1907.] OGBURN— LATITUDE OBSERVATIONS. 169 



Let SFi" and SFo" be the sum of the squares of the residuals 

 at Philadelphia and Bethlehem respectively. Evidence of syste- 

 matic fluctuations would be shown if SF^- + SFg^ is appreciably 

 greater than 2F3- where ^V^^ is the sum of the squares of the 

 residuals derived directly from the differences of the observed 

 latitudes. 



These last residuals must be derived in a way that will elimi- 

 nate the systematic divergence resulting from an apparent constant 

 difference in the times of maxima and minima at the two places. 

 This has been effected by considering P\ as the algebraic difference 

 between Fi and Fo. Without reproducing the details the follow- 

 ing results were found. 



SFr = 0^5706 



SF2- = o .6993 



SF3-=i .2718 



Since SF^- + SF^" differs from SF3- by less than o".oo2 it is evi- 

 dent that these observations show no relation between abnormal 

 values of observed latitude at the two stations. 



If the residuals are reduced to probable error there results : 

 For one night's determination from 10 pairs — 



at Philadelphia ± 0^.053 : For one pair ± o".i7. 

 at Bethlehem ±0 .057: For one pair ±0 .18. 



The part in this latter due to observation alone was nearly ± o".i2 

 leaving ~ * ^ at the two places for the probable error of one 

 observation which is apparently beyond the observer's influence. 



