104 LORD EAYLEIGH ON THE ACOUSTIC SHADOW OF A SPHERE, 



Up to = 60 I used it in the form 



P - (_ n + DP. + i + ttP i 

 (2n+l)P, 



where PI varied from 1 to |- ; each P being thus dependent on its immediate 

 predecessor and successor. 



Beyond 60 I thought it better to use it in the progressive form 



p . _ (2n - llP.P.-.-fr-lVP.-g 



n 



each P being thus calculated from the two preceding orders. 



1 believe that in this way the maximum risk of a 7th-figure error occurs at 60, 

 when Pj = |-, and is not very great even there, whereas the exclusive use of either 

 method would have greatly magnified the error at one end or other of the table. 



Auxiliary Tables. 

 TABLE of Values of log a r and log 2a r . 





