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PROCEEDINGS OF THE AMERICAN ACADEMY 



TABLE III. 



Nearly the same results should be reached by starting with the 

 declination for the argument, using the values of /ia in the horizontal 

 columns. AVith the corrected values thus obtained, curves represent- 

 ing these residuals were drawn with the right ascension as the argu- 

 ment. 



Proceeding in this order, we obtain finally the values of z/« given in 



TABLE IV. 



It will be seen that there is a subtantial agreement between the 

 values in Tables III. and IV. These values have been derived directly 

 from the curves, and no attempt has been made to smooth them by 

 the differences. Inasmuch as it will rarely, if ever, happen that the 

 periodicity in both directions is as great as in this example, the agree- 

 ment of the values mav be taken as an index of the magnitude of the 

 errors likely to be introduced through the process of drawing the 



