A federal judge refused yesterday to intervene on behalf of four Arlington sheriff's deputies who were demoted last month after they publicly opposed the sheriff in a recent election.

U.S. District Judge James C. Cacheris said the most important factor in denying the deputies' request for a temporary injunction was testimony by some deputies during a hearing last month that the four deputies were disruptive at work and that their performance changed after the election.

In this case, Cacheris said in his 16-page decision, "the public interest in having an efficient sheriff's office outweighs the specific interest in {free} speech.

"There appears to be reasons other than First Amendment expressions for the demotion and transfer" of the four deputies, he said.

In December, Sheriff James A. Gondles Jr. gave nine deputies the option of being demoted to the department's lowest rank or being fired, citing his lack of confidence in their ability to perform their jobs.

The deputies, two of whom are considered to hold management positions, were part of a group of 21 deputies whose names appeared in published statements during the campaign. The statements accused the Democratic sheriff of mismanagement and abuse of power and put the deputies publicly on the side of Republican-backed challenger Ronald B. Hager, a former chief deputy.

All nine deputies accepted the demotions but four of them brought suit on grounds that Gondles' ultimatum violated their constitutional rights of free speech. In addition to seeking a return to their previous positions, the four are asking for $1.4 million in damages.

The request for an injunction was a temporary step while the deputies await the outcome of the trial, which has not been scheduled. To win an injunction, the deputies would have had to prove that they would suffer irreparable harm while awaiting the trial.

Cacheris said the financial loss to three of the deputies amounted to a few hundred dollars and he noted the inconvenience of work schedule changes to two deputies, Robin Faye Whitmore and Sean Eldon Whitmore. Since their demotions, the two, who are married, have only four days a month off duty together.

Jonathan Gelber, an attorney for the four deputies, said the accusations of disruptive behavior were based on "hearsay and innuendo," which he intends to show as false during the trial.

William D. Dolan, Gondles' attorney, said of the decision: "Obviously I think it's correct, but I don't take any glee in these suits . . . . "

While Cacheris ruled in favor of Gondles, he noted several points that may figure in his final decision. For example, he said Gondles had failed to prove that three of the four deputies either hold management positions or positions of trust.

Gondles has said he demoted only those deputies whose negative actions could more directly affect the workings of the department, such as managers and persons with whom he had to share confidences.