This is Robert practicing his sextant skills using a compact lifeboat compass.  It will be the same one used on the trip in the event our GPS system fails.
Instead of carrying the full books and tables normally used for celestial navigation we'll be relying strictly on sun sights and the equation of time and the simple table corrections.

By observing the angle of the sun we can determine approximately at what time it was local noon in GMT, as in when was the sun at its highest point in the sky.  We then subtract 12 from it's GMT value in order to see how long the sun has traveled since it traveled over 0 degrees longitude.  We can then convert that value to minutes and multiply it by 15 minutes, since the sun travels 15 minutes of arc per minute of time.  Then by dividing it by 60 we get the result in degrees.  We then apply the correction for the particular date we're on and we get our Longitude.  This is a rough value and not very reliable as it's difficult to determine exactly what time the sun was at its highest altitude in the sky.

We can then take the value we determined as being the highest angle the sun reached and make corrections for dip and semi-diameter.  We then subtract that value from 90 degrees, or 89 degrees, 60 minutes to make the math easier.  We then add or subtract the value from our correction tables for that date and we get our Latitude.  This is a fairly accurate value.
(click on the photos below to expand)