A gain of 62 cents a share on the dissolution of a joint venture in Japan enabled Dow Chemical Co. to report a small increase in second-quarter profits from a year ago.

The company said yesterday that its net income was $197 million ($1.02 a share) on sales of $2.728 billion compared with 1981 second-quarter net income of $189 million ($1.00) a year ago on sales of $3.067 billion.

First-half profits were $351 million ($1.82), which included a 30-cent-a-share gain on the exchange of stock for bonds, on sales of $5.509 billion compared with 1981 first-half profits of $369 million ($1.98) on sales of $5.964 billion.

Executive Vice President Robert M. Keil said overall demand for Dow's products was very weak during the half, reducing operations and thereby raising unit costs. Lower oil and gas prices adversely affected the Dowell oil-well-servicing division. One bright spot was styrene-butadiene latex products.

Eastman Kodak Co. said yesterday that its second-quarter profits declined despite slightly higher sales and that both profits and sales fell in the first half.

The photographic-products giant cited the sluggish world economy, price pressures in the chemicals industry and the cost of introducing new products, but predicted positive results for the full year, partly because of an "enthusiastic response" to one of its new products--the Disc cameras.

Second-quarter net income declined 13 percent to $248.3 million ($1.52 a share) from $284.5 million ($1.77) a year ago as sales inched up to $2.43 billion from $2.42 billion.

First-half earnings slipped 19 percent to $429.6 million ($2.64) from $533.6 million ($3.31), and sales dropped 1 percent to $4.68 billion from $4.72 billion.

Goodyear Tire & Rubber Co.'s earnings and sales declined in both the second quarter and first half, but U.S. sales set records in both periods, and Chairman Charles J. Pilliod Jr. called the company's performance respectable in light of the recession and accompanying low level of vehicle production.

Pilliod said that Goodyear increased its unit sales of replacement auto tires and its share of the truck-tire market, and that its other operations showed good results.

Second-quarter earnings dropped 9.3 percent to $80.5 million ($1.09 a share) from $88.8 million ($1.23) in the same period of 1981, while sales declined 3.4 percent to $2.290 billion from $2.372 billion.

First-half earnings showed a 13.3 percent decline to $126.1 million ($1.72) from $145.5 million ($2.01), and sales dropped 3.3 percent to $4.437 billion from a record $4.589 billion.

This year's second-quarter and first-half results included a $17.2 million extraordinary gain from the exchange of shares of common stock to retire sinking-fund debentures.

PepsiCo Inc. said yesterday its second-quarter and first-half profits rose 14 percent from comparable periods last year on strong U.S. sales by its soft-drink and other operations.

In the quarter ended June 12, profits rose to $99.6 million ($1.06 a share) from $87.5 million (95 cents) as revenues rose 9.4 percent to $1.81 billion from $1.65 billion.

First-half earnings climbed to $159.8 million ($1.71) from $140.3 million ($1.53) as revenues rose to $3.37 billion from $3.12 billion.