II.] INCIPIENT STRUCTURES. 59 



it is obvious that the greater the number of variations 

 which are needed in order to effect an improvement, the 

 less will be the probability of their all occurring at once. 

 It is no reply to this to say, what is no doubt abstractedly 

 true, that whatever is possible becomes probable, if only 

 time enough be allowed. There are improbabilities so 

 great that the common sense of mankind treats them as 

 impossibilities. It is not, for instance, in the strictest 

 sense of the word, impossible that a poem and a mathe- 

 matical proposition should be obtained by the process of 

 shaking letters out of a box; but is improbable to a 

 degree that cannot be distinguished from impossibility; 

 and the improbability of obtaining an improvement in 

 an organ by means of several spontaneous variations, all 

 occurring together, is an improbability of the same kind. 

 If we suppose that any single variation occurs on the 

 average once in m times, the probability of that variation 

 occurring in any individual will be 



!_ 



m> 



and suppose that x variations must concur in order to 

 make an improvement, then the probability of the neces- 

 sary variations all occurring together will be 



1_ 



m x ' 



Now suppose, what I think a moderate proposition, that 

 the value of m is 1,000, and the value of x is 10, then 



!_ 1 JL 



m*~ 1000 10 ~ 10 30 ' 



a number about ten thousand times as great as the number 

 of waves of light that have fallen on the earth since 



