"A superficial examination of one of the instruction books of the Comptometer will convince most anyone that it is not only the mechanism of the machine that made the modern calculator so valuable to the business work, but also the schemes laid down for its use. The instructions for figuring multiplication, subtractions, division, square root, cube root, interest, exchange, discount, Engish currency, etc., involved hard study to devise such simple methods and rules.
"The instruction books written by Felt for the Comptometer reflect the genius disclosed in the invention of the machine itself."
Addition on the Comptometer couldn't be simpler, literally. Unlike today's modern calculators where the number must be first entered into the display and then added to the running total by hitting the "+" key, simply striking a Comptometer key will add that key's value to the register total.
As with all "full keyboard" machines, digits can be entered in any order and zeros are not keyed at all. With all "10-key" machines (including today's electronic calcs) the value must be entered sequentially from left to right, including all zeros.
While these "advantages" are largely obsolete today for obvious reasons, 100 years ago the efficiencies of adding in this manner by trained operators made a sizable difference with back office accounting tasks. It should also be noted that simple "adding" made up 80+% of such operations.
There is/was one final subtle advantage to "key-driven" addition. Operators soon discovered that by using only the low value digits (1 thru 5), they gained considerable speed since it was faster to hit, for example, the 4-key twice than to move the finger to the 8-key further up the keyboard. This discovery led to some later-day machines (not Compts), being made with only keys 1 thru 5 (half keyboard). Click on the picture to see a 1952 ad for this machine. Since the more complex operations such as multiplying were nearly impossible without a full keyboard, these machines never posed a serious threat to the Comptometer.
Still later, this shortcut technique would be utilized in a nicely designed and low-cost "Educator" machine for use in early training and practice. One could pound away furiously just doing finger exercises since there was no answer register! While quite useful as "training wheels" they also became a popular gift for Compt operators and F&T employees. This "cutest ever" Compt was probably made in England.
Multiplication is merely repeated addition with columnar shifting. Suppose we need to multiply 123 by 25. Using both hands, we'd first poise our fingers over the "1", "2" and "3" keys, striking down all three keys together 5 times, shifting our finger position left by one column and striking down again twice. Pretty simple, eh?
While the use of both hands was rigidly taught in the Comptometer schools, there were occasions when one hand would suffice.
Note that accuracy here is dependent on the ability of the machine to handle multiple simultaneous carries between columns since the keys all come down at the same time. This, and its key-driven feature, made mulitplying on Comptometers a very efficent operation.
In manufacturing and distribution, shipping and billing operations were major back office applications. Calculating quantity times unit weights and unit prices made heavy use of the multiplying capabilities of Comptometers where they were widely used.
In financial firms such as banks and insurance companies, the product itself was money and here, multiplication was of lesser importance. However, having a printed "proof list" was generally required, giving the printing machines of the Burroughs Corporation a competative edge.
Subtraction on the Comptometer was done by "complementary addition". For example, the complement of 7 is 3 and that of 25 is 75. Felt reasoned that if he gave the operator a way to add 75 whenever 25 was to be subtracted and prevent the carry, he'd have a machine that could subtract, however awkward.
The "missing zeros" on the 9-row full keyboards are a clue to an added bit of complexity where the units digit of the subtraction amount must first be reduced by one, in the example, the 25 must be entered as complementary 24. Of course, the proper subtraction cutoff tab must be held in place to prevent a "hanging 1" from appearing to the left of the "real" answer.
It doesn't stop there either as 0s must be entered as complementary 9s and 9s must be ignored. And finally, if the amount to be subtracted is larger than the register value, that requires an even more arcane technique to deal with a negative answer. Quite frankly, its all a bit beyond me.
In the author's opinion, beyond addition and multiplication, Comptometers were NOT efficient calculators. Division, square root, cube root, interest, exchange, discount, English currency, etc, were all within the capabilities of this machine and the training required was mostly justified by the need to "perform ALL arithmatic operations". Interested readers can investigate the details by securing a reprint of "Methods of Operating the Comptometer" for their private reference.
This advanced "error detection/correction" feature first appeared on the ill-fated E-model and appears to be the brain-child of Kurt F. Ziehm. It would seem that a keying error was often sensed part way thru the downstroke causing the operator to hesitate. Zeihm reasoned that if he could lock all other columns, this would pinpoint the problem.
Because the register dials are not changed on the downstroke (only on the spring-loaded upstroke), the correct digit could then be entered with a full downstroke without losing the running total in the register!. The Controlled Key was the final step that then unlocked all columns allowing the operation to continue from that point.
While today it is hard to understand how all this worked, remember that these machines were run by trained operators at very high speeds. Any feature that allowed them to correct and continue rather than restart a job was most welcome.
A final word to today's collector. Never, ever force a key when it resists! Such resistance in a normally operating machine is likely from a locked column and forcing it will bend the internal "swinging hook" and that column will not work properly thereafter. The author has two such machines and has yet to effect a repair due to the difficulty of getting at the hook itself.