204 THE SCIENCE OF LOGIC 



amount&quot; 1 from the normal, and hence called the &quot;personal 

 equation&quot; or &quot;personal error&quot;: e.g. &quot;the inclination to record 

 the passage of a star across the wires of the telescope a little too 

 soon or a little too late. . . . The difference between the 

 judgment of observers at the Greenwich Observatory usually 

 varies from T ^ to \ of a second, and remains pretty constant for 

 the same observers. 2 These various sources of inaccuracy can 

 be to some extent detected, and their disturbing influence elimin 

 ated by calculation. But when all this has been done, when all 

 possible precautions have been taken, it will still be found that 

 in the case of delicate measurements a series of equally reliable 

 trials, even when made by the same individual, will never yield 

 exactly, but only approximately, the same results : 3 thus showing 

 that, on account si unavoidable interfering influences, the observed 

 or registered magnitudes are only approximations to the true 

 magnitude. 



Now it may be safely assumed, in the absence of any ground 

 for suspecting the contrary, that the various unknown sources 

 of discrepancy, in the results of such a series of measurements of 

 any magnitude, will tend to neutralize each other, as being 

 indifferent to excess or defect; that the true magnitude will, 

 therefore, lie somewhere between the greatest and the least 

 registered magnitudes ; that by taking the mean of all the 

 registered magnitudes we are approximating to the true mag 

 nitude ; and that this approximation will be closer the larger 

 the series of measurements which furnish this mean. From the 

 assumption that the sources of error yield excess and defect 

 indifferently in the individual measurements which make up the 

 series, the inference is unavoidable that the oscillations on each 

 side of the true magnitude will tend to balance each other in 

 the long run : so that the mean will tend in the long run to co 

 incide with the true magnitude. 



There are two leading methods of determining the &quot; mean &quot; (of a number 

 of measurements) which is most likely to approximate most closely to the true 

 magnitude. The first of these which is called the &quot; METHOD OF MEANS &quot; 

 is applicable only when we are engaged in measuring some single magnitude, 

 such as the length of a line. It consists simply in taking the Arithmetical, or 

 the Geometrical, Mean of the actual measurements. Usually, the arithmetical 



JEVONS, Principles of Science, p. 347. y ibid. 



3 A result which shows a notable discrepancy from all the others of the series 

 should be rejected as being presumably vitiated by some extraordinary, though un 

 detected, error in the measurement. 



