Page:Popular Science Monthly Volume 75.djvu/431

Rh The percentage of nights upon which observations were obtained, during the first five years at the various stations, is given in the following table:

The conditions at Carloforte, in the Mediterranean Sea, must be almost ideal from an astronomical standpoint, still the above tabulation can not be taken as a true index of the weather at the stations. At Carloforte and at Mizusawa two observers are constantly employed, and probably nearly every favorable night is utilized. At the other stations, where all the observations are made by a single observer, some favorable nights must of necessity be allowed to pass. At Ukiah, for instance, the percentage could be increased by at least ten, perhaps fifteen, if two observers were employed. In considering the above table, the further fact should be taken into consideration that Professor Porter, who makes the observations at Cincinnati, has many other duties in connection with his position as director of the Cincinnati Observatory and professor of astronomy in the University of Cincinnati. We should also consider the still further fact that at some stations—for instance, Mizusawa—many nights are rendered incomplete by fog or clouds, and a night upon which only one pair is obtained enters into the above tabulation with the same weight as a complete night of sixteen pairs.

On account of the uncertainties of the weather it seldom happens that observations are obtained at all the stations on the same night—and a complete set of sixteen determinations at all stations on the same night is indeed a rare event. During the first five years that observations were made, there were but nineteen nights upon which some observations were obtained at all the stations, and not a single night on which a complete set of sixteen determinations was obtained at every station.

This seems a little strange at first thought, but a simple computation according to the principles of probability shows that such a result should be expected. Let us ask, first, What is the probability of obtaining at least some observations at each station on the same night? If we assume that observations are made on the average on fifty per cent, of the nights, then the probability of obtaining observations at any one station on any particular night will be one half, and manifestly the probability of obtaining observations at two stations on the same night will be $$\tfrac12\times\tfrac12$$, or $$\tfrac14$$, and the probability of obtaining observations at three stations on the same night $$\tfrac12\times\tfrac12\times\tfrac12$$, and the probability of obtaining observations at six stations $$(\tfrac12)^6=\tfrac{1}{64}$$.