The publisher of The Washingtonian, a local monthly magazine, has charged in a petition filed with the Federal Communications Commission that a magazine published by four major public television stations is losing money at a rate that amounts to $4.2 million a year -- a figure disputed by the television magazine's publisher.

Asking the FCC to reconsider his complaints about on-th-air promotion of The Dial, Philip Merrill offered a financial analysis by a consultant and suggested that the deficit may have to be made up out of the contributions of subscribers who believed they were sending money to support public broadcasting, not to support the magazine.

"Under these circumstances, on-air announcements promoting The Dial as a 'premium' or free benefit provided to noncommercial television subscribers are at best misleading and at worst a fraud on the public," Merrill charged in the petition.

Dial publisher Morton Bailey Jr. said he has not yet seen the petition but described figures quoted from it as inaccurate. "The numbers you quote me are a very interesting set of numbers but they don't bear any particular relation to the truth," he said.

Merrill has challenged the existence of the televison guide with expanded general-interest format since before the first issue appeared. The existence of the competing magazine poses a challenge to The Washingtonian and other magazines by offering an alternative market for advertisers.