The parts inventory numbering systems used by old watch companies are quite interesting, and confounding to the modern way of thinking. But their systems were devised without computers, in fact even before what we would think of as common sense filing techniques. It is odd to think that "modern" numbering and organizing systems were "invented", but it's true.
Here pictured are a couple of new old stock (NOS) Elgin wristwatch parts. One package has a printed label reading "660 138 Lever Setting" and the other one reads "660 40 Clamp Minute Wheel".

The first package contains a setting lever and the second package contains a minute wheel clamp. The back of the packages are transparent so we can see the parts.
So what do the numbers mean?
660 is the grade number of the watch this part will go with.
40 and 138 are the factory part number for this type of part. Not a specific parts, but the type of part. The number 40 is the number for a minute wheel clamp, while the number 138 is for setting levers. You can find a list of these part numbers here:
http://www.rdrop.com/~jsexton/watches/partNumbers1.html
But wait! There's more!

Suppose you need to find a winding arbor for an Elgin grade 667 wristwatch. The factory part type number for an "Arbor, Winding" is 3. One might think you need to look for a package labled "667 3 Arbor Winding". But this is not so. First, one must consult the Elgin interchange tables.
Here we have part of a page from an Elgin Service Manual printed around 1960. This section covers winding arbors.
Note that the forth column over has the number "660" in bold at the top. The numbers below that include 661, 662, etc, and 667. This tells us that a grade 667 watch will need a winding arbor labeled 660.
There is not an obvious system to these parts and numbers in the interchange tables. The fact that a grade 667 watch takes the same arbor as 660, and others, tells you very little about what other parts are shared among those grades. The "master numbers" if you will, such as 660 in this case, are not always the ones in bold for all parts. For another part 660 may be listed in a non-bold column under some other main interchange grade. To find the number of the package you want, you scan the entire section for the grade number and see what the main interchange grade is for that part.
Of course that are caveats.
- The interchange information is not complete. Very late grade are not there. Early Elgin watches (pocketwatches) used a different parts system, although parts for early grade were made and sold using the newer system too. Swiss import grade are categorized differently.
- The interchange data is sometimes incorrect. I have 3 or 4 of these Elgin manuals containing various updates mailed out by Elgin. They are all sprinkled with their prior owners' handwritten corrections and notes.
- Sometimes the part type number is not printed on the package.
- Sometimes the part type number and the grade number are reversed.
- Sometimes the specific grade number is on the package, rather than the interchange grade.
- Sometimes the number on the package is a "cabinet refill number," also called a "bottle number" (see below).
- Lastly, this is not Elgin's only parts system, there are two others!
In earlier times Elgin devised a different system, and it's not as though they switched systems at some point either. These two parts numbering schemes were both in use at the same time. The other parts numbers are known as "bottle numbers", "cabinet numbers", "refill numbers", or sometimes "order numbers." These numbers originate with Elgin parts cabinets, made early on the company's history as a sort of kit for watchmakers that repaired Elgin watches.
As an aside, it's worth mentioning that these parts assortments were an innovation on Elgin's part. They had the watch college where the trained watchmakers in Elgin products, and they had a standardized kit of parts, which could be refilled. It gave Elgin a distinct advantage in that their products were far easier to service, and easier for watch owners to find quality service for. The standardized parts assortments were key to making Elgin one of the largest industrial companies in the world, in its day.
Here are some bottles from an Elgin parts assortment. The key to these parts is a cardboard listing that came with the assortment organized by the type of part, and the watch size, keeping in mind that this system was developed at a time when the products were entirely pocketwatches, and there were relatively few grades.
Bottle numbers occur throughout various parts documentation, and are not limited to parts that were ever actually included in a parts assortment.
Just when you might think it's safe to leave this topic, there is one more set of numbers.
The labeling scheme and the cabinet number were both intended to aid in watchmakers or jobbers obtaining parts. But there are also "factory numbers". Factory number are part-specific numbers, largely used internally, for specific parts. These numbers don't include a reference to the watch model, size or grade, nor do they relate to other systems. Yet it is common to see original Elgin parts labeled with the factory number. The factory part numbers that go with specific grades, by part type, are documented in the Elgin Genuine Materials Catalog (which is different from the Service Manual).

I find Elgin factory original mainsprings particularly annoying to organize since they are commonly labeled with a mix of either a bottle number, a factory number or both. Also, factory numbers are sometimes more specific. In other words there may be different factory numbers for a given cabinet number, at least for mainsprings. And besides all that, the detailed dimension data on original mainspring packages sometimes varies within the same numbers.
I have never seen a complete cross reference of bottle numbers and factory numbers, but it is possible to map them using third party inventory systems, which many watchmakers used and continue to use today, as an intermediary - a topic for another day.