48 
by calculations of the results of unchecked increase for a few years. 
Then, never forgetting that the animal and plant population of any 
country is, on the whole, stationary, we must be always trying to 
realise the ever-recurring destruction of the enormous annual 
increase.”—(Wallace. Darwinism, ft. 122.) 
But if the animal population remains the same from 
year to year it is quite impossible that there should be any 
such a thing as increase in a geometrical ratio at all. A 
geometrical progression is a series of numbers, which is 
increased or decreased by a constant factor, i.e., is always 
multiplied or divided by the same number. Thus, if we 
start with 4 for the first number of a series and take 2 
as the constant factor we have the following series— 
4 (4x2 = ) 8 (8x2 = ) 16 (16x2 = ) 32 (32x2 = ) 64 (64x2=) 128. 
Hence 4, 8, 16, 32, 64, 128 constitute a geometrical pro 
gression, a series of numbers increased by the constant 
factor 2. But if in every generation as many die as are 
born, there can be no such thing as a geometrical pro 
gression, i.e., a series of numbers increased by a constant 
factor generation after generation and year after year. 
Let us, for a moment, consider the enormous difference 
which exists between increase in a geometrical ratio and 
a stationary population. The difference may be shown 
thus— 
4 (4x2 = ) 8 (8x2 = ) 16 (16x2 = ) 32 
4 (4x2-4=) 4 (4x2-4 = ) 4 (4x2-4 = ) 4 
And of course the difference will be greater the greater 
the constant factor employed. In the case given above 
the difference in the output of life in six terms will be 
4 4" 8 4- 16 + 32 4“ 64 4" 128 = 232 
4 + 8+ 8 + 8 + 8 4- 8 = 44 
208 
In this case we are supposing 252 chances of favourable 
variations arising, in a case where only 44 in reality occur.