Analogue computers are now wholly obsolete, but in their day they were the means of choice for solving many problems in physics and engineering. Note that mathematics is not mentioned there- nobody is going to find out the 10,000th digit of pi with an analogue computer. In fact the third decimal place would probably be inaccessible.

An analogue computer uses continuously variable voltages rather than limiting itself to 0 and 1, with the magnitude proportional to the real quantity. This can allow problems to be solved with a minimum of hardware- dividing by two just requires a potential divider, whereas making even the simplest digital circuit capable of division is a major undertaking. The downside is that accuracy is distinctly limited- in a digital computer you use variables of whatever length you like, given suitable software, but in the analogue domain you are dependent on the accuracy of the electrical components and readout devices.

Note that the PACE computer below uses a component oven and a digital voltmeter to achieve the required accuracy. Neither was a cheap option.

Left: A PACE 16-231R analogue computer. Photograph published in 1961. The original caption to this picture reads: "This high-quality computer provides a large metal patch panel of modular design which has provision for one hundred amplifiers and associated non-linear equipment. Special features include an all-electronic digital voltmeter and a high-speed print-out system. Potentiometers and function generators may be automatically servo-set. Selection of problem read-out points is controlled by push buttons. Computing networks are housed in a temperature-controlled oven." The one hundred operational amplifiers- valve, of course- are housed in the lower right of the unit under the desk shelf. ("desktop" on a computer meant what it said in those days) There are 25 quad amplifier modules of type PACE 6.002. The amplifiers were chopper-stabilised and built on printed circuit boards. The balancing trims and indicators can be seen on the front of each module.

SOLVING A DIFFERENTIAL EQUATION WITH AN ANALOGUE COMPUTER
In some ways this is simple and intuitive- if of limited accuracy- but it can get hellishly complicated. This is a very simple example- a first-order differential equation.

The diagram below shows the simulation of a mechanical shock-absorber or damper.

• The input force is F which causes deflection x.
• The spring is defined by constant k so the force exerted by the spring is kx.
• The damper or dash-pot is defined by constant c so the damper force is c times dx/dt (ie velocity)

COMPUTERS & MANUFACTURERS
An incomplete list:

Acronym	Manufacturer
EASE	Berkeley Division of Beckman Instruments.
GEDA	Goodyear Aircraft Corp
PACE	Electronic Associates Inc
REAC	Reeves Instrument Corp

BIBLIOGRAPHY

The Design & Use of Electronic Analogue Computers.	C P Gilbert	Chapman & Hall 1964
Design Fundamentals of Analog Computer Components	R M Howe	Van Nostrand 1961

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