45 
Let us consider what is implied by the fact of increase 
in a geometrical ratio. The result of increase in a 
geometrical ratio is “ one of the greatest marvels of 
arithmetic.” By its aid, if we are to believe the illustra 
tions given and the stories told, the cunning of knowledge 
delights to circumvent the innocence of ignorance. That 
very remarkable abstraction, “ every school boy,” has 
heard of the gentleman who took a great fancy for a 
horse and rashly asked the horse-dealer to name his 
own price. Accordingly it was arranged that he should 
be paid for the nails in the horse’s shoes—a farthing for 
the first and a halfpenny for the second, and .so on to 
the twenty-fourth nail ; by which means the stipulated 
price of the horse amounted to .£17,476 5 s. 3^d. 
In spite of the notoriety of the horse-shoe calculation, 
two persons accepted the offer of a well-known farmer 
of the Brechin district, who proposed to pay the expense 
of a picnic to thirty farmers, provided one of them 
would bring to him in the market on Tuesday one grain 
of oats, doubling the number of grains every Tuesday 
for twelve months. One of the persons accepting the 
offer undertook to carry all the oats on his back at the 
end of the year ; but upon calculation it was found 
that the quantity of oats at the end of twelve months 
would amount to 1,034,834,468 quarters 2 bushels, 
and the value, at 30s. a quarter, was found to be 
¿1,552,251,702 7s. 6d. ! 
To those who have any experience of calculations 
like these, it is obvious that the phrase “ increase in a 
geometrical ratio ” suggests the output of enormous 
numbers, and the expression is none the less significant 
when applied to living beings. In that connection it 
constitutes one of the marvels of the organic world. 
Writers on Natural Selection exhibit elaborate calcu-