168 OGBURN— LATITUDE OBSERVATIONS. [April 20, 



and the mean of the corresponding forty day group in which it is 

 found and the result for each station tabulated side by side. 



Omitting all record of groups where the observations were less 

 than 4, there remian for comparison 209 groups which give the 

 following results. 



Cases where one or the other residual was zero = 27. 



Cases where both residuals were greater than o".i5^ None. 



Cases where both greater than o".io=io: — 7 "like," 3 "unlike." 



Cases where smaller residual was > o".05 and <o".io = 62: — 35 "like," 



27 "unlike." 

 Cases where smaller residual was between o".oo and o".o5 = 109 : — 54 



" like," 55 " unlike." 



An actual departure at both places from the mean latitude in the 

 same direction should manifest itself in the majority of cases by an 

 agreement of sing in these residuals. This is actually found in the 

 case of the residuals greater than o".io but the total number of 

 cases is too small to have much weight. Irrespective of the magni- 

 tude of the residuals there are 96 '* alike " and 85 " unlike." If 

 the two series of observations were entirely independent the theory 

 of probability would require that the number of " like " and " un- 

 like " be 90 each and the difference between this and the actual 

 numbers is so small the inevitable conclusion follows that the two 

 series are practically independent. 



Second Method. 

 Excluding all work in which a determination at either place on 

 any night depends on the observations of less than six pairs there 

 remain 123 common, dates which represent 3,410 separate determi- 

 nations, 1,730 at Philadelphia and 1,680 at Bethlehem. By con- 

 structing to a generous scale the diagram just shown on the screen 

 and drawing smooth curves for the two sets of observed latitudes 

 we may consider these curves as the actual values of the latitude 

 during the period represented in this comparison and the differences 

 between the latitudes at each station and the value derived from 

 the curve will give us a set of residuals which should be a measure 

 of the precision of one night's work on the supposition that the 

 variation is represented by long periods. 



