320 HABIT AND INTELLIGENCE. [chap. 



Algebraic reasoning admits of algebraic statement. If we suppose 

 & atement. ^-^^^ ^^^ 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 neces- 

 sary variations all occurring together will be 



Now suppose, what I think is a moderate supposition, that 

 the value of m is 1000, and the value of a; is 10 : then 



111 



m^ 1000'" 10^' 



To many readers these numbers will have no meaning. 

 But it win speak to the understanding, though it will 

 baffle the imagination, to say that if these suppositions are 

 true, the probability against the concurrence of such vari- 

 ations as would constitute an improvement is expressed by 

 a number which is about ten thousand times as great as 

 the number of waves of light that have fallen on the earth 

 since historical time began.^ And it is to be further 

 observed, that no improvement will give its possessor a 

 certainty of surviving and leaving offspring, but only an 

 extra chance, the value of which it is quite impossible to 

 estimate.^ 

 / Of course this argument falls to the ground if it can be 

 I shown that it is not necessary for more than one variation 

 ' to take place at the same time in order to constitute an 

 improvement. But I think this is inconsistent with the 

 unquestionable fact, on which I have already insisted, that 

 in the highest organization there are both the greatest 



1 In 6, 000 years there are, making no correction for leap years, 

 189,216 X 10^ seconds. In one second there are 635 x lO^^ undulations of 

 yellow light. The product of these two numbers is 101,230,560 x 10^^ or 

 not much more than 10^^ which is the ten -thousandth of 10^°. 



^ See Note at end of chapter. 



