HE ease of driving a car equipped with an automatic transmission makes automatics the overwhelming favorite of American motorists. But while the Hydra-Matic 4T40-E transmissions moving down the final assembly line at a General Motors factory in Windsor, Ontario, may be simple to use, they are far from simple to design and build. Flipped upward like cast-aluminum cornucopias, the partly assembled transmission bodies are fed a harvest of gears, chains, springs, electronics and wires. Exactly how the pieces come together to shift gears is something of a mystery even to the people who make the transmissions, which are soon to be installed in Chevrolet Cavaliers, Oldsmobile Aleros and other cars. When asked about the specifics of the torque converter, the link between the transmission and the engine, the plant's engineering manager, Don Wright, laughed. "As for how it works, you'll have to ask someone else,'' he said. "I'm the guy who knows how to make them."

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But what sets the 4T40-E apart from older models is not the intricacy of its mechanical and hydraulic systems. Rather it is a box tethered to the transmission by a wire. Inside, a sophisticated microprocessor uses special software to replace the electromechanical systems that once controlled automatic transmissions.

By moving to electronic controls, transmission makers have not only been able to introduce new features - like additional gear ratios and transmissions that adapt to different driving styles - but have also narrowed the efficiency and performance gap between automatics and manual transmissions.

Mark Gilmore, the director of transmission development at G.M.'s Powertrain division, acknowledged that the all-mechanical automatics that were being produced by the company when he joined it in 1977 probably deserved their popular pejorative name, "slush buckets." But today, he said, there is legitimate debate on how they compare with manual transmissions. "I think we're now certainly very close with automatics," he said.

Whether manual or automatic, transmissions perform two basic jobs. At low speeds, they allow the drive shaft that powers the wheels to rotate at a lower rate than the engine's drive shaft. Doing that creates the force, known as torque, needed to accelerate the car. At higher speeds, the situation reverses. To prevent the engine from running inefficiently, the transmission creates a final drive shaft rotational speed that is higher than the engine drive shaft's rate. The first automatic and semiautomatic transmissions appeared in the years before World War II, but they were largely experimental and not particularly successful. "They provided acceleration that could best be described as stately," said Bob Casey, curator of transportation at the Henry Ford Museum and Greenfield Village in Dearborn, Mich.

Then in 1939, the first G.M. Hydra-Matic appeared, and it became available on Oldsmobiles during the next year. It used a hydraulic system to make gear changes based on a complex set of factors, including the vacuum pressure of the engine's exhaust manifold, the car's speed and the engine throttle setting, all measured mechanically. Various springs opened and closed hydraulic pistons to shift gears. "It was just insanely complicated, yet the transmissions became extremely reliable," Mr. Casey said.

One of Mr. Gilmore's first jobs as a junior engineer at G.M. was to adapt transmissions to different engines by changing their springs and pistons. "I used to carry a little suitcase around filled with hardware," he said. Eliminating that fiddly process was one reason that G.M. and other transmission makers started looking at electronics. It also quickly became apparent that electronics offered ways to boost performance.

Automatic transmissions, like manual ones, need to uncouple themselves from the engine when shifting. Rather than use a mechanical clutch - basically two abrasive discs that press against each other - the torque converter makes its coupling between the engine and the transmission with hydraulic fluid.

When a car is accelerating, fluid couplings can boost engine torque. But at higher speeds they put the "slush" into slush box.

The obvious solution, introducing a mechanical connection that kicks in at highway speeds, was difficult without electronic controls.

The first G.M. transmission to have all of its gear changes controlled by electronics did not appear until 1989.

Transmission software has become so sophisticated that it can now determine if a car is climbing a hill - a situation that often baffled transmissions in the past - and study drivers' patterns to see if they prefer sporty acceleration or sedate but economical driving. "Our goal is to have the customer not even realize the transmission is doing a whole lot of things," Mr. Gilmore said.