute weight of the mass which it balances on the left pan.
Table 2 shows typical data for several weights of a, set. MEANWG OF WEIGHT CORRECTIONS
The weight corrections are used in the customary way. Whether or not the rider corrections are necessary will depend on their magnitudes. For many balances, it will not be necessary. Balance manufacturers make the claim that the notches can he placed more uniformly than can be detected by measurements such as have been described. I t has been observed, however, 1. The "e5ect" of moving the rider in terms of the absolute that the notches wear and corrode appreciably and in time such errors develop as are shown in Table 1. weight on the left pan. 2. The correction that must be applied to the nominal value Attention is called to the practice followed by the of the rider setting in order to give the absolute weight Bureau (5) in reporting two sets of corrections for Class of the mass balanced on the left pan. M weights. One set of corrections refers the weights Move the rider to the 2.0 notch and repeat the observa- to the International Kilogram. When these weight tions. Table 1 gives a typical set of data. For con- corrections are used and buoyancy corrections are to be venience in using the calibrations, prepare a graph calculated, the volumes of the brass weights are detershowing the value of the correction as a function of the mined and used for the whole-gram brass weights and the volume of the platinum weights calculated from the rider position. Connect the points by straight lines. accepted density for platinum. The corrections of the second type given by the Bureau are called "apparent mass corrections" and are the corrections that would Ldf Po" Rid" be found by comparison with brass standards of den( Abmlulc writhhls Rider Ref Effect in ma.) r or it ion point (Mr.) (Ma.) sity 8.4 g. per cm.2 a t O°C., in air whose density is 1.2 0.0 +0.5 mg. per ml. That is, the corrections for the fractional 6.997 1.0 +0.2 i.006 +0:006 platinum weights are so calculated that the corrected 1.988 -0.012 2.0 +0.8 1.997 C0.014 3.0 +0.1 3.014 3.002 value of the platinum weight is equal to the value of a 4.019 +0.019 4.0 10.2 4.010 brass weight which i t will exactly balance in air. The 5.006 +0.006 5.0 +0.6 5.009 +0.015 6.0 +0.4 6.015 6.012 practical consequence of. this is that in the calculation 6.990 -0.010 7.0 +0.9 7.002 0.000 of buoyancy corrections for a mixture of brass and 8.0 +0.2 8.000 7.991 8.999 -0.001 9.0 +12 9.020 platinum weights for which"apparent mass" corrections 10.003 10.0 +0.4 10.006 +0.006 are given, the platinum weights may he regarded as Sensitivity of balance u d = 0.03 mg, per division of the pointer scale. whm the sign of the correetian is plus. the m a s s of the weight balanced on having the density of brass. "Apparent mass" corthe left pan is great- than the nominal value of the rider by theamount rections are therefore simpler to use. indicated. when the sign is minus, the mass is less. The Bureau of Standards ( 6 ) publishes a table of Calibration of Weights. The weights are calibrated "buoyancy reduction values" for converting the value in a similar way. Since i t is necessary to be able to of a weight based on the International Kilogram to the move the rider in either direction, the Richards scheme "apparent mass" basis. As an example of the magniof the "alpha" weight is used. Place a 5-mg. rough tude of this reduction value and the error that would weight, the "alpha" weight, on the left pan, set the result by neglecting it, the Bureau of Standards data rider in the 5.0 position and determine the rest point. give a buoyancy reduction value of +0.044 mg. for Place the 10-mg. standard weight on the left pan, the converting the value of a 500-mg. platinum weight
,,,,
408
JOURNAL OF
from the International Kilogram basis to the "apparent mass" basis. Such an error cannot be overlooked in precision weighing and it should always be made clear on what basis the weights have been calibrated. , Such a situation naturally raises the question as to what allowance, if any, should be made when comparing an aluminum weight with a platinum one for which the Bureau has given the correction with reference to a brass standard. Since the platinum weight is corrected to give the value of the mass of brass it balances in air, i t follows that an aluminum weight which exactly balantes the weight in air will also balance in air a mass of brass *' the corrected of the platinum weight. Hence an aluminum weight which balances exactly a platinum standard weight in air is given the same correction as the standard, Of course if the aluminum weight differs in "apparent mass" from the platinum weight, as shown by a shift in the rest-point, additional correction must be made for the value of the aluminum weight. The same reasoning may be in calibration of the more modern stainless steel wholegram weights with standard brass weights. If the "apparent mass" of the steel weight is expressed in of the brass stand*d' then the Of brass the steel is used in calculating buoyancy corrections weights. CORRECTIONSFOR
12 of Circular No. 3 for the formula for making buoyancy reduction corrections. ADVANTAGES AND
LlMITATIONS
The follo&ng points are in favor of such a method of calibration in contrast with the Richards and modified Richards methods mentioned above: 1. The absolute weight of an object is obtained by d i p weighing. 2. Errors in ordinary direct weighing cancel out in calibration and weighing. 3. I t has been suggested above that the am-length ratio may change with load. The writer has no evidence that this happens but it must be regarded as apossibility. If it does happen, its effect will be the same during calibration as in subsequent weighings and will therefore cancel. 4 . The calibration of each weight is an independent operation and the additive errors of the Richards method are completely avoided,
Two limitations appear in the determination and use of corrections obtained by this method: 1. The use of calibrations obtained in this way will give absolute weights by direct weighing only on the balance for which they were determined. The writer does not consider this a serious objection since in most laboratories where precision weighing is done, the calibration and weighing are performed on the same balance anyway. On all other balances the corrections will give relative weights. I t is important that a careful record of balance and weight serial numbers be made. 2. An abjection that may be very real in a few cases arises in the necessity for having a set of weights that are known in terms of the absolute standard of mass. In this country it bas been a cmmon~cnstomt o send weights to the Bureau of Standards for calibration in terms of the absolute standard. Several thousand such sets of weights now exist in the laboratories of the country and this therefore no longer seems the objection it would have been a t the time of Richards publication. For those unfamiliar with the service offered by the Bureau, a description is given in circular N ~ 3. ( 5 ) .
ATMOSPHERIC DENSITY CHANGE
The reader's attention is to the fact that the apparent mass corrections obtained in the comparison of weights of different densities a t one atmospheric density will not be correctat another. The error is For example, suppose the small but not "apparent masses" of a set of platinum weights have been determined a t the Bureau in an atmospheric pressure approaching 760 mm. If these weights are then shipped to a high altitude, the density of the atmosphere will be less and the platinum weight no longer exactly balances the same mass of brass it did in the heavier atmosphere. Hence it becomes necessary to recalculate the "apparent mass" values from those based on the International Kilogram. For the example of a 500-mg. platinum weight quoted above for which the "apparent 0.044 mg. had to be added to mass" value, a 20 per cent decrease in atmospheric density produces a 20 per cent decrease or 0.009 mg. in the buoyancy reduction term. This is not an insignificant amount in high-precision weighing., It may also be noted that for a 10 per cent variation m atmospheric density a t any one locality the error in buoyancy reduction value may amount in the case of the 500-mg. weight example t o 0.004 mg., which is an amount usually regarded as more than the error in weighing with a microbalance. The reader is referred to Table
CHEMICAL EDUCATION
SUMMARY '
Three methods of calibrating weights are discussed: to giverelative valusof the weights, 2. &libration to give of the weights. 3. Calibration so the weights will weigh directly the absolute value of the object.
The third method is described in detail and is regarded by the writer as the most satisfactory method since it makes possible obtaining weights by direct weighing and can be used in all circumstances. LITERATURE CITED
(I) Rrc~nnos,T. w., J . Am. Chem. SOC., 22,144 (1900). (2) HOPKINS, A. J., J. B. ZINN, AND HARRIETROGERS,J . Am. Chem. Soc., 42, 2528 (1920). (3) WILLIAMS, J. C., J. CHEM.EDUC., 18, 38 (1941). (4) SCOTT, W. W., "Standard Methods of Chemical Analysis," 5th Ed., D. Van Nostrand Company, Inc., New York. ( 5 ) B~~~h",'df,?~,"'CirL1lla~, N ~3.(1918). (6) laid.,p. 75.
Each excellent thing, once well leorned,serves ns a neostrrefor all other knowledge
