THE LAW OF ERROR. 461 



to take suitable precautions against such occult errors. 

 * It is to the observer/ says Gauss*, ' that belongs the task 

 of carefully removing the causes of constant errors,' and 

 this is quite true when the error 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 esti- 

 mates of the same quantity. The reason obviously con- 

 sists in the improbability that exactly the same constant 

 error will affect two or more different methods of experi- 

 ment. 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 

 considerable that errors constant in one method will be 

 balanced or nearly so by errors of an opposite effect in the 

 others. Suppose that there be three different methods 

 each affected by an error of equal amount. The pro- 

 bability 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 inde- 

 pendent sources of error, the probability becomes very 

 great 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 foresight and 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 such 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. 



t Gauss, translated by Bertrand, p. 25. 



