278 THE PRINCIPLES OF SCIENCE. 



By a similar mode of reasoning we every day arrive, 

 and validly arrive, at conclusions approximating to cer- 

 taintv. Whenever we observe a perfect resemblance 

 between two objects, as, for instance, two printed pages, 

 two engravings, two coins, two foot-prints, we are warranted 

 in asserting that they proceed from the same type, the 

 same plate, the same pair of dies, or the same boot. And 

 why ? Because it is almost impossible that with different 

 types, plates, dies, or boots some minute distinction of 

 form should not be discovered. It is barely possible 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 docu- 

 ment, the probability is less than i in TO,OOO x 9999, that 

 such two coincidences should occur by chance, and the 

 numbers grow with extreme rapidity for more numerous 

 coincidences. We cannot indeed make any precise calcu- 

 lations 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 



