Once I had the panel in place, I was ready to glue. To glue the box together, I am using IPS Weld-On 3 acrylic cement with a syringe and 16ga needle.

You can buy bottles with needles specially designed for gluing acrylic, but this works just as well.  The most important thing to remember while gluing is that less is more.  It doesn't take very much of this stuff to make a very strong bond.  If you use too much the time it takes to cure will be much longer and the joint won't be as strong.

To apply the cement just run the needle down the edge of the two panels while slowly applying a small amount.  Remember not to use too much.  Capillary action will draw the cement in between the two panels.  If cement starts pooling up outside of the seam, then you have used way too much.  If you have done it right, all the cement on the outside should disappear and you should see the seam become transparent.

This should seem self evident to most people, particularly anyone that has ever worked with a syringe, but put the cap back on the needle anytime you are not actually using it.  Do not, under any circumstances, set the syringe down without putting the cap on first.  I don't know what injecting yourself with this stuff will do, but I can't imagine it being anything good.

With the back in place, I was ready to move on to the side panels.  Since I was only able to get bronzed acrylic in 1/8" sheets, I had to glue two sheets together to make one panel.  I decided to glue them in separately, but in hindsight, it might have been better to glue them together first, and then glue the completed panel in last.  At any rate, I put them in separately, starting with the panel on the outside.