American Realty Trust, an Arlington real estate investment trust, yesterday reported a steep earnings decline for the third quarter and first nine months, partly from a halving of property and development sales and lower rental income.

Net income for the quarter ended June 30 was $175,944 (8 cents a share) down from $839,382 (38 cents). Revenues were $2.3 million, compared with $3.1 million.

For the recent nine months, net income was $1.4 million (62 cents) compared with $6.7 million ($2.99). Revenues were $10.7 million, down from $16.4 million. Net income for the first nine months in 1982 included a tax credit of $1.5 million (68 cents). The company said a similar credit was not available this year.

Thomas J. Broyhill, the trust's chairman, said the results were "satisfactory" despite lower property and development sales than a year ago. Those sales were $11.7 million for the first nine months last year compared with $5.5 million for the comparable period this year and $1.5 million, down to $325,000 for the third quarter this year.

The firm's hotel income, however, rose 21 percent for the quarter and nine months compared with the previous year and interest income rose 67 percent for the quarter and 151 percent for the nine months, Broyhill said.

The firm plans to add 93 new rental units to its Hospitality House hotel in Williamsburg, which "is expected to have a positive impact on the hostelry's future operations," Broyhill said.

Logetronics, a Springfield computer company, reported a net loss of $268,000 for the second quarter, compared with a net loss of $31,000 for the same period last year. Revenues were $9.8 million, compared with $9.7 million.

For the six months ended June 30, the company had a net loss of $797,000, compared with a profit of $182,000 (14 cents) for the same time last year. Revenues were $17.4 million compared with $21.1 million.

Potomac Electric Power Co. reported earnings for the seven months ended July 31 of $68.7 million ($1.28), up from $57.6 million ($1.07). Operating revenue was $639.5 million, up from $613.2 million. For the 12 months ended July 31 earnings were $130.1 million ($2.47), compared with $113.6 million ($2.19). Operating revenue was $1.12 billion, up from $1.06 billion.

Family Entertainment Centers Inc., a franchiser of Chuck E. Cheese's Pizza Time Theatres based in Rockville, reported substantially higher revenues and earnings for the second quarter.

For the second quarter of 1983, the company reported net income of $240,000 (14 cents), compared with a net loss of $22,000 (2 cents) for the same quarter in 1982. Sales for the second quarter this year amounted to $5.8 million, compared with $2.3 million last year.

For the first half, the company reported net income of $515,000 (30 cents), compared with a net loss of $73,000 (6 cents) for the first half of 1982. Sales for the first half amounted to $11.1 million, compared with $3.8 million last year.