As you may have read recently, we study antique patterns with an eye toward tatting them using modern tatting techniques. Above all things we try to avoid unnecessary cutting and tying. Well... this one has me stumped! There is no written pattern to follow as we did previously. Here we must study the lace itself. However, to tat this in one pass and maintain the two color thread scheme proved beyond my detective abilities.
As I examined it there proved to be a dead end which forced me to cut and tie. Each scallop can be tatted in one color as a single piece, using the initial ring's long tail to tat the split ring needed to climb into the row of one shuttle work. The outer ring and chain work is all one pass, tatted and joined to the scallops which have already been attached to the hanky. The outer rings do not attach to the first and second nor the penultimate and last rings of each scallop except at the corner where the two rings of the outer edge are made back to back to make the turn.	Here is a diagram of the corner. The proportions are a bit off but you can see the picot placements and the joins fairly well.
	And here are the original stitch counts from the hanky but don't be afraid to improvise. Just maintain any picots used for joins and have fun with the rest. Think about bugle beads covering those bare shuttle threads. Think color, too! If you are going to have to hide ends anyway, why not liven it up a bit?! See https://www.georgiaseitz.com/classes2/bruyerhanky.jpg for an entire side of the hanky.

This pattern will require some thought before working it. One way to make this edging stand out is to create great regularity in the size of picots. A picot gauge is the perfect tool for the job. The picot gauge is a measuring device used while tatting to insure picots of an exact size.

Since the inner scallop is one shuttle work with opposing lines of rings with bare thread space between them, it will be necessary to measure the bare thread space to keep it exact, too. To measure a exact length of bare thread space:

1. Take a piece of card board and from one corner cut a slit in the side the distance of the bare thread space. Insert the tatted ring into the slit, stretch out the shuttle thread to the edge of the cardboard and make that the pinch. After next ring is closed, move the measuring gauge forward.

2. Take a piece of folded plastic the width of the bare thread space and drop over the shuttle thread. Hold in place while next ring is tatted and then move it forward and repeat.