Page:Calculus Made Easy.pdf/23



shall find that in our processes of calculation we have to deal with small quantities of various degrees of smallness.

We shall have also to learn under what circumstances we may consider small quantities to be so minute that we may omit them from consideration. Everything depends upon relative minuteness.

Before we fix any rules let us think of some familiar cases. There are $$60$$ minutes in the hour, $$24$$ hours in the day, $$7$$ days in the week. There are therefore $$1440$$ minutes in the day and $$10080$$ minutes in the week.

Obviously $$1$$ minute is a very small quantity of time compared with a whole week. Indeed, our forefathers considered it small as compared with an hour, and called it “one minùte,” meaning a minute fraction—namely one sixtieth—of an hour. When they came to require still smaller subdivisions of time, they divided each minute into $$60$$ still smaller parts, which, in Queen Elizabeth’s days, they called “second minùtes” (i.e. small quantities of the second order of minuteness). Nowadays we call these small quantities