It was a terrible blow to Chrysler Corp.'s pride.

The naion's tenth biggest industrial company and third biggest automaker has long touted its engineering ability and has pioneered many automotive improvements over the decades.

Last April, however, in an admission that the company cannot afford to keep up with all technological developments in the fast changing automobile industry, Chrysler entered into an agreement with General Motors Corp. in which the nation's biggest auto producer will assist Chrysler in research and development work on fuel economy, emission control and safety.

But the blows to its pride have been nothing when compared to the blows the company's profit-and-loss statements have taken in recent years.

In 1978, when the automobile industry in general was booming. Chrysler recorded a $204.6 million loss. In the second quarter of this year, when all U.S. automakers began to feel a sales slump as result of high gas prices and long gas lines, Chrysler lost $207.1 million, more than it lost all last year.

And things do not promise to get much better. Chrysler executives predict another huge loss in the third quarter, traditionally the worst in the auto industry, and Wall Street analysts, such as David Healy of Drexel Burnham Lambert predict even bigger losses in 1980.

Since 1976, Chrysler has been retrenching worldwide, selling operations to come up with cash to help finance operating deficits and the huge spending required to redesign its products to meet changing U.S. demand and the tough new mileage standards mandated by the 1975 Energy Act.

Chrysler Chairman John Riccardo had undertaken "a near total dismantling of the overseas empire built up b (his predecessor Lynn) Townsend in the 1960s and early 1970s," according to Healy.

Although Chrysler remains a major defense contractor -- it sells so many tanks that it is the army's chief supplier -- it has hitched its star to the car and truck business in the United States.

Yet its position in that business is shaky. It has too many of the big cars that Amercians do not want to buy and too few of the small ones that they do. Its 11 percent share of the U.S. market is the smallest it's been in nearly two decades (when there were more U.S. automakers around). Its truck and van sales, a big part of the company's operations, have fallen off even more disastrously than car sales in recent months.

Furthermore, as hard as it may be to believe about a company that had 13.6 billion sales last year, Chrysler is too small to take advantage of the economies of scale afforded its bigger rivals General Motors and Ford.

Chrysler's profit per car sold (profit margin) is the smallest of the Big Three, in part because it must buy more of its components from outside suppliers than either of its competitors.

One of the reasons Chrysler is in such a bind today on production of its popular Plymouth Horizon and Dodge Omni front-wheel-drive subcompacts is the company's reliance on Volkswagen to make the four-cylinder engines for the cars.

Chrysler was late getting into the small-car market, and when it made the plunge it saved several months and many millions of dollars by buying the engines rather than redoing one of its production plants and making the engines itself.

But VW can supply Chrysler only 300,000 engines a year. Chrysler won't have the ability to make its own four-cylinder engines until model year 1981, which begins a year from September.

The inability to make enough subcompacts is just the tip of the iceberg of problems the auto company faces. It needs huge amounts of cash to undertake the redesign of its products required by federal mileage standards.

So far, the company has been financing the research by drawing on bank lines of credit, selling off assets, making a special sale of preferred stock in 1978 and tapping its real estate subsidiary for dividends and cash.

Its bank lines of credit are still large, but hardly inexhaustible. And it has little left to sell if it intends to stay in the car and truck business in North America (the company has sizable operations in Canada and Mexico).

So Chrysler has gone hat in hand to the federal government, seeking $1 billion in aid over the next two years. Chrysler's argument is simple: Federal mileage standards have required the company to spend billions of dollars on research and engineering.

Since Chrysler was more big-car-oriented than either GM or Ford, the federal standards require a greater shift in its fleet than at either of its rivals.

Surprisingly, or perhaps not so, Chrysler is receiving a warmer response from both Congress and the administration than anticipated. More than half a million workers are either employed directly by Chrysler or by dealers and suppliers affiliated with the automaker.

Even if the company gets the federal aid it seeks, its future remains in doubt.

In 1975, when the big recession and decline in sales triggered big losses at Chrysler, the company slashed spending and reducet its white collar work force sharply. As a result, the automaker's new car introductions have lagged the rest of the industry and its new products have faced many more quality problems than in the past.

"It's fair to say that the image of 'extra care in engineering' that Chrysler long fostered has been eroded in recent years," one rival automaker noted sympathetically.

Unless the company can boost its share of the market, it will remain mired in a high-cost, low-profit quicksand that will cause it to sink further behind GM and Ford.

Last year, Chrysler brought in Lee Lacocca, the hard-driving former president of Ford who had a falling out with Ford Chairman Henry Ford II.

Like Fred Silverman, the programming whiz hired by the National Broadcasting Co. to turn around years of sputtering ratings, Iacocca has boosted morale at the third largest automaker. But Silverman has the resources of NBC parent RCA Corp. to rely on Iacocca is severly constrained by the lack of resources at Chrysler. New ideas, even great ones, cost money to implement and, in the auto industry, it takes years to get from the drawing board to the assembly line.

Although few doubt that the giant corporation will survive, the larger-than-expected second-quarter loss and anticipation of more of the same for a while have evoked worries in some quarters.

"We used to think it inconceivable that big enitities go down the tube," noted one major banker. "But that was before Penn Central, W.T. Grant and New York City.