492 THE ROYAL SOCIETY OF CANADA 



though accurately applied according to their own requirements, need 

 not result correctly at all. 



Modern courts exemplify fundamentally a correct process when 

 the judge or jury seeks to distinguish which of the witnesses are trust- 

 worthy, or which of the statements of each witness are trustworthy, 

 and give a decision according to this test of all the personal, documen- 

 tary and other relevant evidence offered. If this distinction be cor- 

 rectly made, the decision must be correct. A contrary process in 

 this case is the ancient and mediaeval practice of trial by ordeal, 

 or by corsned, or by the eucharist, or by wager of battel, or even the 

 rule of Roman and Canon law, under which testimony was governed 

 strictly by the numerical system, witnesses being counted not weighed 

 {numerantur non ponderantur) , and the corresponding practice in 

 Anglo-Saxon and Norman times, when, according to the importance 

 of the case, proof was made six-handed, twelve-handed, etc., he who 

 had the greater number of witnesses prevailing. All the requirements 

 of such processes could be perfectly fulfilled, and yet the result be 

 incorrect. 



Thus throughout the various branches of science, theoretical 

 and practical, exact and inexact, the same principle of correct pro- 

 cesses fundamentally prevails. It produces also, throughout all these 

 branches, fundamentally the same result. Under accredited opera- 

 tion (a condition equivalent practically to competent operation, 

 because an accredited operator, who is, or may become, incompetent, 

 will be promptly discredited by an excess of error in his results), 

 correct processes cannot ordinarily prevent incidental error entirely; 

 but they guarantee an average of essential correctness corresponding 

 in height to the exactness of the branch of science involved. Even 

 the exact science of mathematics can provide ordinarily, in a series 

 of results prepared for use by others, only a high average of essential 

 correctness. Thus in such a work as Chambers' Mathematical Tables, 

 containing approximately 200,000 numerical quantities, the editor 

 anticipates, and experience teaches, that there is a percentage of un- 

 located errors: and if, e.g.,. the number of such undetected errors be 

 taken at the irreducible minimum of 1, the approximate proportion 

 of incidental error and average of essential correctness would be 

 respectively 1/200,000 and 199,999/200,000; if at 10, 10/200,000 

 and 199,990/200,000; and if at 25, 25/200,000 and 199,975/200,000. 



Trautwine, in his Civil Engineer's Pocket-Book, the standard and 

 foremost work of its kind in America, says that he has detected a 

 great many errors in mathematical tables in common use. The 

 presence of even one such unlocated error stands as a proportion of 

 error against the table as a whole, thereby reducing to an uncertainty 



