28 

 or 



whe 



re 



Prof. H. Xagaoka on the Potential and 



^-^+Kiy^K2j+ 



s/k 



h 



1 



1+ v^- 



In these expansions it is generally sufficient to retain only 



the first term *, as the table for '/— n given below will show. 



For practical purposes a single calculation according to (25) and 

 (27) gives at once the value of M. In order to show the rapid 

 convergence of these (/-series it will be sufficient to indicate the 

 smallness of the corrections e, 6i, and e/= ^^qi+^iy entering 

 in the above two formula. For this purpose the following 

 short tables of corrections were calculated : — 



Table of 6 = 3./~V4-9(7^-12</° and ^- ~ . 



001 



Approximate value 

 of 7= sin- U\ 



22°6 



e. 



"-',■ 



0-0000000 



000000000 



, 002 



31-6 



00000005 



0-00000001 



! 003 



38-1 



0-0000024 



0-00000005 



004 



43-5 



0-0000077 



■ 0-00<J00020 



005 



48-0 



0-0000187 



0-00000063 



; 0-06 



51-9 



0-0000387 



0-00000156 



0-07 



55-3 



0-0000726 



0-00000336 



0-08 



58-4 



0-0001218 



0-00000655 



0-09 



61-1 



0-0001947 



0-00001181 



1 010 



63-6 



0-0002961 



0-00002000 



i Oil 



65-9 



0-0004323 



0-00003220 



: 012 



67-9 



0-0006105 



0-00004974 



013 



69-8 



0-0008382 



0-00007421 



0-14 



71-5 



0-0011234 



0-00010746 



Table of €i = 32?/-40r^/ + 48.?,'-32'^i° + ... and 



2x' 



Approximate value 



e 





of 7=sin-lX'. 



^V 



e^. 



0010 





 67-4 



0-0000316 



-0-0007684 



0-009 



68-5 



0-0000231 



-0-0006249 



0-008 



69-7 



0-000(^62 



-00004958 



0-007 



71-0 



0-0000109 



-00003811 



1 0-006 



72-4 



0-0000069 



—0-0002811 



1 0-005 



73-9 



0-0000040 



-0-0001960 



0-004 



75-6 



00000020 



-0-0001260 



1 0-003 



77-5 



00000010 



-0-0000710 



: 0002 



79-8 



0-0000003 



-0-0000317 



, 0-001 



! 



82-8 



0-0000000 



-0-0000080 



* For the table of q see Jacobi, Crelle's Journal, xxvi. p. 93 

 meUe Werke, i. -p. 363. 



Gesam- 



