396 THE PRINCIPLES OF SCIENCE. [CHAP. 



Detection of Constant Errors. 



The Method of Means is absolutely incapable of elimi- 

 nating any error which is always the same, or which always 

 lies in one direction. We sometimes require to be roused 

 from a false feeling of security, and to be urged to take 

 suitable precautions against such occult errors. " It is 

 to the observer," says Gauss, 1 " that belongs the task of 

 carefully removing the causes of constant errors," and this 

 is quite true when the ejror is absolutely constant. When 

 we have made a number of determinations with a certain 

 apparatus or method of measurement, there is a great 

 advantage in altering the arrangement, or even devising 

 some entirely different method of getting estimates of the 

 same quantity. The reason obviously consists in the im- 

 probability that the same error will affect two or more 

 different methods of experiment. If a discrepancy is 

 found to exist, we shall at least be aware of the existence 

 of error, and can take measures for finding in which way 

 it lies. If we can try a considerable number of methods, 

 the probability becomes great that errors constant in one 

 method will be balanced or nearly so by errors of an op- 

 posite effect in the others. Suppose that there be three 

 different methods each affected by an error of equal 

 amount. The probability that this error will in all fall in 

 the same direction is only ; and with four methods 

 similarly . If each method be affected, as is always 

 the case, by several independent sources of error, the 

 probability becomes much greater that in the mean result 

 of all the methods some of the errors will partially 

 compensate the others. In this case as in all others, when 

 human vigilance has exhausted itself, we must trust the 

 theory of probability. 



In the determination of a zero point, of the magnitude 

 of the fundamental standards of time and space, in the 

 personal equation of an astronomical observer, we have 

 instances of fixed errors ; but as a general rule a change of 

 procedure is likely to reverse the character of the error, 

 and many instances may be given of the value of this 

 precaution. If we measure over and over again the same 



1 Gauss, translated by Bertrand, p. 25. 



