Early cash registers

The cash register is broadly regarded to have been invented in 1879 by James Ritty. Most retellings of this story are misleading for a multitude of reasons.
- Multiple registers had been invented before his, at least three years earlier.
- The machine that he initially invented, now referred to as the "dial", was never sold and has no real place in the lineage of the technology
- The model that came after it, "The Incorruptible Cashier" (IC for short) is much closer to the machines that would catch on and establish the industry.
- However, many sources misidentify the dial as the Incorruptible Cashier
- Furthermore, all photos of the dial are replicas built by NCR which do not work.
All the same, the IC did come out in '79 and is unquestionably the progenitor of all practical cash registers, especially because he sold it to John Patterson, who used it to found NCR and built many machines on it's pattern. Practically speaking the story is true, but the details are widely misunderstood.
The best source of info on this topic I'm aware of is Richard Crandall's book, The Incorruptible Cashier (1988). Note that it is primarily intended as a resource for collectors, and that there are two volumes, the former containing the most useful history in its front half.
Predecessor: Cash Recording Machine
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The 1878 version of the Cash Recording Machine, as illustrated in Scientific American
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An actual specimen of the 1876 original version of the Cash Recording Machine, from Richard Crandall's ebay listing.
Much information about this machine comes from the patents, of which there are two: US188310 and US209827. Some also comes from Richard Crandall's book.
The Cash Recording Machine was patented in 1876, then a second version patented in 1878. They seem pretty similar. Both require the cashier to enter the total amount of the sale as separate digits rather than by pressing buttons for total amounts and both print the total amount of the sale on an internal sales journal. I need to revisit this subject to confirm the rest.
Dubiously, I believe that the 1878 version prints customer receipts, by inserting a slip below the overhang on top, then squeezing the handles together, simultaneously printing customer slip and sales journal entry. There is no bell, and I don't believe there is a counter to accumulate the total amount; the storekeeper is expected to add up the entries on the journal manually.
The photo above is of a specimen Crandall bought from NCR and is currently selling on eBay for several thousand dollars, reasonable given its incredible rarity and significance.
This is probably the first cash register ever invented; Crandall allowed for it to not be the first in his book, but he calls it the first in his eBay listing, with the benefit of another 37 years of research time, so I think we will take it as given that nobody made a meaningful stab at the problem before this.