What exactly do the eighth and ninth symbols in a stargate address represent?

In Stargate, we learn that seven symbols are needed for a stargate to activate and open a wormhole. The first six create a three dimensional axis that points to the destination at the center of the axis. The seventh symbol is for the origin point. That is why every address they use to get from Earth somewhere ends the same.

But in one episodes where O'Neil travels to the Asgard galaxy and in Atlantis they use an eighth symbol. In Universe they use a ninth symbol to get to Destiny. What do these symbols do to the logic of the address?

Answer

For the eight chevron, it's used as an additional calculation for extra-galactic travel (outside of our own galaxy), which serves as distance from here to there. For Atlantis, you'd most certainly need it as it is sitting in its own galaxy and separate from our own.

The ninth chevron is less conventional and is mainly used for Destiny as it points to a specific gate instead of a location. Because Destiny does not inhabit a fixed point in space like every other gate we've come across, it can't be dialed without this chevron due to the nature of where Destiny may be at any given time.

Both require a lot of energy to work and create a functioning wormhole for travel, much more than your average Stargate is meant to handle. However the last chevron, no matter how long the address, will be the point-of-origin and is thus not always the seventh chevron. If you were dialing to Atlantis, you'd still need an extra chevron for the extra-galactic address but the last (now eighth) would be the origin gate. The Atlantis chevron is inserted someplace between the address and origin chevrons. Same for the ninth.

For more information, I found the Stargate Wiki to be a great resource as well as where I remembered most of my Stargate-verse. It's been a while since I've been to visit this universe.

EDIT: More information with thanks to Arammil

The Stargate address can be seen as mathematical equation with the solution being the destination Stargate. Thus, if letters A-F were the first sixth chevrons, with the letter P being the point-of-origin (usually Earth), would make an address/equation look like this:

A+B+C+D+E+F+P = Destination

If you added an eighth chevron, to get to Atlantis, you'd add that extra co-ordinate (which we'll name G) for the extra-galactic travel needed. Our address/equation would look like this:

A+B+C+D+E+F+G+P = Destination

You can see that our P value (point-of-origin) has stayed in the same relative, but not absolute, spot as the first: the last value added to create our destination value.

And, finally, for the ninth chevron, our address/equation would be like so, assuming H for the rough equivalent of Destiny:

A+B+C+D+E+F+G+H+P = Destination

Again, P stays in its relative position to the others and remains as the last variable to be added to our destination address. Of course, how the actual "math" of gate travel is not known, and to my knowledge was never adequately explained in the show, so this is the best I could come up with. I'm sure that if they did, it would be a much more complex equation.