INDUCTION. 143 



following numbers : 



ii ii i 5 691 7 3617 



j ) 5 > j --: j > -> j ctc 



26 30 42 30 66 2730 6 510 

 These numbers are sometimes negative, more often posi- 

 tive ; sometimes in low terms, but unexpectedly spring- 

 ing up to high terms ; in absolute magnitude they 

 are very variable. They seem to set all regularity and 

 method at defiance, and it is hardly to be supposed that 

 any one could, from contemplation of the numbers, have 

 detected the relation between them. Yet they are derived 

 from the most regular ^and symmetrical laws of relation, 

 and are of the highest importance in mathematical analysis, 

 being known as the numbers of Bernouilli. 



Compare again the difficulty of decyphering with that 

 of cyphering. Any one can invent a secret language, and 

 with a little steady labour can translate the longest letter 

 into the character. Biit to decypher the letter having no 

 key to the signs adopted, is a wholly different matter. 

 As the possible modes of secret writing are infinite in 

 number and exceedingly various in kind, there is no direct 

 mode of discovery whatever. Repeated trial, guided 

 more or less by knowledge of the customary form of cypher, 

 and resting entirely on the principles of probability, is 

 the only resource. A peculiar tact or skill is requisite for 

 the process, and a few men, such as Wallis or Mr. Wheat- 

 stone, have attained great success. 



Induction is the decyphering of the hidden meaning of 

 natural phenomena. Given events which happen in certain 

 definite combinations, we are required to point out the 

 laws which have governed those combinations. Any laws 

 being supposed, we can, with ease and certainty, decide 

 whether the phenomena obey those laws. But the laws 

 which may exist are infinite in variety, so that the chances 

 are immensely against mere random guessing. The dif- 

 ficulty is m.uch increased by the fact that several laws will 



