second analytical engine

 Second analytical engine was designed by Percy Edwin Ludgate (2 August 1883 – 16 October 1922) was an Irish amateur scientist.

Working alone, Ludgate designed an analytical engine while unaware of Babbage's designs, although he later went on to write about Babbage's machine. 

Ludgate's engine used multiplication as its base mechanism (unlike Babbage's which used addition). It incorporated the first multiplier-accumulator (MAC), and was the first to exploit a MAC to perform division (using multiplication seeded by reciprocal, via the convergent series (1 + x)⁻¹). 

Ludgate's engine used a mechanism similar to slide rules, but employed his unique discrete Logarithmic Indexes (now known as Irish logarithms (Boys, 1909)), and provided a very novel memory using concentric cylinders, storing numbers as displacements of rods in shuttles. His design featured several other novel features, including for program control (e.g. preemption and subroutines – or microcode, depending on viewpoint). The design is so different from Babbage's as to be a second type of analytical engine, preceding the third (electromechanical) and fourth (electronic) types. The engine's precise mechanism is unknown as the only written accounts of the engine which survive do not detail its workings, although he stated in 1914 that "[c]omplete descriptive drawings of the machine exist, as well as a description in manuscript" – these have never been found.

He was one of a few independent workers in the field of science and mathematics. His inventions were worked on outside a lab. He worked on the inventions only part-time, often until the early hours of the morning. Many publications refer to him as an accountant, but that came eight years after his 1909 analytical engine paper. Little is known about his personal life, as his only records are his scientific writings. The best source of information about Ludgate and his significance lie in the work of Professor Brian Randell. As from 2016, a further investigation is underway at Trinity College, Dublin under the auspices of The John Gabriel Byrne Computer Science Collection.