In 1909, working as a clerk for a corn merchant in Dublin, Ireland, Percy Ludgate invented a mechanical computer, only the second fully general programmable computer to be designed, after Charles Babbage’s Analytical Engine. Ludgate was apparently unaware of Babbage’s work at the time (few knew of it), although he later wrote about Babbage’s designs. Ludgate’s machine bore no resemblance to that of Babbage, using entirely novel mechanisms for arithmetical calculation and storage of values, with a control system that allowed a form of subroutine to be implemented. Like Babbage, he was never able to actually construct a machine to his design.
The accumulator in Ludgate’s machine was fundamentally a multiplier (unlike the adder-based “mill” in Babbage’s engine), implemented using a novel form of computation devised by Ludgate and now called “Irish logarithms”. It allows multiplication of single decimal digits to be implemented by a simple train of gears, chaining digits into multi-digit operations.
Here is a detailed explanation of Irish logarithms and how the odd tables used to compute them are constructed.