TEE INDUCTIVE OR INVERSE METHOD. 279 



common source a . With a certain amount of labour, it 

 is possible to establish beyond reasonable doubt the rela- 

 tionship or genealogy of any number of copies of one 

 document, proceeding possibly from parent copies now 

 lost. Tischendorf has thus investigated the relations 

 between the manuscripts of the New Testament now 

 existing, and the same work has been performed by 

 German scholars for several classical writings. 



Principle 'of the Inverse Method. 



The inverse application of the rules of probability 

 entirely depends upon a proposition which may be thus 

 stated, nearly in the words of Laplace b . If an event can 

 be produced ~by any one of a certain number of different 

 causes, the probabilities of the existence of these causes as 

 inferred from the event, are proportional to the proba- 

 bilities of the event as derived from these causes. In other 

 words, the most probable cause of an event which has 

 happened is that which would most probably lead to the 

 event supposing the cause to exist ; but all other possible 

 causes are also to be taken into account with probabilities 

 proportional to the probability that the event would have 

 happened if the cause existed. Suppose, to fix our ideas 

 clearly, that E is the event, and C x C 2 C 3 are the three 

 only conceivable causes. If C x exist, the probability is pi 

 that E would follow ; if C 2 and C 3 exist, the like pro- 

 babilities are respectively p 2 and p 3 . Then as p 1 is to p 2 , so 

 is the probability of Ci being the actual cause to the 

 probability of C 2 being it ; and, similarly, as p 2 is to p 3 , so 

 is the probability of C 2 being the actual cause to the 

 probability of C 3 being it. By a very simple mathematical 



a Lardner, 'Edinburgh Review/ July 1834, p. 277. 

 b * M&noires par divers Savans/ torn. vi. ; quoted by Todhunter in his 

 ' History of Theory of Probability,' p. 458. 



