we read 17.5 on the index. If we continue this series of readings for several more
swings of the pointer we can compile the following table:
Sum .... 6.9
Sum .... 34.9
Average .... 2.3
Average .... 17.4
Notice that all turning points are read to the nearest 0.1 division on the index. The average right
turning points are easily found by adding all of the left readings, adding all of the right readings,
and then dividing these sums by the number of readings - in this case by three and two
respectively. The rest point of the balance can be found by adding the average left reading to the
average right reading and dividing by two.
Now you can see the importance of reading the first and last turning points on the same side of
the index. If our final reading had been 17.4 the calculated rest point would have been somewhat
less than the true rest point.
(3) Another term that needs defining is sensitivity reciprocal. This means the
amount of mass necessary to change the rest point one full scale division.
Sensitivity reciprocal is a ratio of mass per scale division (mass/div). To
determine the sensitivity reciprocal, the rest point of the balance is first found.
Then a very small weight is placed on one pan and the new rest point calculated.
Record the difference between the two rest points and then divide the size of the
weight by the difference in rest points. This gives the weight per division. For
instance let's say the initial rest point was 9.87 on the index. When a five
milligram weight was placed on one pan the rest point then became 13.50.
Between the two rest points there is a difference of 13.50 minus 9.87 which
equals 3.63 divisions. Then by dividing 3.63 into 5.0 mg we find the sensitivity
reciprocal to be 1.38 mg per division. This sensitivity can be used when making
measurements and should be checked with each weighing as it will change with
the load. An unloaded balance will have a much higher sensitivity than a loaded
balance since there is less friction on the knife edges.
7. Measurement Methods
a. We have discussed the equal arm balance, the standards used for measuring mass, so
now let's discuss the methods of measurement. There are three methods used: the direct
method, the substitution method, and the transposition method. The least accurate of the
methods is the direct method, however it is also the fastest. The direct method is
accomplished by first determining the rest point of the balance. After this is done, then
the test instrument (TI) is placed on one pan and the standard is placed on the other.
(NOTE: The test instrument is the instrument under test.) Weight is then added to the
lighter side to bring the pointer back to the original rest point. The amount of weight