Whenever someone measures a physical quantity -- for example, a length measured by putting a ruler beside it or a mass measured by comparing it with known masses on a balance -- there is some range of uncertainty in the result. No quantity is ever measured with perfect precision. In the examples cited, one can imagine some reasons for the uncertainty. Limitations of eyesight make it impossible to tell precisely where the end of the object falls on the ruler. If the length is read to be 10.25 cm, it could actually be 10.255 cm or 10.245 cm and look exactly the same to the eye. Similarly, there will be a range within which mass may be added or subtracted from the balance pan without upsetting the appearance of balance. Such effects will lead with equal probability to measurements that are too high or too low, and a single observer will probably get different values within the range of uncertainty for successive measurements. Errors of this sort are referred to as random. There may also be sources of systematic error which lead consistently to a number which is too large or too small. This could happen, for instance, with a wooden ruler which had absorbed water on a humid day and increased its length or with a balance which had not been properly balanced when both pans were empty. Systematic errors are more difficult to detect than random errors because they do not produce different values for successive measurements. Nevertheless, the validity and usefulness of an experiment depends critically on the proper assessment of systematic errors.