As temperatures in the Washington area soared into the 90s for the eighth consecutive day, officials in Virginia reported yesterday that sparse rainfall and searing heat have cost farmers in 54 counties substantially more than $196 million in drought-related losses.

The bleak effects of the dry spell are evident in crop estimates issued yesterday by the Virginia Corp reporting Service of the U.S. Department of Agriculture. The state's corn corp now is expected to run 23 per cent below that of last year despite last month's estimate that predicted a harvest slightly larger than that of 1976.

As a result of the drought, the yield of land planted with corn has plummeted to 62 bushels an acre, 14 bushels lower than the lower 1976 yield and the lowest since a 56-bushel yield in 1964.

The summer of 1977 has not yet approached the summer of 1966 when, according to the National Weather Service, the area sweltered through the record number of days on which the mercury reached at least 90 degrees.

In 1966, that level was reached 59 times, including 43 times by Aug. 11. When the temperature reached yesterday's official high of 91 degrees at 3:20 p.m., it marked the 37th such day this year.

The outlook through Tuesday calls for more hot, humid weather possibly broken by thunderstorms that occasionally pass through the area in late afternoon and evening. Forecaster George Schielein said he sees "no long-term break in this stuff."

The fleeting showers that have been dousing afternoon commuters recently also have been cleansing the air.Yesterday's 3 p.m. reading was 75, in the "unhealty" range but far below Wednesday's reading of 115 that preceded a thunderstorm and an influx of gentle breezes.

While recent thunderstorms have eased the impact of the drought in Maryland, they have been too scattered and their moisture has evaporated too quickly to soften Virginia's plight.

President Carter has declared a drought emergency in 38 Virginia counties and is considering applications for such status by 12 other counties that have received emergency status from Virginia Gov. Mills E. Godwin. Four other counties have asked Godwin to make them eligible for federal aid.

These 54 counties have estimated their drought damage at a total of $196 million, and Raymond Vaughn, deputy commissioner of the State Department of Agriculture and Commerce, said yesterday that the total would be "substantially greater" when damage reports are updated.

Federal drought emergency status entitles Virginia farmers to direct federal aid and low-cost loans.

Although Carter first declared an emergency in Virginia June 23, state officials said yesterday that the aid programs, administered by the Department of Agriculture, did not begin running smoothly until this week.

One culprit, according to S. Mason Carbaugh, state commissioner of agriculture and commerce, was a Sept. 1 expiration date the federal government originally imposed on the program for drought-stricken dairy farmers and cattle ranchers.

On Monday, the federal government extended the date to Dec. 1 after Virginia official requested an extension to May 31, 1978. Vaughan said yesterday that the state still hopes to gain the 1978 waiver.

The Sept. 1 deadline "created chaos . . . and uncertainties" among farmers, because they did not know whether they would receive federal aid for the winter, Vaughan said.

Vaughan, said the drought, which began in the northwestern section of the state, has spread in recent weeks to the south and southeast. As a result, he said the latter portions now are in critical conditions. "I probably shouldn't say it can't really get any worse, but it really can't get any worse," he said, referring to northwestern Virginia.

In Maryland, the USDA's Crop Reporting Service said yesterday that corn production will run at 49.6 million bushels, 13 per cent below last year's record harvest but only 500,000 bushels below the 1975 total.The yield per acre will be only 80 bushels, 11 below that of 1976.

While tobacco output is expected to remain at 1976 levels and the soybean crop may run slightly, the hay harvest in Maryland will drop 19 per cent, according to the Maryland-Delaware Crop Reporting Service.