The original visual accounts of the Leonids from 1799 to 1997 are examined and the times and magnitude of peak activity are established for 32 Leonid returns during this two-century interval. Previous secondary accounts of many of these returns are shown to differ from the information contained in the original accounts due to misinterpretations, typographical errors, and unsupported assumptions. The strongest Leonid storms are shown to follow a Gaussian activity profile and to occur after the perihelion passage and nodal longitude of 55P/Tempel-Tuttle. The relationship between the Gaussian width of the strongest returns and their peak activity is established, and the particle density/stream width relationship is found to compare favorably to that expected based on observations of IRAS cometary dust trails. Variations in the width of the 1966 storm as a function of meteoroid mass are shown to be consistent with that expected from classical gas-drag meteoroid ejection treatments. The five largest storms from 1799 to 1966 are found to peak at solar longitudes systematically larger than 55P/Tempel-Tuttle's nodal longitude at the same epochs, suggesting an asymmetry in the dust ejection perpendicular to the cometary orbital plane. The dust-distribution about 55P/Tempel-Tuttle is reevaluated with these new data and predictions are made for the 1999-2000 showers.