Yes but the guy we're discussing never had any instruments. How do you get time, speed and course without instruments? DR without instruments is like a party without people. It ain't gonna happen.
Well, the guy did have an hourglass... and presumably enough pencils and paper to keep track. Therefore it is possible to get your numbers like this:
* Time: a really rough idea of the time of day by picking local noon on a good day using a stick at arms length as a home-made crossstaff and re-setting your hourglass-chronometer by that. (worked for the Polynesians..)
* Speed: a WAG using the old method of occasionally dropping something overboard and counting how long it takes to pass a known distance along the hull. (well you'll get a number to write down, anyway!).
* Course: Knowing the sun's track across the sky for the time of year during the day and picking your angle to the Pole Star/Southern Cross by night ("two points off the starbd crosstree!") it is possible to know roughly where you're headed.
.. none of this will give you an accurate
DR position by any means - but it's better than nothing.
Yep, he certainly needed a lot of luck - and, like Thor Heyerdahl, would have relied on eventually running into something, but don't forget that common practice for hundreds of years before the sextant was invented was to "run your easting down"...
EDIT: One thing about hourglasses is that they do wear out with repeated use and get more and more inaccurate every day. I assume he took a box of them and had some system for swapping them out.. like the old windjammer captains did.