For example in the Atwood's machine experiment to measure g you are asked to measure time five times for a given distance of fall s . Frequently, the result of an experiment will not be measured directly. A first thought might be that the error in Z would be just the sum of the errors in A and B . This idea can be used to derive a general rule. Similarly the perturbation in Z due to a perturbation in B is, .
Errors combine in the same way for both addition and subtraction.
For example, . It should be noted that since the above applies only when the two measured quantities are independent of each other it does not apply when, for example, one physical quantity is measured and what is required is its square. These rules may be compounded for more complicated situations. The Study of Uncertainties if Physical Measurements . University Science Books, 1982.