The discovery position of 337 long-period comets (1840-1967) are plotted. Of these 53% of the direct and 69% of the retrograde comets were found in the morning sky. Prediscovery ephemerides and visibility conditions are worked out. It is shown that, indeed, 70% of the direct and 81% of the retrograde comets could have been first observed in the morning sky. This anomaly is found to occur because of the direction of revolution of the earth in its orbit and the corresponding effect on the rate of change of earth-comet distance. The Holetschek effect is studied, wherein about 32 of known long-period comets came to perihelion when their longitude differed from that of the earth by less than 90 . An estimate is made of the faintest comet visible since this depends upon the relative position of the comet and sun and the latitude of the observing station. The calculation takes into account the size of telescope, the angular extent of the comet's image, atmospheric absorption, sky brightness near the horizon, and the contrast threshold of the human eye. The estimated times of beginning and end of the period of ob- servability for a given comet occur when this threshold magnitude equals the magnitude of the comet. A statistical analysis is made of the rate of discovery of comets in terms of the product of time and their magnitude above the computed visual threshold value. This leads to an estimate of an "intrinsic" distribu- tion of comets, which includes both discovered and undiscovered comets. The statistical probability, based on discovery data, that a comet having specified characteristics will be discovered is worked out.