Building the World's First Computer: Babbage's Analytical Engine

 Changing the long pinion meshing to be to the inner gear solved the problem of bogus multiplication by 1.35. But now there is another problem:  random subtraction of 1. The root cause is excessive gear backlash. When configured for addition there are four gears between the digit wheel that is "giving off" a source digit and the digit wheel in the adder ("anticipating carriage") that receives it.  If I hold the destination carriage wheel I can wiggle the source wheel almost a complete tooth -- which is a full digit -- without it trying to move the destination.  In doing a transfer I can get it to work correctly by "preloading" the gear train. But if I don't do that, then the first digit being given off might be absorbed by the slop in the gear train. This is clearly a major problem. There are three contributors to the backlash: The center-to-center spacing of the shafts is slightly larger than the gears were designed for, which had to be done to make m

 After various mechanical tweaks to allow too-tight gears to turn, the prototype is starting to come to life. But even just moving a number from one digit stack to another disclosed a bug: in the process it multiplies by 1.35! Sort of. Here's the deal... Changing a number wheel by one digit up or down means rotating it about the axis by 360/(3*10) = 12 degrees, because there are three repetitions of the digits 0 through 9 around the circumference. Since there are 30 teeth on a digit wheel, each full tooth movement represents a change of one digit. When a chain of gears is linked together, a movement by exactly one tooth is propagated unchanged through all the gears -- regardless of the diameter and number of teeth of the intermediate gears -- as long as all the gears have the same tooth pitch. That is a parameter called the Diametral Pitch (DP), which is the number of teeth per inch of diameter of the contact circle of the gears. Following Babbage's Plans from 13 through 28, I