Accuracy of Measurement

The degree of accuracy to which measurements can be carried varies very much with different experiments. It is usual to estimate the limit of accuracy as a fractional part or percentage of the quantity measured.

Thus by a good balance a weighing can be carried out to a tenth of a milligramme; this, for a body weighing about 100 grammes, is as far as one part in a million, or 0.0001 percent - an accuracy of very high order. The measurement of a large angle by the spectrometer is likewise very accurate; thus with a vernier reading to 20", an angle of 45° can be read to one part in four thousand, or 0.025 percent. On the other hand, measurements of temperature cannot, without great care, be carried to a greater degree of accuracy than one part in 'a hundred, or 1 percent, and sometimes do not reach that. A length measurement often reaches about one part in ten thousand. For most of the experiments which are described in this work an accuracy of one part in a thousand is ample, indeed generally more than sufficient.

It is further to be remarked that, if several quantities have to be observed for one experiment, some of them may be capable of much more accurate determination than others. It is, as a general rule, useless to carry the accuracy of the former beyond the possible degree of accuracy of the latter. Thus, in determining specific heats, we make some weighings and measure some temperatures. It is useless to determine the weights to a greater degree of accuracy than one part in a thousand, as the accuracy of the result will not reach that limit in consequence of the inaccuracy of the temperature measurements. In some cases it is necessary that one measurement should be carried out more accurately than others in order that the errors in the result may be all of the same order. The reason for this will be seen on p. 48.