1870 pre-dates compulsory metrication, metric was optional from 1868 and compulsory from1877, so the thread could well have been specified in the old Swiss system. Almost certainly an in-house or local thread used by a single manufacturer or group of firms from the same area.
The old Swiss base unit for smaller measures was the pied (fuss) re-defined as 0.30 metres for the transition to metric but subject to local variations. Next down is the pouce at 1/12 th of a pied followed by the linie at 1/144 th of a pied or 1/12 th of a pouce.
Pied and pouce are essentially same as Imperial foot and inch so 1/6 inch diameter is likely to have been 2 linie in the old system. Which is sensible.
The 28 tip pitch doesn't appear to be related to the Thury system, which wasn't defined until 1877 or thereabouts. Thury devised the system as a standardisation of "useful" mathematically related threads close to those commonly used in the watchmaking industry. 28 tip is close to the pitch of a no 1 but the diameter is nearly mid-way between 2 and 3. Sounds too much of an outlier for one of the close to threads previously used.
Clive.