There used to be two ways of writing a lowercase s: the long s, and the terminal s. The lowercase s that we're familiar with today is the terminal s. These two ways of writing the letter s were not limited to handwriting, but were standard in printed works until the beginning of the nineteenth century.
<html> <img align="left" src="http://www.notzen.com/gemma/images/long_s.gif"> </html>
The terminal s was only used if a lowercase s appeared as the final letter of a word--all other lowercase s's were long s's.
A long s, in a standard typeface, looks very similar to a lowercase f, although it either has no cross stroke or only a stroke to the left of the downward stroke. When italicised, a long s becomes a long curved stroke which also descends as far down as the tail of a g or y. It is still seen today in the mathematical symbol for integration.
As you can see from the examples above, the difference between an f and an s can be quite subtle, which may trip up the modern reader.
The change from using both the long s and terminal s, to using only the terminal s, regardless its position in words, occurs around 1800. The first issue of The Times to replace the long s with the terminal s was 12th September 1803.
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