There’s nothing new about the rule of thirds — it’s almost a photographic cliche. Still, as a, well, rule of thumb there’s a good deal of sense in it. Let’s have a look.
One of the worst instincts of amateur photographers is to aim the camera directly at the main subject, as if it were game to be bagged. You can see this in society pages, like one in the back of a magazine I’m responsible for (I try to keep the section’s space to a minimum). The photographer’s strategy in these situations is just about always to line the subjects up in a grinning row facing the camera. You can see what I mean in the above image (I’ve replaced the people’s faces with smilies so as not to embarrass anyone, and to highlight the composition).
The rule of thirds says that you’re better off arranging your composition with a main element a third of the way from one of the edges. In effect you imagine your image as composed of nine equal rectangles. Consider this image from the Sentiero degli Dei in the Lattari Mountains above Amalfi.
You can see that the cliff at the left is a third of the way in from the left edge of the photo. (You can also think of each of the nine squares as a section to be balanced in its own right.)
Or look at this photo from the Sentiero della Republica in the same region.
Here you can see that the image is arranged more or less in three horizontal bands.
One more example. This is at Pompeii.
Here the roof and the vertical element of the main building both relate to the thirds.
Now, I don’t follow this slavishly but it’s a good rule of thumb when you’re shooting quickly (like I tend to do since most of my photography is travel photography and I don’t want to spend all day on one shot). Basically it works because you’re moving the main elements of the photo off center. If you wanted to experiment with variations you could also try what you might call the rule of five-eighths.
I won’t go into the unique mathematical qualities of the golden ratio — you could do a search. Suffice it to say that golden rectangles usually look good to most people. Expressed as a mathematical ratio the golden ratio is 1 : 1.618, or from the other perspective .618 : 1. While the golden ratio cannot be exactly reduced to a neat fraction it’s pretty close to 5/8ths, which is .625.
So 2/3rds is .667, while the golden ratio is .618. Therefore, rather than dividing an image into 1/3 and 2/3 parts, you could divide it into parts of approximately three-eighths and five-eighths. In other words, the two parts created by the dividing element would be a little closer in size to each other than with ninths, and your guidelines would be roughly where the red lines are in the following image (taken in the Vatican museums).
Here’s the same image without the lines (yep, you caught me — I’m looking for opportunities to post photos from my recent travels).