Observations would therefore be made at all six stations on the same night on an average of once in every sixty-four nights. The assumption, 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 (465⁄1000),6 which equals 1⁄99. 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.[1]
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 complete, 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 (1⁄64)2 = 1⁄4096. That is to say, a complete night's work will be obtained at all six stations on an average, in round numbers, 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.[2]
The observations made during the first five years after the international latitude stations were established, and the results deduced from them, have been published in two quarto volumes.[3] 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
- ↑ 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.
- ↑ 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.
- ↑ Resultate 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 Veröffentlichungen, 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.
