Burlington Northern Inc., which operates the nation's longest railroad system, reported yesterday a sharp increase in second-quarter profits. Directors also voted to increase the transportation and natural resources firm's dividend rate.

President Norman Lorentzsen attributed the earnings growth to a 21 percent increase in coal shipments and a 9 percent gain in grain loadings for St. Paul-based B.N.

Profits totaled $36.7 million ($2.77 a share) in the recent quarter compared with $14.7 million ($1.12) a year earlier as revenues jumped 19 percent to $630 million.

That brought BN profits for the first six months to $68.6 million ($5.16) from $58.3 million ($4.57) last year, an increase of 18 percent. Revenues rose $165 million to $1.2 billion.

Directors raised the quarterly dividend rate to 45 cents a share from 40 cents, starting with a Sept. 1 payout to owners of record July 31.

BankAmerica Corp., the parent company of Bank of America, the nation's largest, said yesterday that its net income for the second quarter of 1978 rose 27.1 percent over the same period last year.

New York's Manufacturer's Hanover Trust Co., holding company for the nation's fourth largest bank, also reported higher second-quarter earnings yesterday.

BankAmerica said consolidated income before securities transactions totaled $118.3 million for the second quarter this year compared with $93.1 million a year ago. Per-share income before securities and net income per share were both 81 cents, up 26.6 percent from 64 cents in the second quarter of last year.

Assets totaled $88 billion at the end of the second quarter compared with $75.3 billion for the same period last year.

In New York, Manufacturers Hanover said earnings in the second quarter were $45.4 million ($1.40 a share), 19.7 percent higher than the $37.9 million ($1.27) recorded last year.

United Technologies Corp set earnings and sales records in both the second quarter and first half of the diversified energy and aerospace conglomerate said yesterday.

Second-quarter net income was $56.6 million ($1.22 a share fully diluted), 13 percent more than the $50 million ($1.09) earned in the 1977 second quarter. Sales rose 9 percent from $1.418 billion to $1.549 billion.

First-half net income was $109.5 million ($2.36), a 14 percent increase over 1977 first-half net income of $95.8 million ($2.09). Sales of $3.024 billion were 9 percent higher than in the 1977 first half, when they were $2.78 billion.

Philip Morris Inc., one of the world's largest cigarette companies, reported yesterday that its second-quarter profits were up 22.5 percent over the comparable year-ago period, exceeding $100 million for the first time in its history.

The diversified concern, which also owns the Miller Brewing Co. and recently acquired the Seven-up Co., said its second-quarter profits rose to a record $10.3 million ($1.74 a share) from last year's $85.1 million ($1.42). Operating revenues gained 25.8 percent to $1.67 billion from $1.33 billion, it said.

For the first six months, the company's profit was up 22.5 percent at $191.8 million ($3.20) from $156.6 million ($2.62) a year ago. Operating revenues for the first half gained 23.9 percent to $3.06 billion from $2.47 billion a year ago.

Control Data Corp. reported a sizable increase in its second-quarter profits to $25.5 million ($1.48 a share) from $17.1 million (99 cents) for the same period a year ago. Revenues increased to $449.1 million from $369.8 million last year.

The computing systems manufacturer said it is "very likely" this will turn out to be its strongest quarter this year due to the volume of original-equipment-manufacturer business and the timing of shipments of large computers. This may moderate results for the third and fourth quarters, the company said.

Six-month profits rose to $41.2 million ($2.38 from $30.1) million ($1.74) a year ago as revenues rose to $849.5 million from $708 million.

Weyerhaeuser Co. posted a 30 percent gain in earnings in the second quarter ended June 25 over a year ago, the giant logging and lumber products company reported.

The company had net income of $117.9 million (90 cents a share) on sales of $985.3 million compared with 1977 second-quarter net income of $91.4 million (69 cents) on sales of $842.5 million.

Two of the nation's largest publishers, Time Inc. and McGraw Hill Inc., yesterday reported record earnings and sales gains for the second quarter.

Time's earnings for the quarter came to $33.9 million ($1.65 a share), up 33 percent from the $25.1 million ($1.24) a year earlier. Revenues moved up 30 percent to $404.5 million from $311.2 million.

First-half earnings were $54.9 million ($2.68) against $40.2 million ($1.98) a year ago. Revenues rose 29 percent to $747.9 million from $579.2 million.

Time Chairman Andrew Heiskell said gains came from publishing, video and buildings materials operations. Time earned about $4 million in favorable currency exchanges, mainly from book publishing activity, he said.

Time's publications account for more than 50 percent of the company's sales. Circulation of the five magazines rose 18 percent in the first half, the company said.

Other publishing activities include the recently acquired Washington Star newspaper, Time-Life Books and Little, Brown & Co., a leading trade book publisher.

McGraw Hill, one of the world's largest publishers of technical scientific and business magazines and books, reported a 30 percent gain in net earnings to $13.2 million (53 cents a share) from $10.2 million (41 cents) last year. Sales for the three months reached $176.1 million, up 16 percent from $151.8 million for the quarter last year.

First half net income was $23.8 million (96 cents) on $329.7 million in revenues compared with 1977 first-half net income of $16.9 million (68 cents) and revenues of $284.5 million.