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Errors and Corrections

The determination of an additional figure in a number representing the magnitude of a physical quantity generally involves a very great increase in the care and labour which must be bestowed on the determination. To obtain some idea of the reason for this, let us take, as an example, the case of determining the mass of a body of about 100 grammes. By an ordinary commercial balance the mass of a body can be easily and rapidly determined to 1 gramme, say 103 grammes. With a better arranged balance we may show that 103.25 is a more accurate representation of the mass. We may then use a very sensitive chemical balance which shows a difference of mass of 0.1 mgm., but which requires a good deal of time and care in its use, and get a value 103.2537 grammes as the mass. But, if now we make another similar determination with another balance, or even with the same balance, at a different time, we may find the result is not the same, but, say, 103.2546 grammes. We have thus, by the sensitive balance, carried the measurement two decimal places further, but have got from two observations two different results, and have, therefore, to decide whether either of these represents the mass of the body, and, if so, which. Experience has shown that some, at any rate, of the difference may be due to the balance not being in adjustment, and another part to the fact that the body is weighed in air and not in vacuo. The observed weighings may contain errors due to these causes. The effects of these causes on the weighings can be calculated when the ratio of the lengths of the arms and other facts about the balance have been determined, and when the state of the air as to pressure, temperature, and moisture is known (see Correction of Weighings for the Buoyancy of the Air).

We may thus, by a series of auxiliary observations, determine a correction to the observed weighing corresponding to each known possible error. When the observations are thus corrected they will probably be very much closer. Suppose them to be 103.2543 and 103.2542.

Last Update: 2011-03-15