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weight of the unknown by extracting the square root of the product of the two

weighings. You can approximate the true value of the unknown mass simply by taking

the average of the two weighings (one half the algebraic difference of the two

added to the smaller).

Because our description of the substitution method of

weight measurement was quite extensive, an expansion is not necessary.

3.

ANALYTICAL (MICRO) BALANCE

a. In this section we discuss the conversion of units between the

avoirdupois, troy, and apothecary mass measurement systems.

In addition, we

discuss factors which must be considered in mass measurements.

The factors

discussed are buoyancy volume, density, and sensitivity.

After we establish

relationships between buoyancy and volume and density, we discuss the sensitivity

of a balance. The section ends with explanations of the construction and operation

of a typical analytical balance.

b. Mass Measurement Systems.

Although the kilogram is an

accepted standard

for mass measurements, most manufacturers use the avoirdupois

system, which is

based on the ton, pound, dram, and grain. The basis for any of

the three systems

mentioned is the grain.

The grain, which is the same in all

three systems, is

defined as being equal to .064798918 grams, or conversely:

15.432356 grains = 1 gram

The relative magnitude of the units in each systems follows: