Longtime readers of The Post may remember when my predecessor, Gerald Strine, followed the line of a thoroughbred from conception through his racing career.

His columns described the birth of a son of Northern Dancer and his sale for $70,000 as a yearling here. Readers took part in a contest that gave the colt his name, Swallow the Sun, but that was their last chance for a rooting interest in his career. Swallow the Sun never amounted to anything on the track and was sent to stud duty in South America, where he vanished from everybody's memory.

He did, at least, until last week, when a horse named Greenness appeared in the Saratoga entries.He was coming here after winning one major stakes race in Argentina and placing in a couple others. The breeding line in his past, performances said the name of his sire was Swallow the Sun.

That was a minor illustration of a major genetic phenomenon. Horses carrying the blood of Northern Dancer have dominated racing throughout the world. Not only have many of his sons and daughters been great champions, but his sons have become great sires and produced great race-horses, too. Even his sons like Swallow the Sun have distinguished themselves at stud.

But until last month, few people could have guessed just how great was the worldwide demand for Northern Dancer's genes. One man who does understand supply and demand, Nelson Bunker Hunt, remarked last month before the Keeneland Yearling Sale, "(The buyers) are all looking for the same kind of yearling -- by Northern Dancer or one of his sons -- and there are not many of those."

With intensely competitive bidding for all of them, Northern Dancer's 10 offspring at Keeneland sold for an average of $1.3 million apiece. They included the three most expensive yearlings in history. The progeny of three of Northern Dancer's most illustrious sone -- Lyphard, Nijinsky II and The Minstrel -- averaged more than $340,000. And the same bloodlines will be in equally strong demand at the Saratoga Yearling Sales this week.

After Northern Dancer won the Kentucky Derby and Preakness of 1964 and was retired to stud, no breeding expert could have guessed that he was going to alter the history of his species. He wasn't a physically imposing animal. When Windfields Farm had offered him for sale as a yearling for $25,000, there were no takers; buyers thought he was too small. And he had obvious limitations as a racehorse. Trainer Horatio Luro needed to employ all of his skills to get the colt to go the Derby distance; the Belmont's 1 1/2 miles were beyond his capabilities.

Northern Dancer was retired to stud in his native Canada, where he was a national hero. When his first, offspring started running so well, owner E. P. Taylor moved his to Chesapeake City, Md., where he would have access to better mares. In 1970 Taylor syndicated him for a modest $75,000 a share. But even after his greatest son, Nijinsky II, had won the English Triple Crown, Northern Dancer wasn't an extraordinarily hot property.

But by the mid '70s, breeders and owners on both sides of the Atlantic were beginning to perceive what an exceptional stallion he was. His son, The Minstrel, won the Epsom Derby and was considered one of Britain's best horses of the decade. Lyphard, who had not been an exceptional racehorse, emerged as the leading sire in France. Nijinsky II was becoming one of the Europeans who had seen these horses run were becoming the most aggressive buyers at the American sales.

Northern Dancer's record has shown the buyers that they can win in either of two ways with one of his offspring. One of his colts might develop into a great racehorse, but even it he doesn't, he might sire great racehorses. Rarely does a stallion achieve such a reputation, for reasons of geriatrics.

"In most cases a horse doesn't prove that he's a sire of sires, until he is gone," said John Finney, president of the company that conducts the Saratoga Yearling Sales. "But when a horse does live to prove it, his sons raise papa's progeny to new dimensions. Look at how much yearlings by Nijinsky II bring. People say, 'If they're worth so much, what is a horse by the real thing worth?'"

Northern Dancer is 20 years old now. Joe Hickey, the manager of Windfields Farm said, "He's on borrowed time right now. Anything you get from now on is a bonus. But he's a remarkable horse. His only concession to age is a little dip in his back. He looks like a horse half his age."

Because there are not going to be many more progeny of Northern Dancer, the demand for his blood will continue to intensify. Breeders will be begging to pay $300,000 to send a mare to him. Buyers will be continue to pay millions for his untested yearling sons. And even at these stratospheric prices, they may be getting a bargain.