I'm not completely sure. But I've always assumed it was because the dime used to be made out of silver, which is more valuable than copper and nickel. Therfore, 5 cents worth of nickel would be larger than 10 cents worth of silver. Just my own theory. I could be completely wrong though. LOL. I'm sure someone will correct me soon if I'm wrong though.
Years ago it was believed that in order for a coin to be accepted it had to contain its full face value in metal. The cent, being made of copper which was much less valuable than silver, was considerably larger than the dime. In the 1860's the government realized that at least for the minor coinage they did not have to contain their full value because they were merely tokens for the convenience of making change and they would circulate anyway. So the cent was made much smaller than it was before. It still contained about half of its face value in metal and that still left it slightly larger than the silver dime. In 1865 the new five cent piece had about two and a half cents worth of metal in it and it was also considerably larger than the silver dime. In 1964 silver reached the point where the metal in the dime was now worth more than the face value of the coin. So they had two choices, make the dime even smaller, or change the material it was made of. They decided to change the metal. Now when they did that they could have put more metal into the coin to make it close to the face value which would have made a larger coin, but by this time vending machines were a large part of American life and it would have created a great deal of confusion to have two coins of the same value but widely different sizes circulating and to try and get the machines to recognize and accept both of them. (They had enough problems just trying to get them to accept the two different compositions with the same size.) Also the government was trying to convince the public that there was no reason to hoard the silver coins because they would "stay in circulation side by side with the new clad coins for many years to come." This would be much harder to put over if the two coins were greatly different in size. So they went the simple route and kept the dime the same size it had been since 1828.
To carry Conder101 explanation a little futher..... Installment #1 CENTS Large cents were first introduced in 1793. The initial Chain and Wreath Cents (1793) , and subsequent Liberty Cap (1793-1796) cents were 13.28 grams of pure copper. The weight of the Draped Bust, and Classic Head (John Reich) coins were only10.89 grams of pure copper. All these coins were esentially 29 MM in diameter. This standard applied untill the passing of the Large Cent in 1857. Although The new, smaller (fat) CN Flying Eagle Cents (19mm diameter weight 4.67 grams, 880 copper and 120 nickel) first debuted in 1856, it was not until 1864 (Indian Head Cents) that the 3.11 gram 19 mm, .950 and.050 zinc cent that we all knew existed until the middle of 1982. All these changes occured, during various downturns in the economy, vs the price of copper at the time. Of course we all know cents produced since the middle of 1982 are copper plated over a zinc core. Installment # 2 Dimes, HALF DIMES, and Nickels.......... Stay Tuned!!!
In reality, the government was secretly removing these coins from circulation and melting them down. This combined with the fact that silver prices skyrocketed in 1970's due to the Hunt brothers, is why you rarely find silver coins circulating along side the copper sandwiched clads. Those spiffy silver eagles you're buying probably started life as a Morgan dollar or a silver Washington.
That is true. At the same time they were telling the people there was no reason to hoard the silver coins they had two large machines at Federal reserve banks that processed all of the coins returned to the Fed by the banks separating the silver coins from the clad. They did that until early 1970 by which time the amount of silver recovered had dropped to the point where it was no longer worthwhile to operate the machines. Do as I say, not as I do.
It's hard for people today who view money as electronic information to fully realize that money used to be a specific weight of metal. For example, a dollar WAS 371.25 grains of fine silver. The dollar WAS NOT the monetary value of that quantity of silver. So if you tried to tell someone from the early 19th century that we couldn't "afford" to make dollars out of silver because silver was too expensive, the logic of that argument wouldn't make sense to them.