After four years of decreasing crime, Montgomery County saw a 7.8 percent jump from last year in crime reports between July and September of this year, county police officials say.

Police spokesman Sgt. Harry E. Geehreng said the quarterly increase, coming after a 2 percent increase between April and June, may be a sign that the four-year trend has bottomed out.

Those years of decreasing crime followed a decade of steady increases.

In the first nine months of this year, 46,065 crimes were reported to county police, a 5.1 percent increase over the 43,829 in the same period last year. That works out to about one crime for every 13 residents in the county of nearly 600,000 persons.

Police said they had made 7,794 arrests in the first nine months, including some for crimes in past years.

Crime figures for the third quarter of this year were not available in other local jurisdictions, but Lt. William White of the D.C. police said serious crime in the District increased 1 percent in August after declining earlier in the year.

In Prince George's County, serious crime during the month of August was down 5 percent, police there said.

According to FBI figures, crime reported to police around the country declined 5 percent during the first half of this year, and similar declines were noted in every Washington area jurisdiction except Montgomery.

Compared with the same period in 1983, the Bethesda district saw an 5.8 percent increase in crime, while reports were up 12.7 percent in Silver Spring and 6.3 percent in the Wheaton-Glenmont district. The only decline, 2.9 percent, was in the Rockville area.

Hardest hit was the sprawling northern half of the county, where fields of corn and cattle are fast giving way to residential developments. In that area, covered by the 104 patrol officers and 11 detectives from the Germantown police station -- about the same number assigned to other districts -- there was a 16.9 percent increase in the number of crime reports between July and September, up from 3,353 last year to 3,919 this year.

Even with the third-quarter increases, the average of 64.3 serious crimes reported each day remained well below the daily average of 82.5 during 1980, the year when crime in the county reached an all-time high, police noted. This year, there were three murders during the quarter, compared with four last year; 34 rape reports, compared with 37; and 140 robberies, compared with 147.

Burglary accounted for more than half the increase in serious crimes for the latest quarter, police said. There was an 14.2 percent increase in the number of burglary reports, which grew from 1,287 to 1,470.

As in previous quarters, about two-thirds of these were residential burglaries, police said.

The Germantown district -- which, with 295 square miles, covers more than half the county's area -- did not even have a police station until 1980.

That district stretches from Shady Grove north to Frederick and Howard counties, and from the Potomac River to Georgia Avenue. It includes all of Gaithersburg, Montgomery Village, Poolesville and Damascus.

It is difficult to correlate population growth in the northern area of the county with the increase in crime because no census has been taken since 1980. But county planning officials say the county's fastest residential growth is occurring in the Germantown police district.

According to the 1980 census, there were 61,985 people living in the planning district that includes Gaithersburg and some surrounding areas, but planning officials estimate that the population in that district is increasing by more than 4 percent each year.

Farther north, in the planning district that surrounds the town of Damascus, which had 14,896 persons in 1980, the population has been growing about 2.6 percent each year.

Officials at the Germantown station could not be reached for comment, but Geehreng said the increased crime there, as in other parts of the county, came as no surprise to police.

County police "expect other jurisdictions will experience the same bottoming out effect," he said. "If not now, then in the future. . . there's going to be an increase and it's not unusual. We are just ahead of the other departments" in the area.

Captain Thomas D. Rufty, who heads the Rockville district, said he is pleased that crime reports were down in his district, but said he was unable to explain why it has happened.

"I don't wish to take credit for the decrease because I don't want to take the blame if crime goes up," he said. "I really can't tell you why it's gone down."

Rufty, who was head of the police investigative services until June, attributed Germantown's increase to a growth in population, which increases both the pool of potential criminals and the number of potential victims.

Chief Jarred Stout of Rockville's police force said the area has benefited from the coordination of two police forces, but that slowing residential development in Rockville has helped keep crime down.

"The rest of the county has had the development," he said. "Residential development within the city has been from slim to virtually none."

But Stout, like other police officials, said the precise factors at work in fluctuating crime rates remain elusive. "It's a combination of things and no one . . . is sharp enough to know which of the several forces at work is accounting for it," he said.