Like the golden spike that joined the transcontinental railway more than a century ago, the technological link that will permit totally automated securities trading is about to be forged.

In the near future, Fidelity Investments Group, the country's second-largest discount broker, plans to inaugurate a computer program to perform automated verification and approval of customers' orders. And Charles Schwab & Co., the largest discount broker, plans to start its own automated order entry service during the first half of next year.

Though the two systems are somewhat different, they both boast software that will forge a connection between a customer's personal computer and one of the various computerized systems already used by the industry to execute orders electronically. The systems will make it possible for a customer to trade some securities from home or office without a broker's help.

For customers, computerized investing will mean a slightly faster execution of buy and sell orders. For the securities industry, it could mean significant cuts in costs and personnel.

"It's the wave of the future," said John Wall, executive vice president of the National Association of Securities Dealers.

This final link -- providing computerized processing of customers' buy and sell orders -- follows other advances in computer technology that have made a fully automated system possible. Customers using personal computers are able to telephone computerized information services to do their research on stocks. The personal computers then initiate buy and sell orders.

At the other end, there has been a steady automation of stock exchanges and over-the-counter markets in recent years permitting faster trading and, increasingly, trading without brokers, floor traders or other specialists. One such program, NASD's Small Order Execution System (SOES), is scheduled to make its debut Dec. 14. And the New York Stock Exchange recently announced that its Super Dot 250 system providing instantaneous trades is now capable of handling over 400 million shares a day.

Traditionally, a customer telephoned a broker, who passed the buy or sell order to a wire operator, who transmitted it to the exchange floor for execution by a specialist, who sought a buyer or seller on the crowded trading floor. The fully automated systems such as Investors Express, as Fidelity calls its new service, offer a dramatic change.

It works like this:

A customer uses a personal computer to get quotes on the desired security, then sends an order to the broker's terminal. Instead of the broker calling up the order on his or her screen and personally verifying it, Fidelity's computer automatically evaluates the order by matching it against parameters set for the investor.

The machine verifies the customer's identity through several levels of passwords; checks to see there is enough money in the account to cover the purchase; checks to see that the size of the order is within the limits permitted the customer, and, if necessary, makes sure that the customer is authorized to trade options, buy on margin or sell short.

Such verification is essential to protect the broker from liability. "If a customer puts in an order for 100,000 shares and then heads for the Bahamas, or if he tries to take control of GM while drunk and then claims the morning after it was the broker's error, the broker is on the hook with a trade that goes through automatically," said a broker.

If the order does not match the parameters, the computer will not send it on for execution, but alerts a broker to review the order and determine whether the customer should be contacted. Once approved, the order is sent for execution.

The Securities and Exchange Commission has supported development of automated systems. However, it has expressed concern about possible fraud, suitability of orders and disclosure of tape delayed quotations. For instance, the agency is worried that an unsophisticated customer might be persuaded by a broker or adviser to place a computerized order for an esoteric, high-risk transaction such as oil options. SEC Chairman John S. R. Shad indicated that these concerns probably could be satisfied by after-the-fact monitoring of trades.

Eric Kobren, Fidelity's group marketing director, estimates that five years from now 75 percent of the orders placed by personal computer will be fully automated, and that 25 percent of the company's total volume also will be handled without human intervention.

Some observers remain highly skeptical. Joel Seligman, professor of law at George Washington University and author of a recent paper entitled "The Future of the National Market System," calls total automation a smaller revolution than discount brokerage. He compares home brokerage to home banking, which he says has been a flop.

Korben and others believe that buying and selling stocks through a machine will become as popular as getting money out of an automated teller machine. But NASD's Wall believes the human broker will never be eliminated, "if only so the investor has some one to blame when the stock goes down." (Large and institutional orders are handled individually because fees are negotiated.)

At the moment less than 10 percent of Fidelity's orders are electronically entered. Market research reveals that the users are sophisticated professionals, with incomes of more than $75,000 and stock portfolios well over $100,000. They are somewhat younger than the average investor, more active traders and more apt to buy speculative issues. Two-thirds of the orders are placed over the weekend for earliest execution Monday morning -- one indication of the value of home stock trading.

The number of services offering stock information and other services to computer investors has grown in the past year, although not all permit automated trading.

Trade Plus Inc. of Palo Alto, Calif. was the first at-home system to join with a discount brokerage, C. D. Anderson of San Francisco, in July 1983. According to Derek Anderson, it now has 500 users who pay a $50 initial charge and $12.50 per month plus line charges.

"The jury is still out," he added. "We will need a couple thousand subscribers to make a profit. As time goes on, a lot more people will use personal computers. To discount brokers, this system will help keep costs down. [Full-service] brokers still want the personal touch; it will take a while before they realize the market is changing."

On the other hand, Texas Securities of Fort Worth dropped the program after six months when fewer than 100 people signed up and the brokerage was facing $4,000 a month in line charges. Chemical Bank in New York and Fidelity in Boston are Trade Plus' other major customers.

The Source, a subsidiary of Reader's Digest located in McLean, offers partially automated trading through Spear Securities Inc., a Los Angeles discount broker. The system still requires trade confirmation by brokers, but the entire trading process -- including order entry, stock transaction, online confirmation and portfolio updating -- takes two minutes, according to The Source. More than 57,000 personal computer owners use the system, which costs a typical user $60 a month with two hours on line. Up-to-the-minute quotations from the New York Stock Exchange, the American Stock Exchange and NASD cost an extra $20 a month.

E. F. Hutton, Dean Witter Reynolds and Goldman Sachs are among the full-service brokerages that send customers research on securities through their personal computers. To place orders, customers still must telephone a broker.

At the other end of the line, the automation of stock trading is proceeding rapidly:

*The NYSE's Designated Order Turnaround System (DOT) and the Amex's Post Execution Reporting System (PER) are electronic switching services that transmit an order to the specialist on the floor. SUPERDOT speeds up the process by automatically reporting a trade if the specialist does not respond within three minutes. NYSE's Registered Representative Rapid Response Service (R4) offers immediate execution based on the best quote in the Consolidated Quotation System, a current list of stock prices on the exchanges and over the counter. The Big Board also is experimenting with immediate reporting (five seconds) for 50 stocks, to be increased to 500 stocks in the first quarter of 1985.

*On the regional exchanges, systems with names such as Scorex and Max send orders electronically to floor specialists, who then have 30 seconds in which to offer a better price before the trade is executed automatically at the best price shown on the Consolidated Quotations System. Another system called Pace has no delay. Regional systems are less expensive for brokers than those of the Big Board, but since the markets have less liquidity, there may be no net advantage for the brokers.

*The Intermarket Trading System electronically links the floors of nine exchanges so the trader can choose the best price. The actual trade is then made by telephone or telex to the floor on the exchange selected.

*Last year witnessed the expansion of Instinet (for Institutional Networks Corp.), an electronic trading system for institutions that allows them to deal with one another without going through a broker. Known as the fourth market (in addition to the NYSE, Amex and NASD), Instinet enables institutions to buy and sell at the touch of a computer button in many Nasdaq stocks plus NYSE and Amex listed stocks.

Now, along comes a challenge to Instinet in the form of SOES, which will link 450 market makers in 750 locations around the country to a mainframe computer in Connecticut. When a broker pushes the button, the computer instantly finds the best price available from listings provided by traders in advance and executes the trade within three seconds -- 10 times quicker than a manual execution.

The process eliminates agency desks or those people who call market markers for prices. It also eliminates broken trades, or manual mistakes made by humans in the frenzy of floor trading. SOES will begin automating 25 of the most active over-the-counter stocks and then phase in all national market system stocks over a six-month period.

The next logical step, according to Seligman, would be for the SEC to allow all markets to compete with one another by the creation of a universal message switch. This would permit exchange retail firms to compete directly with exchange specialists and assure that every customer always gets the best price -- so long as the computers don't malfunction