﻿by Change in Angular Velocity. 5 



than 15 were obtained by the use of the first three terms 

 of the asymptotic expansion. For smaller arguments the 

 values were found by interpolation from the twelve-figure 

 tables in Gray & Mathew's ' Treatise.' Curves representing 

 Table I. are shown in fig. 1, from which figs. 2 and 3 

 have been derived graphically. The calculation was made 



1-0 

 ■9 

 ■8 

 7 



\m 













Fig.S. 





\\ 





















ft 





















6 



w 



v \ 







M) 



r^ — 











1 



\ ^ 



















\ 



\ 







\\ 











\ 



\ 





\ IK ^ 



K XvC 









V 







4 V X 



\\vV 



















L O^M 













8 \ 



X 





\\\^ 











%-^s 









p s ^^7 v ^^^r >, ^v^ 















"^h^*«-*L, "i" — f^^irr*'""- 





O .02. 04 .06 



.12 J 4- .Ut. .16 J8 .90 



with the aid of Chambers's seven-figure logarithms. It 

 was checked throughout, once everywhere and twice or 

 three times in parts. 



For large values of t, the angular velocities are pro- 

 portional to Ji(ai?')/r {0 <r<_l). Most of the experimental 

 curves are roughly of this form for a large value of t. 



The solution, being non-dimensional, applies to all sizes 



