In 1819, Baltimore merchant Alexander Brown received a letter from his son, William, who managed the family's trading and shipping business in Liverpool, England. In his elaborate script, William wrote that he was thinking about investing money in a cotton mill for one of his children.

The idea did not sit well with William's father or brothers, who quickly responded that the cotton business was extremely uncertain and that getting involved in a risky venture could injure William's reputation as a financially strong businessman.

"If we look around here," wrote Alexander Brown, "we find that those persons who have kept steadily in one pursuit are far the richest men."

The advice was similar to the sentiments Alexander Brown expressed earlier when William proposed going into the insurance business and speculating on real estate, according to the firm's history.

"The risks are too great and we know nothing about the business," Alexander Brown wrote to his venturesome son. "We are doing well enough as it is. Be content."

Seven generations later, the descendants of Alexander Brown are still running the firm that he founded, still displaying the red-and-white company flag that flew on the Alex. Brown & Sons sailing ships as they hauled agricultural products to Europe and returned with Irish linens and other goods.

Indeed, 190 years after Alexander Brown opened his business in Baltimore, caution is still the watchword at Alex. Brown & Sons Inc.

"We don't do sea changes around here," said Benjamin H. Griswold IV, the great- great-great-great-grandson of Alexander Brown, during an interview in the firm's historic building in Baltimore.

Growth and change, he insisted, come slowly and steadily at Alex. Brown and then only by what he called "logical extension."

But change does come. And it has been coming faster and faster at Alex. Brown Inc., a holding company for Alex. Brown & Sons, a brokerage firm that is spreading its wings nationally and internationally and is moving into an ever-widening range of financial activities.

Once dependent on its retail brokerage operations, Alex. Brown has grown into a major force in investment banking in the last decade, rivaling the powerhouses of Wall Street. From a moderate-size regional firm, Alex. Brown has rapidly become a national specialty firm.

Alex. Brown, which did 55 public offerings and raised $3.4 billion last year, is running at a similar pace so far this year, with 22 offerings worth $1.8 billion.

The firm also moved into the mutual fund business in recent years and now has $520 million in its equity and fixed-income funds, plus $1.9 billion in its money market funds.

Griswold said he doesn't spend a lot of time thinking about the generations of Browns looking over his shoulder. But he acknowledges that his job brings with it "a highly developed sense of stewardship."

His generation's goal, he said, is to develop the business and "get it to the next generation in better shape than we got it."

Looking ahead to the decade of the 1990s, Griswold said he could foresee a time when retail commissions, investment banking revenue and money management fees would each account for one-third of the firm's total revenue. Fee income is highly prized, of course, because it is resistant to the market's cycles of boom and bust.

Moving the firm toward that balance will be helped by the "logical extensions" that Alex. Brown has recently announced.

Only a few days ago, for example, the firm said it had formed a restructuring group to advise debtors and creditors in bankruptcies and near-bankruptcies. After an era of corporate buyouts, which has left many companies wallowing in debt, the restructuring crew at Alex. Brown will try to help troubled companies work their way out of their financial excesses.

It is ironic, perhaps, that the head of the restructuring group will be Barry W. Ridings, who did similar work at ill-fated Drexel Burnham Lambert Inc., where much of the nation's corporate debt was created.

In March, Alex. Brown teamed up with Woodbrook Capital, a Baltimore investment group, to form ABS Merchant Banking Ltd. Using its own money, the merchant banking group will try to invest in management buyouts of companies that have annual sales of $25 million to $250 million. In the initial funding, Alex. Brown will put up 75 percent of the money and Woodbrook 25 percent.

The idea is a "logical extension" of the firm's major effort in the area of mergers, acquisitions, private stock offerings and even venture capital. During 1989, Alex. Brown did 42 M&A deals worth almost $7 billion.

In February, Alex. Brown leaped into the international real estate market when it created a new $4 billion company that will invest in real estate for state, local and corporate pension funds.

Alex. Brown accomplished this by buying a large West Coast real estate investment firm and then bringing in a British partner, Kleinwort Benson Group PLC, a leading merchant bank.

The project was a "logical extension" of Alex. Brown's earlier experience in persuading public pension funds to invest in real estate, and was aided by the international links the firm had developed in London over the years.

Another recent foreign link was the request from Nomura Securities in Tokyo for Alex. Brown to manage a $50 million fund, investing Japanese money in American growth companies.

Alex. Brown doesn't plan to open an office in Tokyo, but it does have one in London. The firm, in fact, now has 20 offices in cities including Atlanta, Boston, Dallas, Los Angeles, New York and San Francisco. With 1,650 employees, the firm has 345 retail brokers and about 100 sales and institutional brokers.

The firm also has 41 analysts who follow stocks in seven major categories: energy, environment, health care, financial services, technology, transportation and consumer companies.

The firm's goal, Griswold said, is to create a "core of knowledge" that can flow through virtually all the activities of the firm, from retail and institutional brokers to the investment banking and money management operations.

The industry knowledge that can help a broker sell stocks to a customer also can help a portfolio manager decide which stocks he wants to buy for his fund and can help investment bankers decide what kinds of companies they want to take public.

Similarly, the investment bankers, who get to know officials of the companies they take public, can encourage those executives to use Alex. Brown to manage their corporate pension funds, to handle their mergers or acquisitions and even to supervise their personal investments.

In a historic sense, perhaps the biggest change at Alex. Brown in recent years was its decision to give up its traditional partnership organization and create a public company in order to raise the capital needed to help the firm grow.

The firm, which had about $50 million in capital before it went public in early 1986, today has about $200 million.

Working at the firm with Chairman Ben Griswold, who is 49, is his younger brother, Jack S. Griswold, 47, who is vice chairman. Although Ben Griswold would be happy to see the family's role in the firm continued by the Griswold children, there is no way to predict what the future will bring, he said.

Family participation was much more predictable in the old partnership days, he noted. But it may be much less so now that Alex. Brown is a public company, with ownership widely spread. The Griswold families own about 7 percent of the stock.

Although the Griswold brothers hold key posts in the firm, the day-to-day management is in the hands of President Donald B. Hebb Jr. and Chief Operating Officer A.B. Krongard.

Alex. Brown stock, which once sold for as much as $28 before the 1987 market crash, has been in the $9 to $14 range for most of the last two years. In recent days, the shares have moved up and the stock closed Friday at $15.

The firm's book value per share was $11.28 on March 30 and in view of the relatively low price of the stock, the firm has been buying back its own stock in large quantities.

But then, the Alex. Brown folks have always had a keen eye for a bargain.