The replica the science museum made used 19th century tools, methods and engineering tolerances in it's construction. It has been found to be accurate, robust and reliable.
Deano,
The 19th Century was 100 years long, so tools, methods, and eningeering tolerances from just which
part of the 19th Century did the museum use? The advances in engineering, measurements, and machining between 1801 and 1900 were rather substantial.
Babbage first proposed the Engine in 1822, but no manufacturer could achieve the precision he required. Babbage was able to build a less capable model in 1847 but again the bleeding edge nature of the machines's manufacturing requirments hobbled his efforts. Take micrometers for example.
Those measurement tools, which are far more accurate than vernier calipers and - very importantly - far more repeatable, had been around since the late 1600s. However, the first commerically available micrometer and the first micrometer that scientists trusted wasn't developed until 1888. That's a wee bit after Babbage's time.
I still believe an examination of the 'mainframe era' in computing will answer most of your questions regarding the applications for such machines and the number of machines that may be used. Oddly enough, the programmable nature of these machines will
limit the number of applications and users. Let me explain.
Up thread someone mentioned using Babbage engines as fire control devices. That would be a 'waste' of the machine's abilities. While a Babbage engine would be very useful in calculating ballistic tables for whichever gun is being tested, using a Babbage engine to control the aiming of a single gun or battey of guns would be a 'waste' of computing power. You can - and people in the OTL actually did - construct purpose-built, mechanical, fire control computers for that task. (Specially built computers were made ofr other tasks too, check out the US Census.)
These computers were 'programmed' by their physical construction and they could only handle a task or group of similar tasks. You couldn't aim a gun with such a computer one minute, then throw a few switches and run an inventory check the next. A Babbage engine would be used to calculate the ballistic tables for the RN's latest big gun, but the RN warship carrying that big gun wouldn't use a Babbage engine to aim it. Instead, it would use a purpose-built, 'one-program-only', fire control computer(1).
Because we have microchips, we can 'throw away' computing power. Your instant coffee maker has far more computing power than it absolutely needs, more than the LEM flew with in 1969. That's because chips are very small and very cheap. We use them more like a commodity and less like actual machines. Babbage engines wouldn't have had any of those attributes, so Babbage engines wouldn't be used like computer chips.
Bill
1 - Successful, working Babbage engines routinely producing useful results would spark the construction and use of more of these purpose-built, one-program-only machines. The engines show that mechanical computing works and is of obvious benefits, so 'stripped down' models permanently dedicated by their physical contruction to a single task or similiar tasks would be developed. Because they'd be less complicated and less difficult to make, they'd be cheaper and thus more widely used.