7
Instrumentation Ralph O. Leonard The Perkin-Elmer Corp. Norwalk, Conn. 06856 ^ Electronic Laboratory Balances It may be questionable whether the balance is still the most ubiquitous in- strument in today's chemistry labora- tory, but it is certainly the oldest. One from Egypt is said to be dated around 5 000 B.C. (1 ) and works on the same principles as most of our modern labo- ratory balances. The unknown weight is simply balanced out with a known force. That's what it was all about some 7 000 years ago, and we're still doing it today. Most improvements since that time have been for better accuracy and op- erating convenience. Knife edges ap- peared in the 16th century and gave better sensitivity. Pointers and scales were then added for easier measure- ments. Riders, adjustable chains, and keyboard weight changing systems made it easier to balance out smaller weights. Air dash pots and eddy cur- rent devices were then added to damp out swinging beams. Weighing methods have been im- proved too. There were "transposi- tion" weighing, then "complimentary" weighing, and finally "substitution" weighing. The last, introduced in 1884, maintained constant balance sensitivi- ty with changing loads, eliminated beam arm errors, and was, in general, the best technique for both conve- nience and performance. Substitution balances did not be- come popular until 1946 when Erhard Mettler introduced the first practical commercial model into the rapidly ex- panding postwar scientific market. These were more expensive than two- pan balances, but their convenience made them popular, and they have now replaced equal-arm balances in most chemistry laboratories. Figure 1. Simplified block diagram of general type of closed-loop servo system used in many electronic balances In 1955 there occurred another sig- nificant introduction, the precision top-loading balance. Due to their de- sign, top-loaders generally sacrifice at least one order of magnitude of read- ability, but their tremendous conve- nience has now made them the most popular precision balances ever of- fered. For those interested in further stud- ies of these mechanical balances, there are several good reviews of early histo- ry (2, 3), recent history (4-6), and theory, use, performance, and the many other factors influencing mass measurement (7-12). New "Way to Weigh" All of the balances discussed so far have been based on comparisons of weights. However, in 1895, K. Ang- strom (13), son of A. J. Angstrom of the Angstrom unit, published a de- scription of the earliest known balance which utilized electromagnetic princi- ples. His objective was to develop a re- storing force (to balance out the load on the sample pan) other than gravity weights. He hung a magnet from one end of the beam into a coil, adjusted the current in the coil to restore the beam to its zero or null position, and measured the current with a mirror galvanometer. The current was rea- sonably linear with weight, and a new "way to weigh" had been developed. Many similar balances have ap- peared in the literature over the years. The majority were either for micro- weighing applications, where handling of the tiny weights is a serious prob- lem (14, 15), or for recording of weight ANALYTICAL CHEMISTRY, VOL. 48, NO. 11, SEPTEMBER 1976 · 879 A

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Page 1: Electronic Laboratory Balances

Instrumentation Ralph O. Leonard The Perkin-Elmer Corp. Norwalk, Conn. 06856

^ Electronic Laboratory Balances

It may be questionable whether the balance is still the most ubiquitous in­strument in today's chemistry labora­tory, but it is certainly the oldest. One from Egypt is said to be dated around 5 000 B.C. (1 ) and works on the same principles as most of our modern labo­ratory balances. The unknown weight is simply balanced out with a known force. That's what it was all about some 7 000 years ago, and we're still doing it today.

Most improvements since that time have been for better accuracy and op­erating convenience. Knife edges ap­peared in the 16th century and gave better sensitivity. Pointers and scales were then added for easier measure­ments. Riders, adjustable chains, and keyboard weight changing systems made it easier to balance out smaller weights. Air dash pots and eddy cur-

rent devices were then added to damp out swinging beams.

Weighing methods have been im­proved too. There were "transposi­tion" weighing, then "complimentary" weighing, and finally "substitution" weighing. The last, introduced in 1884, maintained constant balance sensitivi­ty with changing loads, eliminated beam arm errors, and was, in general, the best technique for both conve­nience and performance.

Substitution balances did not be­come popular until 1946 when Erhard Mettler introduced the first practical commercial model into the rapidly ex­panding postwar scientific market. These were more expensive than two-pan balances, but their convenience made them popular, and they have now replaced equal-arm balances in most chemistry laboratories.

Figure 1. Simplif ied block diagram of general type of closed-loop servo system used in many electronic balances

In 1955 there occurred another sig­nificant introduction, the precision top-loading balance. Due to their de­sign, top-loaders generally sacrifice at least one order of magnitude of read­ability, but their tremendous conve­nience has now made them the most popular precision balances ever of­fered.

For those interested in further stud­ies of these mechanical balances, there are several good reviews of early histo­ry (2, 3), recent history (4-6), and theory, use, performance, and the many other factors influencing mass measurement (7-12).

N e w " W a y to W e i g h "

All of the balances discussed so far have been based on comparisons of weights. However, in 1895, K. Ang­strom (13), son of A. J. Angstrom of the Angstrom unit, published a de­scription of the earliest known balance which utilized electromagnetic princi­ples. His objective was to develop a re­storing force (to balance out the load on the sample pan) other than gravity weights. He hung a magnet from one end of the beam into a coil, adjusted the current in the coil to restore the beam to its zero or null position, and measured the current with a mirror galvanometer. The current was rea­sonably linear with weight, and a new "way to weigh" had been developed.

Many similar balances have ap­peared in the literature over the years. The majority were either for micro-weighing applications, where handling of the tiny weights is a serious prob­lem (14, 15), or for recording of weight

ANALYTICAL CHEMISTRY, VOL. 48, NO. 11, SEPTEMBER 1976 · 879 A

Page 2: Electronic Laboratory Balances

Figure 2. Model AD-2Z Autobalance shown in use in a fume hood with controls and display mounted outside

Figure 3. Functional block diagram of Model AD-2Z Auto­balance 1) Photodiode detector, 2) beam flag, 3) light emitting diode, 4) LED emission controller, 5) servo amplifier, 6) beam, 7) range selection, 8) autoranging, 9) amplifier, 10) filters, 11) amplifier, 12) electronic digital display, 13) temper­ature compensation, 14) coarse and fine zero, 15) calibration, 16) autozero, 17) magnet, 18) coil, 19) central bearing ribbon, 20) torque motor, 21) coun­terweight bearing ribbon, 22) sample bearing ribbon

changes in vacuum or controlled at­mospheres for thermal gravimetric studies, adsorption studies, magnetic susceptibility, etc. (10, 16), where the advantages of a continuous electronic control and readout are obvious.

The routine availability of "off the shelf" commercial electronic analyti­cal and top-loading balances for scien­tific applications began in the late 1960's and early 1970's.

How They Work As a general rule, most balances,

whether mechanical or electronic, have a position sensor and a restoring force. In mechanical balances the posi­tion sensor is the pointer, the pointer scale, a magnifying glass, and the op­erator's eye, and the restoring force is the set of weights. Thus, the unknown weight is determined by precise com­parison to known weights.

In electronic balances, however, the position sensor is usually an electronic device such as an LVDT (linear vari­able differential transformer), a vari­able capacitor, electro-optical sensor, variable reluctance Ε-core, etc., and the restoring force is usually a force coil type linear force generator or a torque motor. Thus, the unknown weight is determined by precise com­parison to a variable electromagnetic force (which has been calibrated by comparison to a known weight).

Whereas earlier balances utilized deflection, most modern electronic laboratory balances are null-restoring devices. The deflection caused by the unknown weight is sensed by an elec­tronic position sensor, and a propor­tional force of opposite polarity is ap­plied through an electromagnetic force generating device to restore the sys­tem to a null. The current in this de­vice can then be amplified and dis­played as an analog of weight. There­fore, most of these balances are simple closed-loop, electromechanical, servo

devices (Figure 1). For descriptions and analyses of the mechanics of these balances, see Zimmerer (17) and Gast (10).

The Hybrids The first successful commercial

electronic balances (14) were, in a sense, hybrids. That is, they were combinations of mechanical and elec­tronic systems.

For example, the commercial ul-tramicro balances now offered by Per-kin-Elmer (Figures 2 and 3) and oth­ers are good, if highly automated, il­lustrations of this technique. General­ly, they use a fairly conventional beam design with sample and counterweight pans. However, the restoring force is provided not only by the counter­weights but also by a torque motor mounted at the central fulcrum. This technique has made it possible to weigh small samples as easily as large samples, and these balances are now

common laboratory tools. The torque motor suffers from a

mechanical disadvantage in this loca­tion and is impractical for use in bal­ances designed for higher loads. Hy­brid beam-type analytical and top-loading balances with capacities of 100 g or more required different tech­niques.

The EA-1 from the Torsion Balance Co. was probably the earliest (about 1965) commercially successful hybrid balance of this type. It uses a standard balance beam with torsion band pivots and with a substitution-type weight changing system, but instead of the typical optical scale, it has an "E-core" differential position sensor to detect and a force coil to restore any residual unbalance. Note that this is an "open loop" balance in which the operator manually adjusts the current to compensate for the weight and to restore the beam to null.

(Continued on page 884 A)

Figure 4. Schematic representation of top-loading hybrid balance 1) Sample pan, 2) beam—note parallelogram bearing configuration, 3) substitution weights, 4) photo-optical position sensor, 5) amplifier, 6) force coil, 7) flexible connector, 8) analog output

880 A · ANALYTICAL CHEMISTRY, VOL. 48, NO. 11 , SEPTEMBER 1976

Page 3: Electronic Laboratory Balances

Figure 5. Electronic top-loading balance in use in food laboratory Up to 35 different compounds are weighed and tared to produce a required mixture of flavors

ΒΗΠΗΠΙΠΙΜΙΙΙΙΙΜΒΒΚ^ Figure 6. Schematic representation of top-loading hybrid balance with capaci­tance-type position detector and conductive knife-edge bearings (not illustrated) 1) Balance pan, 2) pivot rod, 3) secondary knife edges, 4) primary knife edges, 5) balance beam, 6) force coil, 7) magnet, 8) null sensor, 9) error signal, 10) position, 11) coil current, 12) control and coil drive electronics, 13) sampling and analog electronics, 14) power supply, 15) analog signal, 16) display electronics (A/D converter), 17) 5-digit display

Shortly thereafter, both Mettler and Sartorius converted certain of their s tandard analytical balances and top-loaders into hybrids by adding beam position sensing and automatic force-coil restoration (Figures 4 and 5). They are "closed-loop" but are ba­sically modifications of s tandard me­chanical balances.

At about the same time, Ainsworth introduced their Digimetric balances (now manufactured by the Digimetric Co., a division of Sybron Corp.). These are top-loading balances using a dif­ferential capacitor as the position sen­sor and a force coil as the restoring de­vice (Figure 6). The Digimetric bal­ances are good examples of the wider dynamic ranges (up to 2 000 000:1 from this company) tha t are available in single hybrid packages, as opposed to the beamless balances to be dis­cussed later.

A new group of hybrids, distin­guished by their low profile, ultramod­ern design, has recently been intro­duced by Voland. They are a unique combination of a beam and flexure pi­vots and feature a " t rue tare", a slid­ing poise which does not subtract from the capacity of the balance.

Several more companies have now added electronic deflection sensors to their mechanical analytical balances to make them easier to read and to provide BCD outputs. Switches on the weight dialing mechanism control the display for the larger digits and the deflection sensor controls for the smaller ones. Using substitution weights can provide even higher dy­namic ranges—Voland claims up to 3 kg to 0.1 mg, or 30 000 000:1, which can be displayed on an eight-digit readout.

This entire group of hybrid balances has proven its utility by its continuing popularity and commercial success. Most of these same balances are still in demand nearly 10 years after their first introductions, and new models are still being introduced, all in spite of the availability of the "pure" elec­tronic balances described in the fol­lowing section. One of the reasons is tha t many of these hybrids offer very wide dynamic ranges similar to the mechanical balances from which they were derived, as well as the many ben­efits of electronic control and display. Thus, there may be a place for these hybrid units in laboratory applications for many more years.

Beamless Electronic Balances A new company called Scientech

was probably the first to achieve com­mercial success with this new ap­proach to the design of electronic bal­ances—virtual elimination of the beam and associated pivot bearings. They placed the sample pan directly

on the movable member of the force coil, which was suspended on flexures, utilized capacitive position detectors, and displayed the coil current as weight.

Mettler 's electronic balances are probably the best known of this type. Their P T and P L series electronic top-loading balances use capacitive and photoelectric detectors and force-coil compensation systems (Figure 7).

Their PS-1200 balance uses an en­tirely different system, one that , to our knowledge, is completely unique in the industry and certainly deserves

special mention. It is a deflection bal­ance, not a null balance, and measures the changing frequencies of vibrating strings in tension and compression as the sample weight deflects supporting flexures. One can sometimes even hear the changing frequencies of the strings (Figure 8)'.

One of the most interesting new de­velopments in beamless balances is the recent offering of a series of new electronic top-loaders by Arbor Labo­ratories. Details of their operation are still proprietary, but they use a newly designed digital control (instead of the

884 A · ANALYTICAL CHEMISTRY, VOL. 48, NO. 1 1 , SEPTEMBER 1976

Page 4: Electronic Laboratory Balances

Figure 7. Schematic representation of "beamless" force coil system used in Met-tler PT balances 1) Magnets, 2) sample pan, 3) coil, 4) capacitive position sensor system, 5) amplifier, 6) automatic tare, 7) display, 8) digital output

ordinary continuously variable analog voltages), a very clever new position sensor, and a modified voice coil sys­tem for restoring the sample pan to a very precise null position. The compa­ny claims that their techniques pro­vide superior performance in several areas, especially linearity. It is certain­ly reasonable to expect that they could offer such advantages, and it will be interesting to watch the progress of this product line.

Sartorius has now introduced their newest line of electronic balances. The 3700 Series is their second generation of beamless electronic balances. They make use of c-mos components which are more compact and use less current than earlier devices. This, and other careful design improvements, result in a smaller package, about one-third the size of earlier balances, thus saving valuable laboratory bench space. It also results in cooler operation, which means that the case does not have to be ventilated and the interior mecha­nisms are not subject to dirt or corro­sion from laboratory atmospheres. Cooler operation could also mean longer life.

At this writing a major price break­through has been achieved by Ains-worth. They have introduced a new electronic balance in a very small package and with a limited range (200-0.01 g) at about one-third to one-half of the price of balances with simi­lar ranges from other manufacturers.

Nearly all of the beamless electronic balances discussed so far use a single touch bar for all operator functions: on, off, and zero (tare).

Advantages and Disadvantages

It is very important to note that, in spite of all the recent activity in the electronic balance field—sales promo­tion, advertising, exhibition, etc.—the

standard mechanical analytical and top-loading substitution balances still outsell the electronic models by a wide margin. There are two conspicuous reasons.

Mechanical laboratory balances have wider weighing ranges. They will probably end up being able to weigh more different things than the elec­tronic balances, which is what most laboratories would seem to want.

Also, electronic balances still have a substantial price disadvantage. Me­chanical utility balances with dynamic ranges similar to some electronic bal­ances can be had for under $100. While mechanical substitution bal­ances now list for around $1000 up to $2500 or so, electronic balances still go for about $1200 up to almost $8000 (with the one new exception men­tioned above).

Therefore, if the mechanical bal­ances generally seem to do more for less money, we should also examine the other side of the coin: What are the reasons for the existence and the rapid growth of electronic balances in this market?

Speed and Convenience. Most electronic balances are substantially faster than comparable mechanical balances, and most of the new ones also have very few controls, so that op­eration is substantially simpler. These advantages were recently presented to the general public on network TV. When the U.S. Government went into the gold selling business, several TV news broadcasts showed gold bars being check-weighed, individually and very rapidly, on an electronic balance.

This application illustrates one of the most important advantages of electronic weighing—serial, repetitive weighings can be made much faster and with fewer errors. With equal-arm balances, weighing was a delicate op­

eration which required lots of pa­tience, manual dexterity, technique, and extensive training in both opera­tion and interpretation for best re­sults. Even substitution balances re­quired repeated arresting and releas­ing of the beam, up and down dialing of weights, index adjustments, and scale interpretations. Most electronic balances, on the other hand, permit the sample to be set on the pan quick­ly and with minimum care, and the weight will almost instantly be indi­cated on an error-free, unambiguous display. If many weighings must be made in a minimum time and/or with minimum skills, the extra cost of the electronic balance becomes well worthwhile.

Environment. Another important advantage of electronic balances is a greatly reduced environmental re­quirement. Steady tables are required, but gone are the marble tables, vibra­tion isolation systems, and constant temperatures which are required for some knife-edge balances. Electronic balances can be used almost any­where.

Automation. Most electronic bal­ances readily lend themselves to auto­mation. For example, automatic tablet weighers for the pharmaceutical in­dustry are offered by several manufac­turers. They will automatically weigh and sort a specified number of sam­ples according to preset high and low limits while transmitt ing the data to a calculator for statistical analysis and printing.

The balances manufactured by Scientech are notable because they are specially designed for repetitive indus­trial weighing applications (as well as for laboratories), and their catalog contains an interesting variety of illus­trations and descriptions such as auto­matic weight counting, remote weigh­ing, live weighing, "on line" impact weighing, batching, conveyor belt weighing, and centrifugal check weighing.

Readouts. Another important ad­vantage is tha t in addition to easy-to-read electronic displays, they will often also have analog and/or digital outputs which can be used with print­ers, calculators, recorders, etc. They can be used for record keeping (opera­tors do not have to write down re­sults), data processing (averages, stan­dard deviations, percentages, etc.), limit alarms (in check weighing), and parts counting.

Balance designers have also taken advantage of the electronic nature of these units to incorporate a number of new features. Many of the following examples are selected from the au­thor's own experience at Perkin-Elmer:

(Continued on page 890 A)

886 A · ANALYTICAL CHEMISTRY, VOL. 8, NO. 11, SEPTEMBER 1976

Page 5: Electronic Laboratory Balances

Figure 8. Schematic representation of "beamless" deflection top-loading balance using "vibration strings" to measure to deflection 1) First oscillator, 2) second oscillator, 3) frequency to weight converter, 4) automatic tare, 5) display, 6) digital output

Electronic Calibration. Simple adjustment of current or voltage vs. a known weight makes it possible to eliminate tedious scale calibrations and sensitivity adjustments which previously required a serviceman.

Ranging. Range switching permits some electronic balances to cover a wider dynamic range than the display would ordinarily permit. Perkin-Elmer has borrowed from voltmeter design and included automatic range switching (Autoranging) to suit the size of the unknown sample, with no assistance required from the operator.

Filtering. Since environmental vi­brations usually appear as electrical noise at the position sensor, it is possi­ble to apply electrical filtering to get a clean readout signal in an adverse en­vironment. Some manufacturers per­mit the amount of filtering to be var­ied to suit the environment and the required sensitivity.

Integration. Animals can be weighed even when they are shifting around on the balance pan, simply by integrating the readings over a period of time. Variable times are offered by some manufacturers.

Temperature Compensation. It is often possible to apply thermistors or other temperature sensitive elements to compensate for all or par t of the temperature coefficient of the balance and its associated electronics.

Electronic Taring. Most modern electronic balances offer a single "Au­to tare" push button to bring the dis­play quickly to zero, with an empty container in place. Perkin-Elmer also offers a "Clear" feature to permit the operator to see the sum of all units on the pan, like the subtotal key on a cal­culator.

Negat ive Readings. Loss of weight or check weights below the s tandards can often be displayed. Also, the nega­tive portion of the display can often be used to extend the useful range of the balance or to read the total tare after the samples and containers have been removed.

Error Signals. Samples too large for the weighing range, too much tare, low-power line voltages, and other error sources can be signaled to the operator, usually by blanking or flash­ing the display.

Ultramicroweighing. The ability to read very small currents which are analogous to very small weights makes possible ultrasensitive balances as low as U T 8 g (18).

Remote Weighing. The controls and display can be out on a bench while the sample and weighing mecha­nism are in a fume hood, a radioactive "ho t" box, a dry box, etc.

Ruggedness . The use of flexures and torsion bands in most electronic balances has eliminated the need for

knife edges and their complex protec­tive arrestment devices. Good knife edges are delicate and must be han­dled with care. Built-in weights can get dirty or get loose. Both knives and weights require regular servicing, which is now unnecessary on beamless or flexure balances. Transportat ion and installation are also much easier.

The advantages listed above accrue largely to the user, but the many ad­vantages to the manufacturers (easier production), distributors (easier dem­onstrations), and service departments (repair by replacing chips) are certain to influence the development and pro­motion efforts applied to these units.

While this paper was being pre­pared, there was a notable decrease in the prices of these balances. Most like­ly, the prices of electronic balances will continue to be lowered over the next few years, and the technology will continue to advance and provide im­proved operation and performance at the same time. As their capabilities per dollar approach and pass the me­chanical and hybrid balances, the pure electronic balances will rapidly be­come ubiquitous laboratory tools like today's mechanical balances.

What to Look for

Over 20 years ago Macurdy et al. published new recommended defini­tions for the terminology used in de­scribing balance performance (19). Standardization of possibly ambigu­ous terms such as sensitivity and read­ability made it much easier for the user to interpret the manufacturer 's literature.

Electronic balances have now reached a state of maturi ty which makes it appropriate to consider a new list of standard definitions. In the ab­

sence of such a list, the following arbi­trary, brief, and unjuried definitions are suggested, solely to help the user understand the performance and op­erating differences between the vari­ous available electronic balances. Note that the specifications listed by the manufacturers (including Perkin-Elmer!) do not necessarily comply with all of these definitions, and in many cases certain of the specifica­tions are not even mentioned by the manufacturer. However, this author believes tha t they are all important parameters in balance selection.

Capacity: The maximum weight which can be placed on the sample pan without interfering with normal operation of the balance.

Tare: Mechanical: the maximum weight which can be balanced out util­izing substitution weights, tare weights on a counterweight pan, or a counterpoise device. Electrical: the maximum weight which can be elec­tronically subtracted from the display. Note: should include a s tatement on the effect, if any, on the weighing ranges.

Weighing Ranges(s): the full scale weights which can be displayed on each available range of the balance readout.

Resolution: the number of counts (bits, units, points) available on the balance display. (For example, 19 999 counts, not 4% digits).

Sensitivity (Readability): the mass value of the smallest digital count.

Precision: the reproducibility of a balance expressed as the s tandard de­viation of a single weighing. When the balance has mechanical taring capa­bility of selectable weight ranges, the largest of the following applies for a given weighing:

890 A · ANALYTICAL CHEMISTRY, VOL. 48, NO. 1 1 , SEPTEMBER 1976

Page 6: Electronic Laboratory Balances

Ultimate Precision: the reproduc­ibility of the balance, expressed in mass units as the standard deviation of a single weighing of a small sample.

Precision as a Fraction of Weighing Range: the reproducibility of the bal­ance on any selectable weight range, which is expressed as a fraction of that range.

Precision as a Fraction of Load: the reproducibility of the balance near its maximum capacity expressed as a

standard deviation as a fraction (such as ppm) of the load when all or a por­tion of the weight of the sample and/ or container has been mechanically tared.

Accuracy: the degree of agreement (not including precision) of the weigh­ing with the true weight, including:

Linearity of the complete balance system, including as necessary, the po­sition sensor, restoring or deflection measuring system, and readout.

Calibration accuracy (or NBS Clas­sification) of any weights used.

Some of these specifications are not applicable to some of the new elec­tronic balances, but where they are applicable, we feel that they should be stated.

Commercial Models of Electronic Balances

The examples discussed in this arti­cle and listed in Table I are not meant

Page 7: Electronic Laboratory Balances

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t o b e all inc lus ive . W e apologize t o a n y m a n u f a c t u r e r s w h o m a y h a v e b e e n n e ­g lec ted . T a b l e I s h o w s on ly a sma l l n u m b e r of t yp ica l e x a m p l e s a n d is in­t e n d e d on ly as a g u i d e for r a n g e s a n d r e a d a b i l i t y vs. p r i ce . C a p a c i t y is a l so l i s ted t o i n d i c a t e if a n d h o w m u c h r a n g e s can be e x t e n d e d by c o u n t e r ­w e i g h t s or s u b s t i t u t i o n we igh t s . F o r c o m p l e t e p r o d u c t l i s t ings p l u s fea­t u r e s a n d o p e r a t i n g a n d p e r f o r m a n c e de t a i l s , t h e i n d i v i d u a l m a n u f a c t u r e r s s h o u l d b e c o n t a c t e d d i r ec t ly . T h e d a t a in T a b l e I a r e e x t r a c t e d f rom i n f o r m a ­t ion p r o v i d e d in m a n u f a c t u r e r s ' p u b ­l i shed p r o m o t i o n a l m a t e r i a l . N o t e s t s h a v e b e e n p e r f o r m e d b y t h e a u t h o r , a n d t h e r e h a v e b e e n n o a t t e m p t s a t c r i t ica l e v a l u a t i o n .

Acknowledgment I a m gra te fu l t o t h e r e p r e s e n t a t i v e s

of t h e b a l a n c e m a n u f a c t u r e r s w h o p r o ­v i d ed t h e d a t a , m a t e r i a l s , a n d s t i m u ­l a t i ng d i s cus s ions n e c e s s a r y for t h e p r e p a r a t i o n of t h i s m a n u s c r i p t .

References (1) C. H. Page and P. Vigoureaux, "The

International Bureau of Weights and Measures 1875-1975", NBS Special Publ. 420, GPO, Washington, D.C., 1975.

(2) R. Vieweg, "Die Waage In Der Kultur-geschichte", "Progress in Vacuum Mi­crobalance Techniques", Vol 1, pp 1-24, Heyden, London, England, 1972.

(3) B. Kisch, "Scales and Weights", Yale Univ. Press, New Haven, Conn., 1965.

(4) J. T. Stock, Anal. Chem., 45 (12), 974A (1973).

(5) J. T. Stock, "Development of the Chemical Balance", HMSO, London, England, 1969.

(6) R. E. Oesper, J. Chem. Educ, 17, 312 (1940).

(7) R. F. Hirsch, ibid., 44 (12), A1023 (1967); 45 (1), A7 (1968).

(8) A. H. Corwin, "Weighing", in "Tech­niques of Organic Chemistry", Vol 1, Par t 1, Chap. 3, 3rd éd., pp 71-130, Weissberger.

(9) M. Randnitz, "Handbuch des Waagen-baues", Verlag Β. Η. Voigt, Berlin, Ger­many, 1955.

(10) T. Cast, J . Phys. E., 7 (11) (1974). (11) L. B. Macurdy, "Measurement of

Mass", in "Treatise on Analytical Chem­istry", I. M. Kolthoff and P. J. Elving, Eds., Pa r t 1, Vol 7, pp 3247-4277, Wiley-Interscience, New York, N.Y., 1959.

(12) A. A. Benedetti-Pichler, "Essentials of Quantitative Analysis", Ronald Press, 1956.

(13) K. Angstrom, "Ofersigt Kongl. Veten-skaps-Akad. Forh.", pp 643-55, 1895.

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(15) A. F. Plant, Ind. Res., 36-39 (July 1971).

(16) S. Gordon, and C. Campbell, Anal. Chem., 32 (5), 271R-89R (1960).

(17) R. W. Zimmerer, "New Techniques in Measuring Mass", in "Measurements and Data", ρ 110, September 1971.

(18) J. Rodder, "An Automated Bakeable Quartz Fiber Vacuum Ultra-microbal-ance", in "Vacuum Microbalance Tech­niques", Vol 8, Plenum, New York, N.Y., 1971.

(19) L.~B. Macurdy, et a\., Anal. Chem., 26 (7), 1190 (July 1954).

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