In Nashville, the police officers call it "The Iron Segeant" - a grim looking silent witness that is always with them, observing and recording just how their patrol cars operate 24 hours a day. In Washington, it is referred to less decorously as "another of the police department's emtrapment ideas" or "that thing in the truck."

The D.C. Police Department's field inspection division says that whatever it is called, the device-known as a Tac-O-Graph-will reduce accidents and save more than enough money to pay back the city's investment. The device looks like an oversized speedometer with a clock in the middle. The instruments are being installed in 22 District police cars as part of a pilot project to monitor the speed of the car while in operation, idle time, distance traveled, the time the engine is not running, and when the siren and emergency lights are used.

In 1977, according to police officials, D.C. police cars were involved in 416 accidents, costing more than $300,000, not including time lost by injured officers, loss of equipment use during repairs, investigating costs and the cost of early retirement for severely injured officers. Totalling all of these costs up, according to one police official, the average minor "fender bender" - even without injuries-costs about $500.

And $500 is just about what one Tac-O-Graph costs. If it eliminates one accident for each of the cars in which it's installed, police officials figure, it will have paid for itself. Anything more than that is gravy.

All of the information recorded by the device is recorded, minute for minute, on a coated disc locked inside. The device itself is tamper-proof and the information it records is said to be accurate to within one minute, one foot and one mile per hour. The disc is changed daily.

Since police regulations require officers in nonemergency situations to observe speed limits in the city (25 mph unless posted otherwise), the Tac-O-Graph will, in effect, catch police speeders.

"Obviously," 1st District Captain M. D. Carney said, "the guys do exceed the speed limit sometines, and they do it when they're not using their emergency equipment sometimes and sometimes they have accidents. The object is to cut accidents."

By Jan. 1, 22 of the devices will be installed in scout cars used by police in the 1st District, covering Southwest and lower Northwest Washington.If the pilot project is judged successful there, it will be instituted elsewhere in the city.

The D.C. Fire Department, which has been using Tac-O-Graphs for more than a year, has decided to install them on all ambulances and all other new equipment it purchases.

But nobody likes to have the boss peering over his shoulder all day long, and police officers are no different.

"I see no reason why we should have them," said one officer, who asked not to be identified. "It's just a waste of money." The whole purpose of using the device, according to this officer, "is to see how long we're out of service . . . to see how we're doing our job, and I don't think it's necessary."

Officers foolish enough to try sleeping on the job-"hoodling" as D.C. police officers call it-will be found out by the device. "I think," the officer continued, "they're trying to catch officers-especially on the midnight shift," although he added, "I don't think there's much of that going on."

Other officers expressed similar objections to the device, one noting that he occasionally bends department regulations to respond more quickly than the book allows when another officer calls for assistance.

"Personally," said this officer, who also asked not to be identified, "I feel protecting one of my fellow officers is more important than going 5 or 10 miles over the speed limit."

One superior called the devices "a real morale disaster . . . The whole purpose of them is apparently to reduce accidents, but they're cutting into the officers' hustle."

But other police officers expressed indifference. "I don't believe in driving fast, so it doesn't bother me," said J. J. O'Connor.

Police officials insist that the reason for installing the devices is to reduce accidents. "There's no denying that it can be an asset to management," said Lt. James Teague of the department's field inspection division, "but it's being installed primarily as a safety devide . . . I think what most of the fellows fear is that they'll be used in a negative way. If a guy's doing his job, he's got nothing to worry about."

Teague cited one instance, in Nashville, in which an officer who had opposed the "Iron Segeant" later became a believer.

After being suspended for 15 days for dismantling the device, the Nashville police officer was involved in a traffic accident while on patrol. He claim he had his emergency lights and siren on. The person he struck said he did not. The testimony of the "Iron Segeant," admitted in the court case, corroborated the police officer.

Teague, who said he used to be in a scout car himself, expressed little sympathy for officers who bend the rules. "It's our job to enforce rules, so we have to abide by them ourselves," he said, adding, "They wouldn't do it if the sergeant were riding by them in the front seat."

And in a sense, Teague said, he will.