Professor Jeremy Siegel wrote a book and he called it, The Future for Investors. I read it and wept.

A chart on page 126 shows how $1,000 invested in stocks back in 1871 would be worth about $250,000 today. That's nuts. But if you'd only reinvested those dividends! That $1,000 would have ballooned to nearly $8 million.

But what's so "accidental" about that?
After all, I just described a fairly obvious way to invest -- back in 1871, anyway. In those days, investors actually bought stocks for the stream of cash flow they provided -- their dividends.

You may even recognize that last bit as the definition of the word "investing." But sometime in the early-1960s, things took a nasty turn. Suddenly a new generation of "investors" bought stocks solely to sell them to somebody else at a higher price. Sound familiar?

It should, because by 1987, unless you were retired (or hopelessly out of touch), dividends were an afterthought. And by the go-go '90s, any self-respecting company with the gall to pay you to invest stood accused of being "mature" -- i.e., washed up and entirely out of ideas.

Enter my accidental uncle
The year was 1965, and hotshot brokers were hawking the American dream of "capital appreciation." Back then, it was the Nifty Fifty's mega chemical and manufacturing conglomerates like 3M (NYSE:MMM) and consumer monsters like Coca-Cola (NYSE:KO).

But these stocks also paid dividends. And that's how my uncle accidentally got rich. The "cheaper" these hot stocks got during the bear market of the '70s, the BIGGER his dividends got as a percentage of the new shares he bought. That's right, my uncle got rich ... in the worst market in half a decade!

Because even as he was missing the boat on "new economy" wonders like office products giant Xerox (NYSE:XRX), he was locking in some of the highest yields in history and ended up with thousands of shares of stock. Then, when the market turned in 1981 ... shocker! The stocks went up, the dividends went up, and the rest is history.

But Uncle, how'd you ever afford so many shares?
That's a funny story best told by example. Just look at what happened in the case of three household names: PepsiCo, Philip Morris, and Johnson & Johnson.

Pepsi -- $2,000 invested in Pepsi as recently as 1980 is now worth more than $150,000. You would have started with 80 shares, but by reinvesting dividends, you would have 2,800 shares today.

Philip Morris -- $2,000 invested in Philip Morris in 1980 is worth just under $300,000 today. You would have started with 58 shares. Today, thanks to stock splits and reinvesting dividends, you would have more than 4,300 shares.

Johnson & Johnson -- $2,000 invested in Johnson & Johnson in 1980 would be worth close to $140,000 today. You would have started with only 13 shares of stock. Today, thanks to reinvestment and splits, you would own more than 2,000 shares.

Believe it or not (I didn't believe it myself), if you'd bought those three stocks and reinvested your dividends, you'd have a portfolio now worth close to $600,000 after starting with an investment of only $6,000. And that's if you never added another penny.

Surely, it's too late for you and me?
Not even close. And I'm going to prove it using nothing more than a modest IRA rolled over from my stint in corporate America and a dividend nut named Mathew Emmert. Mathew swears he can help me beat the market and lower my risk by owning dividend-paying stocks.

So with Mathew's help, I'm stuffing my old rollover IRA full of dividend payers. I've already got a handful, including Anheuser-Busch (NYSE:BUD) and beaten-down Merck (NYSE:MRK) with its ridiculous 4.3% yield. But I have a few bucks left to put to work.

The only rules are that every stock must offer a better-than-average dividend, and all dividends must be reinvested. That's why I'm conducting this little experiment in my IRA instead of my brokerage account. This way, I can avoid the taxman until ... well, later.

This is something you might want to try
I guess we all have to grow up sometime and start playing the odds. That's why I've turned to Mathew and his Motley Fool Income Investor newsletter service for advice on my most important investment. I have a hunch that in 30 years, I'll be glad I did. Maybe I'll accidentally get rich like my uncle.

Mathew's latest pick yields 9.6%. If you agree that would be a great place to start, you can enjoy a 30-day guest pass to Income Investor. You won't pay a cent, and you get to check out all the picks this instant. And if, down the line, you do subscribe, you can probably cover the cost with your dividend checks (though I'd recommend you reinvest those). To learn more, click here.

This article was originally published on Feb. 13, 2006. It has been updated.

Fool writer Paul Elliott owns shares of Merck and Anheuser-Busch. Merck is an Income Investor recommendation. Anheuser-Busch, 3M, and Coca-Cola are Inside Value recommendations. The Motley Fool isinvestors writing for investors.