John
With 1815/16 hallmarks your examples are the lowest and highest serial number I have recorded and one might infer that this accounts to ~700 watches produced in that year (2933-2238); but does it?
I think there are many questions for which we (I) need the answer, before it is safe to draw any conclusions regarding production of this 'maker' and any other.
Let us for the moment assume that the serial numbers were allocated sequentially in chronological order, we need to know
- when were the numbers allocated?
- were they allocated by the frame or movement maker at the commencement of manufacture?
- if so how many survived to the end of the process, i.e. what was the failure rate?
- were all the available numbers allocated?
- does the interpretation of the individual digits carry significance?
- perhaps the first two identify an order for a batch of movements and the number in the batch was <99
- did movement 'design' influence the way that serial numbers were allocated?
etc.
From my observations I would say that it was not unusual for serial numbers to be allocated early in the manufacturing process; even if there were no complications to a sequential allocation of all available numbers, I doubt if all movements were finished. What would be a reasonable estimate of wastage 5% 10% 15% or higher - I just don't know. I would not be surprised if for the Liverpool 'manufacturers' (viz. middlemen / entrepreneurs / finishers / signatures) it was in the range of 10% to 20% of the serial numbers allocated. Then there is the question how many of the completed movements were actually cased and sold?
If pressed I would guess for a range of 700 serial numbers, the actual production of finished watches was probably less that 500.
It is possible for English watches to identify relationships between discrete serial number sequences and case hallmark dates, it is very rare to maintain a relationship across the complete production of a 'manufacturer'. It is very difficult, possibly impossible, to draw conclusions regarding the production figures for completed watches that were actually sold.
My knowledge of American history and what influenced the 'watch' trade between England and America in the early part of the C19th is somewhat lacking. I have never found a lucid account that identified all the factors that were determinate. However, I share your perception that prior to ~1815 many English watches that found their way to America were in genuine English cases and that there was subsequently a period when uncased movements were exported together with exports of movements in unmarked cases or possibly with faux hallmarks. Those uncased movements found their way into cases of various designs and of variable quality. There is also evidence of continental 'fakes' were being smuggled into America at this time (e.g. 140 Geneva made watches with fictitious English names were seized in 1810 bound for Charleston). How that influenced the English trade is not clear to me.
John