As well as measuring the play in the chain, I also use a straight edge to make sure the rear cog; and ergo the rear wheel; are also in alignment. My theory being that it is nearly impossible for the cog to be out of alignment with the wheel without you knowing about it (horrible grating noise when rotating wheel, totally worn out teeth on one side of the cog, chain flying off at speed!).
You could just use the lines marked on the rear axle eyes to do this but there are 2 potential problems there - 1) To see the marks properly you will either have to jack the rear of the bike up to clear the mufflers (on the Adventurer, maybe not an issue on other models) or remove the mufflers, and 2) you must also be confident that the marks are accurate. IE that there is no play in the swinging arm bearings, your swinging arm is not slightly bent, and that the bloke at the factory was having a good day when he made them.
Here's how I go about it -
Place the ruler flat against the cog with the end sitting just at the point of the curve. Don't go too far back towards the rear as that messes up the measurements, and make sure the ruler is sitting nice and square against the chain, applying pressure from underneath and in towards the cog itself.
...here I held the front of the ruler up with the angle iron because again it's not easy to take a pic at the same time as holding everything, but you can see by looking down the ruler, and even better by looking from above, if everything is lined up nicely. It doesn't have to be mega perfect, but try to get it as close as possible.
And don't forget to recheck both chain tension and alignment with every small turn of the adjuster screws, as a tiny movement can make a big difference. They really should have made the threads on the adjuster screws a lot finer in my mind, but that's something we can't change, so just be wary of it.
As a final check I use the pocket light to make sure the marks on the axle "eyes" are in agreement with my measurements at the cog/chain. Obviously if one side is a whole mark different to the other then I would be looking for the cause of the problem. Luckily for me all went smoothe and the marks line up exactly the same on both sides.
I like to sit on the bike at this point and jump up and down a few times, then check the chain tension with my fingers while sitting on the bike. You can tell if it's too tight as it gets a "hard" feeling to it. I can't explain it, but you'll know when it feels right.
Before tightening the axle bolt, make sure the adjuster bolts are locked into position by tightening their lock-nuts. Take your time here as one tiny movement of those blasted adjuster bolts means you're going to have to do it all again! Use 2 13mm spanners, make sure you are holding the bolt firmly with one of them before tightening the locknut. You will find that you can only turn it a tiny bit at a time, so be patient and go slowly.
Once you're satisfied you can then tighten the rear axle nut using the reverse of step 1 above. And make sure that thing is tight, it's "B@stard Tight" on the ArferBrick scale of backyard mechanic's Torque settings!
There's potentially a couple of tons of force being held back by those flimsy adjuster bolts and that nut, so make sure you do it right. If in doubt, (or you have the correct flashy expensive tools!), then use a torque wrench.
The tensioning system is actually a lot better than in days gone by, most bikes had only a pressed steel U-bracket with an adjuster bolt threaded into them. They would strip very easily because they were made of soft steel, very annoying when you opened the throttle hard and the thread gave way, making the wheel go sideways and popping the chain off
I remember many times limping home with an old bolt or socket lodged in front of the axle to keep the damn wheel straight!