Repeat the process as you did with the 280. Once the work is smooth, with no visible sanding marks, turn the cloth around so that the non-abrasive side faces the work. Stop and check your work. The wood should be smooth and slightly polished after burnishing. One reason for burnishing is to see if you've polished out all of the scratches.
Scratches usually appear as marks which extend around the circumference of the barrel.
Look closely to be sure you've smoothed out all of the scratches. If not, you will probably see scratches. You may smooth again with the 400 grit cloth, if necessary. Your last step should be to burnish the barrel with the non-abrasive side of the cloth. When using a Model 360 Series, you will probably find that it is unnecessary to use the 280 grit abrasive cloth as the controlled, smooth tool movement results in few, if any, cutting grooves that require a coarse abrasive to remove.