238 Dr. J. R. Airey on the Addition 7 heorem of the 



to —0*10, so that Z (V) and Z^.r) can be found to six places 

 of decimals when x is greater than 15*5, the largest value of 

 the argument in Meissel's tables *. Lommel gives Jo(«^) 

 and Ji(#) to six places of decimals from ^ = 0*1 to 20*0 by 

 intervals of 0*1 ; J</(#), iJ</'(#) an d J-eV'O 1 ')? e ^ c * are a ' so 

 tabulated for purposes of interpolation. 



In order to increase the accuracy of the tables, the last 

 • figure is given with or without a "point/' This point 

 means that the residue is greater than 0*25 and less than 

 0*75 units of the last place and is exactly equivalent to 5 in 

 the first place of rejected decimals. 



Values of a and a 1} /3 and /3,, with first and second 

 differences A 

 decimals. 



A 2 in units of the sixth place of 



h 



p' 



ao. 



A,. 



A 2 . 



&. 



*r 



A 2 . 



0,00 



1,000000 



-4967 





0,000000 



2. 





0,01 



0,995033 



-4901 • 



65. 



002. 



6. 



4 



0,02 



0,990131 . 



-4838 



63. 



009 



11 . 



5 



0,03 



0,985293 . 



- 4775 . 



62. 



020. 



15. 



4 



0,04 



0,980518 



-4714 . 



61 



036 



19. 



4 



0,05 



0,975803 • 



-4655 



58* 



055. 



23 



3. 



0,06 



0,971148 • 



-4596 • 



58. 



078. 



27 



4 



0,07 



0,966552 



-4539 



57- 



105. 



30 



3 



0,08 



0,962013 



-4483 



56 



135. 



33. 



3. 



0,09 



0,957530 



-4428 



55 



169 



37 



3. 



0,10 



0,953102 





54 



206 





3 



-0,00 



1,000000 



5033. 





0,000000 



2. 





-0,01 



1,005033. 



5102 



68. 



002. 



7 • 



5 



-0,02 



1,010135 • 



5171. 



69. 



010 



12. 



5 



-0,03 



1,015307 



5243 



71. 



022. 



18 



5. 



-0,01 



1,020550 



5316 



73 



040. 



24 



6 



-0,05 



1,025866 



5390. 



74. 



064. 



29. 



5. 



-0,06 



1,031256 • 



5467. 



77 



094 



36 



6. 



-0,07 



1,036724 



5546 



78. 



130 



42 . 



6. 



-0,08 



1,042270 



5626 • 



80. 



172. 



49. 



7 



-0,09 



1,047896 • 



5708. 



82 



222 



56. 



7 



-0,10 



1,053605 





84 



278. 





7- 



* Gray and Mathews, ' Bessel Functions,' pp. 247-266. 



