The first back across can also be belayed down to the midpoint and then make his own way by way of jumars up from midway point. The advantage of another rope on the first back across will become apparent when we see the necessity to retrieve everything from atop the pinnacle (West).
So now we have one climber on this side (East) and one climber on tuther (insert Yorkshire pommy gardener accent here) side (West). Climber A on other side (West) now has to attach the two ropes together using either an
overhand knot or triple
fisherman's knots. He will do this before releasing any tension from the system. He will release the muenter mule but not release the z drag. He will also have been searching for a convenient bomber natural anchor that he can run the rope around before he joins the two ends together.
Heh heh look at him running around in circles looking for a dirty great tree that isn't there. He'll just have to settle for slinging the rope around that giant boulder perched precariously (nah it's bomber) on top of the pile. Okay he's got his anchor sorted so now it's over to the climber B on this side of the gulch. Hey buddy, enjoy the ride. Down to the bidness bro, guess what, hope you were paying attention over there on the west side cos you've gotta do exactly the same thing over here dude, that's right tension the other rope you just brought over. Run that rope around that giant tree (on the East side) just like the other one (also on the East side) and then set up a z drag to pull some tension into the rope. There ya go just pull it up just like the other one dude, you've done this before why am I even telling you this? So now on this side (East side) we have two ends of rope running around the tree using
no knots and
figure of eights on the bight clipped to the main lines.
Climber A on other side (West side) can now release his z drag. As climber A is attaching himself to the traverse he will have two ropes to choose from. He can be attached to one and use the other one as a back up. The best rope to attach himself to is the rope that does not have the joining knot in it as it will be on the other side of the giant boulder. The strand or line with the knot in it will be slightly less strong than that without if you get my drift. Obviously our second traverser (climber A) will repeat exactly the manoeuvres that the first went through to cross the void.
Left: Climber A also tyrolean traverses back to the East side.
So now we have our two heroes back over on this side (East) and they can now simply retrieve their rope by pulling it from this side as it is simply run around the natural anchor on the other side (West) of the chasm. Obviously they will pull the strand with the knot on this side of the boulder so that the knot does not have to be pulled all the way around the boulder. Imagine it as just like having to pull a rap rope that has a knot in it through an anchor, you would pull the knot side down and not the free side down as it is obvious that you cannot pull a knot through an anchor can you?
In Summary 
To make the concept really simple, a rope is dragged across from the East side then a second rope is joined to the first on the West side and the second rope is dragged back across to the East side so that we now have two ropes spanning a void. There will be a knot where the two ropes are joined. This knot will be set up something like how you would set up a knot for a twin rope abseil. You do not want this knot halfway down the abseil nor do you want this knot halfway across the tyrolean traverse. You will have to do a bit of tensioning of these ropes across the void and to do that you will need anchor knots that are easy to adjust but are absolutely bomber under load and as close to 100 percent rope strength. You will also need to be proficient at z drag hauling to be able to achieve the desired rope tension. You will need to be able to set bomber anchors from which to do your hauling and tensioning.
The thing that really needs stressing is that you will be placing a lot of faith in the anchors you will be using so make sure they are good ones. Another thing that bears mentioning is that when you are at the bottom of the traverse and are ready to come up the other side you will need to prevent yourself from sliding back down the rope as you make your way up. This is very much like a sort of sideways jug so you will be needing 2 prussiks or 2 jumars. Mate it can be hard work particularly if you have a pack to haul. Don't wear it on your back. Suspend it from the biner attached to the rope. It might even be suggested to wear a chest harness to keep yourself from inverting as you grow tired.
Do we need to go through all the disclaimers again, ya orta know it all off by heart by now and of course all climbers know that they take responsibility for their own actions. Climbers generally are the sort of people who know how to assess risk and would never do anything to jeopardise their own or their partners safety so obviously if you are going to take any of this advice then you will of course try this all out in a completely risk free and safe environment and test, test, test and then do a bit more research to confirm in your own mind that the system works.
Use Of Pulleys
A word of caution when using a pulley in a tyrloean traverse. You should definitely use two pulleys or a double inline pulley which is meant for aerial cableways. The use of a single pulley has resulted in deaths when a load shift happens and the sheave of the pulley is overloaded and it can be twisted off the axle. Two pulleys or the double inline pulley have the necessary redundancy and resistance to the twisting load. The large knot passing Kootenay pulley from Petzl or similar design pulleys from other manufacturers are fine. If you have no alternative to using a small pulley then do use a screwgate biner backup independent of the pulley.
The "No Knot"
I'm referring to the "no knot" as the friction knot. What you do is take the end of the rope and throw it around a tree three times. The tail of the rope you place a figure of eight on the bight and clip that to the main line which of course is the other tail of the rope that you sent three times round the tree. Really this is almost too simple a concept and should not be overcomplicated. We teach the strength and simplicity of this knot by demonstrating how effective simply running the rope around a tree and trying to pull it, it won't undo, the figure of eight on the bight is simply there to ensure that the wraps won't work their way around the tree during the load/unload cycles of rapping.
The man with a quiet voice and supernatural shoulders has a reputation for bold, run out, trad horror shows, including one such ascent captured on film during the making of the well known climbing movie "Hard Grit". With first ascents that include the hardest route at Mt Arapiles, Punks Addition (32), some scary stuff on Taipan Wall and a wealth of bold FA's and repeats throughout the world, it's a wonder Dave has time to earn a living. As a film maker/multi-media designer Dave runs a company called Transience out of Natimuk.
