1897.] 



DOOLITTLE- —VARIATION OF TERRESTRIAL LATITUDE. 43' 



We find a pretty satisfactory agreement with the theoretical results 

 as given by Chandler's formula, the range of variation being about 

 o''.4, as indicated both by observation and theory. The phase, 

 however, is a little more discordant, that is the times of maxima 

 and minimal as shown by observation, do not quite agree with 

 those indicated by theory. However, the amount of material is 

 not yet sufficiently great to warrant any sweeping conclusions. 



As to the quality of the work, the probable error of a single 

 observed latitude is found to be o".i4. This is derived from the 

 mean of everything, whether the conditions were favorable or 

 otherwise. It does not take into account the errors of the star 

 places used, but is simply what is sometimes called the internal 

 probable error. 



The probable error of the mean of one series of ten observations 

 will be something over ".04. Nevertheless we find in comparing the 

 results from consecutive evenings ranges sometimes as great as o'^5, 

 or say twelve times the probable error. Such variations from even- 

 ing to evening are not peculiar to our own work, but are found in 

 every extensive series which I have examined. In some cases the 

 range has been found as great as o^.y. The cause of these dis- 

 crepancies is at present very much of a mystery. They are pre- 

 sumably due in great part to atmospheric causes, producing anoma- 

 lous refraction phenomena. It is apparently a very difficult matter 

 to deal with, but unless means can be found for doing so it would 

 appear that we have about reached the limit of accuracy attainable 

 in this class of work. 



The instances before mentioned are the extreme ones. The fluc- 

 tuations from night to night are usually far within the amounts 

 mentioned. Usually it will be difficult to determine whether the 

 variation is a real one or simply represents the error of observation. 

 An unusually favorable opportunity for investigating this matter 

 was furnished by the work of Marcuse, of Berlin, and Preston, of 

 the U. S. Coast Survey, who, in 1891-92, carried on similar series 

 of observations at Waikiki, in observatories separated by only a 

 few feet. A comparison of the results with reference to this, point 

 was made by Marcuse, but the result was not very decisive. In a 

 general way the number of cases of agreement in the direction of 

 the variation was about twice as great as that of disagreement. 

 One case in particular was very interesting, where for nine consec- 

 utive days the latitudes given by the two different observers always 



PROC. AMER. PHILOS. SOC. XXXVI. 156. 2 D. PRINTED EFB. 3, 1898. 



