THE ERRORS OF PRECISION. 



We must most positively protest against the universal 

 assumption that the mere arithmetical mean of the experi- 

 mental chemical determination is the true value of the 

 atomic weight of any element. 



But since this declaration is in conflict with universal 

 practice, it may be advisable to first present a simple case 

 from common experience in which the fallacy of the mean 

 is palpable, and about which there cannot be any doubt. 



As such we shall give the case of the determination of the 

 weight of a coin of given value a common silver dollar 

 by actually weighing a number of such coins in circulation. 



Having done this work, we shall be able to understand 

 why the mean cannot be taken as the true value in most cases. 



We shall thereby be relieved from one of the most com- 

 mon errors of modern scientific practice. 



It is impossible to overlook the glaring error of the mean, 

 since according to the object or cases operated upon, the 

 resulting mean values do differ from one another, as a matter 

 of fact. See the atomic weights of gold determined by 

 Mallet, pp. 24-28. 



The Probable Error. 



In order to obtain a sort of indication of the reliability 

 of such a mean, chemists have tried to determine the "prob- 

 able error" 1 " 1 of such means by an application of general 

 principles of probability put into practical form by mathe- 

 maticians. 



We shall therefore, be compelled to show how this simple 

 though somewhat tedious calculation is effected, and above 

 all, call attention to the necessary limitations imposed by 

 mathematical science, under which alone this method can 

 possibly be used. 



We shall see that these necessary limitations have been 

 overlooked practically in all the applications of the calcu- 

 lation of the probable error made by chemists, both in 

 America and in Europe. 



To what an extent this reckless use of a method under 

 conditions where it is absolutely inapplicable has been 



