THE LAW OF ERROR. 453 



precision ; and whenever the neglecting of decimal frac- 

 tions, or even the slight alteration of a number will much 

 abbreviate the computations, it may be fearlessly done, ex- 

 cept in cases of high importance and precision. It has been 

 stated that the voyages of the Great Britain steamship to 

 Melbourne from Liverpool, up to May, 1871, have been 

 thirteen in number, with the following durations in days : 

 62, 63, 59, 60, 58, 61, 57, 57, 57, 57, 56,- 63, 55. The 

 mean duration of the voyages is 58*85 days, which is the 

 most probable length of any similar future voyage ; but 

 to calculate the probable error, we may take the mean to 

 be 59 days. The sum of the squares of the errors is only 

 88, and the probable error thence calculated 0*49 day, or, 

 say half a day. It is as likely as not, then, that any par- 

 ticular voyage will be not less than 58 1 days, nor more 

 than 59 J days. 



The experiments of Benzenberg to detect the revolution 

 of the earth, by the deviation of a ball from the exact 

 perpendicular line in falling down a deep pit, have been 

 cited by Encke as an interesting illustration of the Law 

 of Error. The mean deviation was 5*086 lines, and its 

 probable error was calculated by Encke to be not more 

 than '950 line, that is, the odds were even that the true 

 result lay between 4*136 and,6'O36. As the deviation 

 should, according to astronomical theory be 4*6 lines, 

 which lies well within the limits, we may consider that 

 the experiments are consistent with the Copernican system 

 of the universe. 



It will of course be understood that the probable error 

 has regard only to the differences of the results from 

 which the mean is drawn, and takes no account of con- 

 stant errors. The true result accordingly will often fall 

 far beyond the limits of probable error. 



Taylor's 'Scientific Memoirs,' vol. il pp. 330, 347, &c. 



