242 THE PRINCIPLES OF SCIENCE. [CHAP 



for the hand of the most skilful artist to make two objects 

 alike, so that mechanical repetition is the only probable 

 explanation of exact similarity. 



We can often establish with extreme probability that 

 one document is copied from another. Suppose that each 

 document contains 10,000 words, and that the same word 

 is incorrectly spelt in each. There is then a probability of 

 less than I in 10,000 that the same mistake should be 

 made in each. If we meet with a second error occurring 

 in each document, the probability is less than i in 10,000 

 x 9999, that two such coincidences should occur by chance, 

 and the numbers grow with extreme rapidity for more 

 numerous coincidences. We cannot make any precise 

 calculations without taking into account the character of 

 the errors committed, concerning the conditions of which 

 we have no accurate means of estimating probabilities. 

 Nevertheless, abundant evidence may thus be obtained 

 as to the derivation of documents from each other. In 

 the examination of many sets of logarithmic tables, six 

 remarkable errors were found to be present in all but 

 two, and it was proved that tables printed at Paris, Berlin, 

 Florence, Avignon, and even in China, besides thirteen 

 sets printed in England between the years 1633 and 1822, 

 were derived directly or indirectly from some common 

 source. 1 With a certain amount of labour, it is possible 

 to establish beyond reasonable doubt the relationship or 

 genealogy of any number of copies of one document, pro- 

 ceeding possibly from parent copies now lost. The rela- 

 tions between the manuscripts of the New Testament have 

 been elaborately investigated in this manner, and the same 

 work has been performed for many classical writings, 

 especially by German scholars. 



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. 2 If an event can 



1 Lardner, Edinburgh Review, July 1834, p. 277. 



2 Memoires par divers Savans, torn. vL ; quoted by Todhunter in 

 bis History of the Theory of Probability, p. 458. 



