The negotiating dance between the United Mine Workers of America and the Bituminous Coal Operators Association continued yesterday as the two sides waltzed around the bargaining table, trying to find a peaceful stopping point before the music stops at 12:01 a.m. Tuesday.

The UMWA, playing the role of an institutional Cinderella, has warned industry representatives that it must get home with a tentative agreement by that time if it is to end a 15-year string of contract strikes that began with a 17-day walkout in 1966. Both union and industry officials say they have been chastened by the last strike, a record 111-day dispute that began in late 1977 and ran through the early part of 1978, and want to end their talks in peace this year.

The contract does not actually expire until March 27, but the union says it needs 10 days to complete the ratification process. However, some union officials were sayng yesterday that there is a possibility they could win ratification in nine days.

The two sides recessed bargaining at about 8:20 p.m. last night with intentions of resuming at 10 a.m. today. Left unresolved were a number of issues, including the BCOA proposal to scrap the industry's current multi-employer pension plan and replace it with company-by-company pension coverage.

Under the current pension plan, the 130 companies represented by the BCOA pay benefits from a common financial pool. Small coal companies enjoy this arrangement because it helps defray their insurance costs. But it also means that the larger firms, such as Consolidation Coal, Peabody and U.S. Steel, are helping to subsidize the expenses of their smaller competitors.

The big companies are having the biggest say in the coal talks, which began here in earnest Jan. 22, and they're saying that the current pension fund arrangement, especially in light of the closings of many coal companies, is too expensive. Surviving coal firms with UMWA workers are stuck with a $4 billio unfunded liability under the current plan, according to industry officials.

However, UMWA President Sam Church has argued throughout the talks that going to company-by-company coverage would jeopardize pension benefits for many of his members, and, as one union official put it last evening, "giving in on the pension thing is one thing Sam can't afford to do."

Other issues involved in the talks include work rule changes demanded by the industry that, according to the industry viewpoint, will increase productivity; the elimination of the Arbitration Review Board, which the union feels is too pro-industry in grievance procedures, and, of course, basic economic issues that had earlier included a union demand to reinstitute the cost-of-living allowance (COLA), eliminated in the 1978 contract.

Union officials, basically the only people willing to say anything about the intense talks, cautioned last night that many of the latter issues "are still on the table." But one UMWA official, expressing what appeared to be a popular union sentiment, said: "Most of that stuff, the economic package and what have you, probably could fall into place pretty fast if the industry people back off their pension demand."