Page:Calculus Made Easy.pdf/28

would receive £$10$ and the boy $2$ shillings. Ten pounds would be a small quantity compared with £$1000$; but two shillings is a small small quantity indeed, of a very secondary order. But what would be the disproportion if the fraction, instead of being ${\tfrac {1}{100}}$, had been settled at ${\tfrac {1}{1000}}$ part? Then, while Mr. Millionaire got his £$1000$, Mr. Secretary would get only £$1$, and the boy less than one farthing!

The witty Dean Swift^[1] once wrote:

“So, Nat’ralists observe, a Flea
“Hath smaller Fleas that on him prey.
“And these have smaller Fleas to bite ’em,
“And so proceed ad infinitum.”

An ox might worry about a flea of ordinary size–a small creature of the first order of smallness. But he would probably not trouble himself about a flea’s flea; being of the second order of smallness, it would be negligible. Even a gross of fleas’ fleas would not be of much account to the ox.

1. On Poetry: a Rhapsody (p. 20), printed 1733–usually misquoted.