I have two pocket watches. One is a fusee from 1884 and the other is a chronograph from 1895. Both have been professionally cleaned and adjusted. My problem is this: both watches run fast or slow depending if they are hung, laid on their back or laid on a side. Can you advise the best way forward
Positional rate inaccuracy is an issue on all watches particularly watches that are this old. Some watches of poor quality could vary between 5 and 10 per day minutes between positions (or more depending on the condition they are in!)
If they are fine quality watches (typical of railroad watches manufactured after the late 19th century) then this rate differential can be minimized by adjustment or repair. The weight of the balance screws can be adjusted to compensate for positional error. Also the pivots on the balance staff can be polished or repaired, and the balance jewels may need to be replaced. For that matter if there is any wear at rotational pivot points (jewels, pivot holes or pivots) anywhere in the powertrain it could cause positional timing issues. If the mainspring is incorrect or worn out this also could cause problems. The hairspring could be bent, off center or not level. And the list goes on.
If I had them on my bench I could better make an evaluation. I know this answer is somewhat broad, but at least helps you understand some of the issues.