The letter came to the Interior Department from a woman in the mountains of east Tennessee and her question was to the point.

"I thought Carter's strip-mine bill was going to help us," wrote Kate Bradley of Petros, in the heart of Tennessee's coalfields. "What is wrong?"

Her letter told of widespread, speeded-up stripping of the hills by coal operators mining without permits and leaving the terrain disrupted "worse than it has ever been."

A litany of similar complaints from residents of Appalachia and the western coal states pushed Congress to passage last year of legislation putting the first federal controls on the strip-mining industry.

The years-long legislative battle resulted in a law designed to require strippers to restore mined land to a usable condition, to stop stream pollution and to prevent mining on mountain slopes too steep to reclaim.

Heavy lobbying by coal companies and electrical utilities - major users of stripped coal - led to enactment of a compromise regulatory bill that would put most of the enforcement powers in the hands of the states.

The idea was that the Department of Interior would lay down the enforcement guidelines, the states would carry them out with federal financial help but Uncle Sam would reserve the right to monitor and, if necessary, take over any state program that doesn't work.

One answer to Mrs. Bradley's letter is that delays - almost inevitable with the creation of a new bureaucracy - have slowed enforcement of the federal strip-mine control law signed by President Carter in August 1977.

Another answer is that Interior's new Office of Surface Mining, despite criticism from Congress, the coal industry, state officials and environmentalists, is inching ahead with its enforcement program.

OSM cleared an important hurdle last month when a federal district judge here rejected most of an industry effort to have the proposed regulations scattled on constitutional grounds.

OSM's first big problem, however, came not from protesting mine operators, but from Congress. The agency came into existence in August 1977 but did not get full operating funds until last March.

The delay in the congressional appropriation held up OSM's hiring of key management personel and field inspectors and its establishment of staff officers in the coalfields.

Our feeling is that we're making progress in the program by being careful - by exposing our proposed regulations to wide public view and by trying to get qualified people instead of just warm bodies." said Paul Reeves, acting deputy director of OSM.

Although six weeks late, OSM last week took a major step forward with publication of complicated proposed regulations that will govern the industry and the states that choose to run their won regulatory programs.

The complexity of OSM's proposals is best described by size: The regulations weigh 15 ounces and cover 274 pages with detailed rules for an industry that accounts for slightly more than half of the country's coal.

The public wil l have until Nov. 17 to comment on the proposals and OSM will solicit views at hearings next month here and in Knoxville, Charleston, W. Va., Indianapolis, Kansas City and Denver.

State regulators will have until Feb. 3 to submit their won proposals for complying with the federal law. If state law changes are needed, extensions up to six months may be granted by OSM.

In any case, a permanent encorcement program - be it state or federal in any given state - must be ready to go in force in June 1980.

In the meantime, an interim enforcement program is being carried out by OSM. State reclamation agencies and an OSM inspection force of 65 are overseeing a set of interim environmental standards.

The permanent regulations published last week by OSM are, as director Walter N. Heine put it, an attempt "to regulate the regulators as well as those who are engaged in the mining of coal."

Any proposed changes, he said, will be measured "against the directions the Congress has given to us in the statute."

Heine's proposals already have taken heavy flak from the coal industry and coal-state officials, led by West Virginia Gov. John D. Rockefeller IV, a one-time strip-mine abolitionist who changed his mind.

At a hearing called by Sen. Dale Eumpers (D-Ark.) earlier this month, critics charged that OSM's regulations are confusing and burdensome to state regulators. Among the critics were coal-state Sens. Jennings Randolph (D-W. Va.). Wendell H. Ford (D-Ky.) and John Melcher (D-Mont.).

Environmentalists, led by the Environmental Policy Institute, reacted by criticizing Bumpers for holding a onesided and "unfair" hearing that precluded more citizen representatives from speaking out.

While the arguments continue over the shape of the permanent regulatory program. OSM has a small inspection force in the field and is citing companies for violations of the interim standards.

Richard Hall, assistant OSM director for enforcement, said the agency has hired 107 inspectors and hopes to have 200 on the job during the next year.

More than 800 inspections of individual mines have been carried out Kentucky. Pennsylvania and West Virginia mines, in that order, have undergone the most inspections and had the most notices of violation.

As designed by Congress, the law provides a number of opportunities for citizens to become involved in monitoring of strip-mine operations and to complain to enforcement officials.

Hall said that most of OSM's inspections so far have been conducted at the agency's initiative, but that complaints from citizens also have sent inspectors to mine sites.

To intensify public involvement, the Center for Law and Social Policy and the Environmental Policy Institute have just published a handbook for citizen-enforcers.

The handbook provides details of the law and outlines steps that individuals can take to get action from OSM during the interim enforcement period.