296 ON ZENGER'S SOLUTION OF KEPLER'S PROBLEM. [38 



f 1 3 1 



so that /= e 4 I - e 2 + ^r; e 4 , etc. Y . 



V. J 



The order of accuracy of the approximation will not be altered by confining 

 ourselves to the first two terms of this value of f, so that we may take 



e (I -e"} sin z 



tan (x z) = , nearly. 



1 e ( 1 -e" } cos 2 



The error is still of the 3rd order, but its maximum amount is less than 

 before. 



If f be taken = e -! 1 - e" sin 2 z I , 



, , / sin z 



and tan ( x z) = ~ ^ - , 



I J cos z 



the error in the determination of tan (a? z), and therefore in the determi- 

 nation of x, will be only of the 4th order. 



There are several misprints and some errors of calculation in Professor 

 Zenger's paper, on which I need not dwell. True anomaly in line 8 of the 

 paper should be eccentric anomaly, and the same error occurs on p. 448. 



