II.] INCiriENT STRUCTURES. (55 



ing variations in tlie cooperating parts ; while it is obvious 

 that the greater the number of variations whicli are needed 

 in order to efToct an improvement, the less will be the 

 probability of their all occurring at once. It is no reply to 

 this to sa}', 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 w^ord, im- 

 jiossible that a poem and a mathematical proposition should 

 he obtained hy 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- 

 t;iini!ig 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 



m*. 



Now suppose, what I think a moderate proposition, that 

 the value of 7n is 1,000, and the value of x is 10, then — 



771' ~ 1000^" ~ 10'°* 



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 



