The Capped Bust Half Dollar is a significant piece of early American coinage, minted by the United States from 1807 to 1839. This series marks an important period in American numismatics due to its historical context and the evolution in design and minting techniques it represents. Designed by John Reich, the Capped Bust Half Dollar features a classic portrayal of Liberty and showcases the early artistic direction of the U.S. Mint.

### Design
- **Obverse:** The obverse of the Capped Bust Half Dollar features the profile of Lady Liberty wearing a cap (hence the term "capped bust") and facing left. Liberty's cap is often depicted as a Phrygian cap, symbolizing freedom and the pursuit of liberty, and it's banded by the word "LIBERTY." The date appears at the bottom of the coin.
- **Reverse:** The reverse displays an eagle with outstretched wings, holding an olive branch and a bundle of arrows, which symbolizes the United States’ desire for peace but readiness for war. The eagle is encircled by the inscriptions "UNITED STATES OF AMERICA" and "E PLURIBUS UNUM," with the denomination written as "50 C." for fifty cents.

### Varieties
The Capped Bust Half Dollar series can be divided into two main varieties, differentiated by their edge and diameter:
1. **Lettered Edge (1807-1836):** Early versions of the coin feature a lettered edge with the inscription "FIFTY CENTS OR HALF A DOLLAR." These coins have a larger diameter of approximately 32.5 mm.
2. **Reeded Edge (1836-1839):** Later versions have a reeded edge and a slightly smaller diameter of about 30 mm. This change was part of several modifications aimed at streamlining the minting process, including the introduction of steam-powered coin presses.

### Specifications
- **Composition:** 89.24% silver and 10.76% copper.
- **Weight:** Initially 13.48 grams (Lettered Edge), later reduced to 13.36 grams (Reeded Edge).
- **Diameter:** Varies from 32.5 mm (Lettered Edge) to 30 mm (Reeded Edge) over the series' lifespan.

### Historical Significance
- The Capped Bust Half Dollar reflects the young United States' growth and its evolving identity during the early 19th century. The series encapsulates an era of expansion and the development of the nation's monetary system.
- Changes in the coin's design and specifications correspond to broader transitions within the U.S. Mint, including improvements in minting technology and adaptations to the country’s economic needs.

### Collectibility and Value
- **Key Dates:** Certain years and mint marks are particularly sought after by collectors. The 1815/2 overdate and the 1836 Reeded Edge coins are among the rarer and more valuable in the series.
- **Condition and Rarity:** As with all collectible coins, the value of a Capped Bust Half Dollar greatly depends on its condition (grade), rarity, and specific historical significance. Coins in better condition and those with less common variations command higher prices.
- **Popularity:** The series is highly regarded among numismatists for its historical importance and the beauty of its design. Collectors often seek to complete sets of Capped Bust Half Dollars, adding to their demand and collectibility.

The Capped Bust Half Dollar is cherished among collectors for its embodiment of early American spirit and artistry, representing a pivotal chapter in the nation's numismatic history.