556 THE ROYAL SOCIETY OF CANADA 



inadvertent, incidental errors by the operators, must necessarily 

 exclude accidents ; and even the trespasser has ways or processes where- 

 by he expects, if he does not fail in their application, to exclude an 

 accident; and therefore, while men shrink in terror from lightning 

 with its lesser perils, they accept as railway employees the greater 

 dangers of the railroads with equanimity; they plan, as passengers, 

 railway journeys for pleasure; and from trespass, they are deterred, 

 if at all, by railway detectives and fear of the courts, not by the dangers 

 involved to life and limb. 



Summary of precedence and proper use of the three forms of probability; 

 and the required average of essential correctness in history. 



1. Formal probability, or the application of correct processes, 

 should be invariably used where this is possible. Where further 

 test is impossible or unreasonably inconvenient, any individual 

 conclusion reached by formal probability should be accepted in scienti- 

 fic investigation, and in practical applications of the sciences, and in 

 practical affairs generally. Formal probability is the basis of all 

 trustworthy intercourse. Formal probability is also the basis of all 

 professional and expert services required by persons who either cannot 

 perform these services for themselves at all, or who cannot perform 

 them with reasonable convenience. It is the basis, too, of all results 

 prepared ( = services rendered) by any scientist for the use of fellow 

 scientists, such as a mathematical table prepared by one mathemati- 

 cian for the use of other mathematicians or of engineers. Formal 

 probability does not exclude incidental error; but universal experi- 

 ence in trustworthy intercourse and in the services rendered by accredi- 

 ted (competent) operators of correct processes, shows that this form of 

 probability guarantees the essential correctness of any series of its 

 results as a whole; and it establishes each of its individual conclusions 

 as prima facie correct, and as a moral certainty in the sense that the 

 conclusion, apart from countervailing evidence, is "sufficiently strong 

 to justify action upon it," or "so strong that the opposite may be dis- 

 regarded especially as a basis of conduct or action." 



Under these scientific principles, the historian has the best of rights 

 to use without further test any statement in a record or part of a record 

 exemplifying the requisites of trustworthiness, and nowhere is his 

 scientific right to do this stronger than when such record is the only 

 source for the events in question. Such a record or part of a record, 

 like the series of results in a mathematical table, is essentially correct. 

 The mathematician, in the strength of this essential correctness, is 

 justified and required as a reasonable man to use any individual result 



