II.] INCIPIENT STRUCTURES. 65 



ing variations in the cooperating parts ; while 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 what- 

 ever is possible becomes probable, if only time enough be 

 allowed. There are improbabilities so great that the com- 

 mon-sense of mankind treats them as impossibilities. It 

 is not, for instance, in the strictest sense of the word, im- 

 possible that a poem and a mathematical proposition should 

 be obtained by the process of shaking letters out of a box ; 

 but it is improbable to a degree that cannot be distin- 

 guished from impossibility ; and the improbability of ob- 

 taining an improvement in an organ by means of several 

 spontaneous variations, all ' occurring together, is an im- 

 probability 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 



and suppose that x variations must concur in order to make 

 an improvement, then the probability of the necessary vari- 

 ations all occurring together will be 



Now suppose, what I think a moderate proposition, that 

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



JL _L_ J_- 



m* ~ iOOO 1 " ~~ 10 55 ' 



A number about ten thousand times as great as the number 

 of waves of light that have fallen on the earth since histori- 

 cal time began. And it is to be further observed, that no 

 improvement will give its possessor a certainty of surviving 



