14 THE ERRORS OF PRECISION. 



The sum of these twenty squares foots up to 7821. The 

 20 observations multiplied by the next lower number (here 

 19) gives \hQ#roduct 380. 



Dividing the sum 7821, by this product, 380, we obtain 

 the quotient 20.58. 



Extracting the square root of this quotient we obtain 4 .54. 



Subtracting one third herefrom, there remains 3 .03 as its 

 two-thirds j which therefore is the probable error of the mean 

 of the twenty silver dollars, in centigrammes. We drop the 

 second decimal as unreliable. 



The operations involved in this calculation of the prob- 

 able error of the mean are all simple enough although 

 quite tedious if a large number of such calculations has to 

 be effected. 



Shall we use this Error? 



If the so-called probable error possesses any scientific 

 value, it will then be proper to calculate the same. But 

 if the value so obtained is practically worthless it would be 

 worse than pedantry to carry out these calculations. 



If the so-called probable error of the mean should convey 

 a false idea, or have been obtained in any case under condi- 

 tions which prohibit this mode of calculation, then false 

 data of fact would be foisted upon science, and a fraud 

 would be committed. 



So far as science is concerned, the fraud would exist, 

 even though the person guilty be not aware thereof on 

 account of lack of understanding. 



In science, there can be no excuse given for stating a 

 false fact or a false result obtained by using a false method 

 or process, whether of practical laboratory work or of 

 calculation. 



It is the duty of the scientist to test the methods of 

 practice and of calculation which he employs. If he con- 

 tinues to employ them after they have been shown to be 

 erroneous, he is surely guilty of committing a scientific 

 fraud in using them. 



