SHIFTING OF THE EARTH'S AXIS 427 



The percentage of nights upon which observations were obtained, 

 during the first five years at the various stations, is given in the fol- 

 lowing table : 



Percentage or Observing Nights 



Per Cent. Per Cent. 



Mizusawa 50 Gaithersburg 42 



Tsehardjui 35 Cincinnati 32 



Carloforte 72 Ukiah 48 



The conditions at Carloforte, in the Mediterranean Sea, must be al- 

 most 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 Cincin- 

 nati. We should also consider the still further fact that at some sta- 

 tions — 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 observa- 

 tions were made, there were but nineteen nights upon which some ob- 

 servations 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 computa- 

 tion according to the principles of probability shows that such a result 

 should be expected. Let us ask, first, What is the probability of ob- 

 taining 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 mani- 

 festly the probability of obtaining observations at two stations on the 

 same night will be \ X \ > or i? an< i the probability of obtaining ob- 

 servations at three stations on the same night | X 2 X i an d the 

 probability of obtaining observations at six stations (|) 6 = % 4 . 



