428 THE POPULAR SCIENCE MONTHLY 



Observations would therefore be made at all six stations on the same 

 night on an average of once in every sixty-four nights. The assump- 

 tion, however, that observations are made upon fifty per cent, of the 

 nights is somewhat in error, the true percentage being almost exactly 

 46.5. The probability of this event occurring would be therefore 

 ( 46 %ooo)j 6 which equals % 9 . The event would occur on an average 

 therefore of once in every ninety-nine days, or nineteen times during 

 the five years under consideration. This result is in exact agreement 

 with the observed number. 4 



Let us now ask, What is the probability of obtaining a complete 

 night's work at all six stations on any particular night? The ratio 

 between the number of complete nights and the total of nights is not 

 given in the published results, but is probably not far from one half. 

 At Ukiah about sixty per cent, of the nights upon which observations 

 are made are complete, but the percentage is known to be less at some 

 of the other stations. If now we assume that observations are made 

 upon fifty per cent, of the nights, and fifty per cent, of these are com- 

 plete, then a process of reasoning similar to that just used will bring 

 us to the result that the probability of the occurrence of the event under 

 consideration is (%4) 2 = -J4o96- That is to say, a complete night's 

 work will be obtained at all six stations on an average, in round num- 

 bers, of once in every 4,000 nights, or once in about eleven years, so 

 that it is not at all surprising that this rare event did not occur at all 

 during the first five years of observations. 5 



The observations made during the first five years after the interna- 

 tional latitude stations were established, and the results deduced from 

 them, have been published in two quarto volumes. 6 These observations 

 show periodic changes in the latitude similar to those found from 

 earlier observations. The results obtained at the various stations, 

 from the beginning of 1902 to the end of 1905, are represented 

 graphically in Fig. 5, taken from the second volume just mentioned. 

 All the observations obtained at each station during a certain period, 

 about a month, are combined into an average value, these mean results 

 are plotted, and represented in the figure by the small circles. The 

 small figures standing adjacent to the circles indicate the number of 



4 The exact method of computing this probability is, of course, to take the 

 product of the six separate probabilities rather than the sixth power of the 

 average probability. The result comes out sixteen rather than nineteen. 



5 If more exact figures were used in this computation it is certain that the 

 probability of this event would be much reduced, perhaps by nearly one half, so 

 that the event would not occur more than once in twenty years. 



6 Re suit ate des Internationalen Breitendienstes. Band I. (1903), von Th. 

 Albrecht. Band II. (1906), von Th. Albrecht und B. Wanach. Centralbureau 

 der Internationalen Erdmessung ; neue Folge der Veroffentlichungen, Nos. 8 

 und 13. A review of these volumes was published by the writer in Publications 

 of the Astronomical Society of the Pacific, Vol. 19, pp. 139-58. 



