Errors

Errors. Observations are of various kinds, and require different senses. Thus observations of length are most generally done by sight; in measuring the length of a table, a scale or rule of known length is placed in contact with the table and a comparison effected by sight. They may be done by the sense of touch also; if a bar is to be turned in a lathe so as to be exactly one inch in diameter, it is convenient to test its diameter with a pair of callipers opened out to one inch, and the sense of touch helps to compare the two. Again, observations of time are usually done by sound, though other means may also be adopted. But on whatever sense the observation depends, absolute accuracy cannot be obtained. The sense is not sufficiently refined, nor are the instruments. The first introduces what are called errors of observation, the second errors of adjustment. The latter may be eliminated when careful testing of the instrument has been effected and an estimate of their errors obtained; or they may, in a sense, eliminate themselves by repeating the observation in different ways and taking the average result. Certain errors of observation are fortuitous, and there is as much likelihood of an error one way as the other. Thus if a hundred average men take a measurement of the same length to one-tenth of an inch it will probably be found that they differ among themselves as to the correct result. But there will be about as many below the average as there are above. The average is the best result that can be taken, though the fact that there is a difference of result shows that this answer cannot be taken as perfectly correct. The majority of the hundred answers will closely approximate to the average, and large errors will occur in but few cases. The method of Least Squares (q.v.) shows to what degree of accuracy this average may be expected to be correct. Personal errors that are not fortuitous generally admit of elimination in the same way as do errors of adjustment, i.e. either by determining the personal equation (q.v.) of the observer, or by repeating the observation in different ways and taking the average.