c. Principles of Substitution Weighing
(1) In order to adequately describe the substitution balance it is necessary first to look at the principles of an ordinary
equal arm balance. Referring to figure 3, if the equal arm balance shown is correctly made, two equal weights placed
on the pans will show an indication of 0. If weight 2 is heavier than weight 1, the pointer will deflect as shown on
figure 4. However, if the equal arm balance is not correctly made, a direct comparison between two weights cannot be
readily made without introducing significant errors because:
(a) the so-called "equal arms" are not actually equal
(b) the sensitivity of the balance may vary with the size of the weights placed on the pan thus eliminating the
possibility of calibrating the index for direct reading purposes.
(2) Both of these problems can be eliminated by what is known as a Substitution balance. Such a balance is shown
schematically in figure 5. The beam is designed so that the load (1) is just balanced by counter weight (3). In order to
weight a sample, it is placed on the pan (2) and sufficient weight must be removed from (1) until the beam returns to
balance as shown in figure 6. Thus the total load suspended from the beam is the same as it was in figure 5.
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