James et al,
This thread has generated a number of interesting responses and has gone on some interesting tangents, but I'm not sure your basic initial question has been answered. And, I'm not sure I can answer it to your satisfaction, either, but have finally decided to give it a try. In part, because I find such basic definitional questions to be useful/interesting, but mostly because this thread has intersected a number of my interests.
As I think you already surmise, sweep numbers on gouges indicate carving tools. However, as others have noted, not all carving tools are so numbered. So, how to tell the difference between firmer gouges and straight carving gouges if no sweep numbers are present? (I'm mostly referring to 19th and early 20th century English/American gouges, consistent, I believe, with your initial question.)
In larger sizes, firmer gouges can be distinguished from carving gouges by the presence of distinct shoulders which narrow down to a shank which continues back to the bolster. Also, the inside of the gouge has a fairly uniform depth and is recognizable as a portion of a cylinder. This can be seen in the lower gouge in the first photograph below.
By contrast, the carving gouge lacks such shoulders and simply tapers inward to meet the bolster, as evidenced by the upper gouge in the first photograph. Also, note that the inner wall of the carving gouge gets shallower as it approaches the handle. This allows for the carving gouge to be relatively delicate at the cutting edge, yet be heavy enough toward the handle to be driven with a mallet. This is why shortened carving gouges, which have been ground/honed back over the years, look so stubby and chunky.
I've included the second photograph primarily to show that both gouges are, indeed, fairly heavy near the handles.
In smaller sizes, firmer gouges sometimes have shoulders and sometimes do not. In the latter case, it can be a little trickier telling whether it is a firmer gouge or a carving gouge (if no sweep number is present). In the third photograph (in the next post) one of the gouges is a firmer and the other is a carving gouge. Pretty difficult to tell from the top view. However, as shown in the fourth photograph (also in the next post), the firmer gouge has flat "shoulders" at the edges of the gouge, which continue the full length of the blade. By contrast, the carving gouge begins with a flat shoulder at the bolster, but this transforms into a rounded area which nearly terminates in an arris at the intersection of the inner surface. This allows the carving tool to be more "delicate" at the cutting edge and work in close to other details without fouling them.
Firmer gouges can be used in carving, but can be somewhat of a handicap because they lack the finesse at the cutting edge. However, they can be useful for roughing work, both for carving and general work in the shop. Regarding the latter, it can be useful to think of them as somewhat analogical to a "roughing" plane in situation where access for saws may be limited.
As to the sweep numbering system(s), yes it seems very confusing. The origins of the London Pattern/Sheffield List system aren't entirely clear. But, there is some circumstantial evidence that it arose in London, possibly associated with S. J. Addis, and introduced into Sheffield (sometime between 1870 and 1880) by Ward & Payne (who bought the rights to the S. J. Addis marks after his death) and J. B. Addis. London was the pre-eminent center for carving activity in England, and the Sheffield makers worked hard to overcome a prejudice against non-London-made carving tools. To the point that Ward & Payne actually had a London stamp made up to use in conjunction with their S. J. Addis mark.
However, I believe some of the confusion about the sweep number regime is due to a lack of understanding of the system. It is often assumed that every gouge of a given sweep number is supposed to have an arc determined by the same radius. Not the case. Instead, the width and depth of each sized gouge in any sweep are proportional. For those who might be interested, I've written a short article outlining my surmise as to how this system might have been developed:
http://www.planemaker.com/articles_gouges.html
The continental sweep number systems are built along very similar lines, but differ from the London Pattern in a more complex way than simply being different by one number (as already noted by John). I have no idea which system is the earliest.
As has been noted, Sheffield did emerge as one of the pre-eminent centers for producing steel and edge tools during the 19th century. This emergence was built on a very long tradition of iron and steel working there (and in Birmingham), which had resulted in a good sized highly skilled work force. However, according to David Hey ("The Development of the English Toolmaking Industry during the Seventeenth and Eighteenth Centuries"), Sheffield's rise to dominance in the 19th century was mostly due to this skilled work force, locally available sandstone suitable for grinding, and a plentiful supply of water power. The local iron ore was unsuitable for high quality steel, so most of the raw materials for blister/cementation and crucible/cast steel production was imported from Sweden in the form of wrought iron bars.
I have a number of older carving tools, and have to say that they seem to have been pretty consistently made of very high quality cast steel which was properly heat treated. Additionally, as Mary has noted, they have a delicacy, yet toughness, that makes many of the currently produced tools (especially from England) seem very clunky and clumsy by comparison.
(Incidentally, the emergence of the Bessemer Process had little, if any bearing, on high quality edge tool manufacture. That process resulted in a lower quality, inexpensive, steel suitable for railroad rolling stock, rails, boiler plates, etc. At least as late as 1910, most edge tools were still being made from crucible/cast steel. After this, tool quality steel was later produced by one of the electric furnace processes.)
Hope this has been of some interest/use.
Don McConnell
Eureka Springs, AR