Of course the best way to stay on course in the wilderness is with a compass, but you may be in a circumstance where you need to travel through the wilderness and you don't have a compass. You would think that traveling in a straight line would be an easy thing, but it is not. It is very common for people who are lost in the wilderness to walk in circles. If you think this would not apply to you, try the following experiment:
1. Go out into a large field, parking lot, or other unobstructed area. It's a really good idea to have a friend with you to stop you from running into something or walking out into the street.
2. Take a sighting on an object or landmark on the opposite side of the field.
3. Put on a blindfold and walk in a straight line toward your landmark.
4. When you take the blindfold off, I guarantee that you will be nowhere near your goal.
You see everyone has one leg that is a little shorter than the other, and everyone has one leg that is a little stronger than the other. The difference in the stride of your right leg and your left leg may be tiny, but over the course of thousands of steps it is enough to cause you to move in a curved path. Eventually you will curve all the way around and end up back where you started.
The only way to stay on a straight course without a compass is to use landmarks. You need to begin your journey from a recognizable landmark, sight on a distant landmark, and walk toward it. Turn back on a regular basis and note the location of your starting landmark. When you reach your goal, look back to the landmark that you started from, then turn to the front and select another landmark that will keep you moving in the same direction. This method will work over long distances if the country is fairly open.
If you are in dense forest you can use the same method on a much smaller scale, sighting from tree to tree in a straight line. It is time consuming, but not as time consuming as walking for two days only to end up back where you started from.
Legend has it that the early Spanish explorers could only cross the vast, treeless plains of North Texas by driving stakes in the ground and sighting from stake to stake in order to keep a straight course. This is supposedly where the name of this region, the "Staked Plains", came from. I doubt if this legend is true because compasses were widely used by this time, and I can't imagine a large expedition that would be without one; but it makes a good story, and it would be a very practical way to cross an area with no natural landmarks.