After a grim first quarter, Woodward & Lothrop Inc., the 15-store independent retail chain, yesterday announced a 10.4 percent increase in second-quarter profits, while the company's management issued a cautious warning about the rest of the year.

During the company's second fiscal quarter, which ended on Aug. 1, Woodies reported profits of $1.025 million ($41 cents a share) on sales of $65.612 million, compared to 1979 profits for the same period of $928,000 (38 cents) and sales of $63.994 million.

The slight second-quarter improvement followed the three-month period beginning with February when the company showed a 53 percent decline in profits, the largest quarterly percentage decline in the company's 100-year history.

At the time, Edwin Hoffman, the chain's chairman, blamed the company's sagging record on tight consumer spending patterns and the Federal Reserve Board's credit restraints. In a statement yesterday, Hoffman said the company's six-month sales figures "have been severely affected by the current economy."

Hoffman said the company continues

to show decline in credit sales and even though the government's controls on consumer credit were lifted in July, sales have not returned to earlier levels.

"We view the fall with extreme caution," Hoffman said. "Unless we see a dramatic improvement in the economy and customer buying habits, the balance of the year promises to be difficult.

"We are confident the programs we have in effect to closely monitor all facets of the business will minimize the impact of the current slow-down in retail sales in our profits."

For the six-month period ending July 31, Woodies reported a sales increase of 4.5 percent, as sales rose from $125.314 million in 1979 to $130.978 million for the same quarter this year. Profits for the first half decreased 24.6 percent, falling from $2.071 million in 1979 to $1.562 million in 1980.

In other reports, Baltimore Gas and Electric Co. has reported a sharp drop in profits for the seven-month period ending July 31 as profits fell from $71.086 million ($2.28 per share) in 1979 to $57.920 million ($1.81) for the period this year. The company said the profits decline could be attributed to high costs and a lack of growth in electric and gas sales.

The James River Corp. reported profits of $1.882 million, a 54 percent drop in profits for the company's first fiscal quarter ended July 27. Sales for the Richmond-based company dropped 11 percent to $77.871 million, compared with $87.266 million in sales for the same quarter in 1979.