OF CLOCK RATES UPON LONGITUDE WORK. 131 



The diurnal term given by these observations is +o".i4 cos T, 

 where T is reckoned from noon. The solution gives also a small sine 

 term, with coefficient o".03, which does not appear to be distinct 

 enough to adopt. The cosine term is less than one half the difference 

 in the observed clock corrections at sunset and sunrise. It is of the 

 same size approximately as that of the fourteen-month term of the 

 latitude variation. 



Since the axis of figure of the earth does not coincide with the 

 axis of rotation of the earth, the pole of figure makes a daily revolu- 

 tion about the pole of rotation. The pole of figure advances only 

 o°.8 on its curve, representing the fourteen-month rotation, so the 

 daily revolution will be nearly circular. 



If the deviation of the two axes is constant during a day, there 

 could be no resulting variation of latitude, according to the accepted 

 definition of that coordinate, assuming that the axis of rotation does 

 not shift its position during the same period. 



If the position of the instantaneous axis of rotation of the earth 

 with respect to the celestial sphere still requires correction, depending 

 upon an error in the adopted constant of nutation, these several 

 anomalies of observation may possibly be reconciled with theory. 



As observations of this character have served to determine our 

 astronomical constants, modern refined observations may indicate a 

 need of revision of the values. 



The test should be sought in fundamental observations with the 

 meridian circle, since the full amplitude of variations can be more 

 effectually observed, while other classes of observation have given 

 mainly tests of differential changes. 



Since aberration has minimum effects upon transits of stars near 

 sunset and sunrise, and also minimum effects upon zenith distances 

 of stars near noon and midnight, the two diurnal variations in our 

 results do not appear to indicate any correction to the constant of 

 aberration. 



The diurnal term in observed </> may indicate a small correction 

 (o".02) to the constant of nutation. 



The solution of a diurnal term is commonly involved with that 

 of an annual periodic term, when dealing with observations of any 



PROC. AMER. PHIL. SOC, VOL XLI, J, AUG. 3I, I922. 



