14 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



TABLE II. 



The /)th Root in Order of Magnitude of the Equation Jq (x) 

 is denoted by x^. 



and these latter we have computed for certain values of 2 / / and a \ I 

 by the help of Gudermaiin's tables.* The results appear in Table III. 

 To avoid possible errors arising from combining so many <pjaiitities, we 

 generally used seven places, although the time required for the com- 

 putation, which was done in duplicate, was thereby increased by some 

 weeks. 



* Gnderniann, Tlieorie der Potenziiil oder Cykliseli-liypcrbolisclien Functinnen, 

 Berlin, 1833. Willson and Peirce, Bulletin of tlie American Mathematical Society, 

 1897. 



