236 
PllOFESSOR M. J. M. HILL ON A SPHERICAL VORTEX. 
d = 10 a (^1 - = 10 « (^1 - ^ nearly = 10 a - 
Tills result shows how rapidly the disturbance due to the passage of the vortex 
sphere dies away as the distance from the axis increases. 
Table L —Table for calculating the surfaces of revolution (Pt^ — a~) = — 
di = ^ rla -71 
4 ' 
(z — 0 
fp 
2a^ 
~ ~9 
rja 
•58 
•63 
•69 
•75 
•82 
- 
0 
•23 
-24 
•21 
0 
11 
rja 
•53 
•55 
•6 
•67 
•8 
•83 
•85 
c^- 
- 2)/a 
0 
•19 
•29 
•32 
•22 
•14 
0 
_ 
~ 6 
rja 
•46 
•5 
•6 
•64 
■7 
•8 
•89 
- 2}/a 
0 
•29 
•42 
•43 
•41 
•32 
0 
_ 
¥ 
rja 
•36 
•4 
•5 
•58 
•? 
•8 
•93 
(- 
- Z)la 
0 
•38 
•55 
•58 
•53 
•43 
0 
11 
rja 
•11 
•13 
■2 
•33 
•4 
•5 
•6 
•7 
•8 
•9 
•95 -99 
- 2)/a 
0 
•5 
•81 
•88 
•87 
•84 
•78 
•7 
•58 
•42 
•29 0 
Table IL- 
—Table for calculating the surfaces of revolution r" 
r 
d^ = (•!), 
rja 
1-03 
1 
•9 
•8 
•7 
•6 
•5 
•4 
•36 
•34 -33 -32 
(z - Z)la 
0 
•27 
•53 
•69 
•82 
•94 
1-08 
1-33 
P6 
1-92 2-28 X 
Cl 
11 
c? 
rja 
11 
1-05 
1 
•9 
•8 
•7 
•6 
•57 
•56 
•55 
(z — Z)la 
0 
•37 
•52 
•74 
•94 
1-18 
1-72 
2-28 
2-79 
X 
di = ¥(’5), 
rja 
117 
1-1 
1 
•9 
•8 
•75 
•71 
{z - Z)/a 
0 
•46 
•77 
1-04 
1-46 
1-94 
X 
rja 
1-325 
1-3 
1-2 
1-1 
1 
(z — Z)la 
0 
•36 
•87 
1-42 
X 
d' = a" (1’6), 
rja 
1-5 
P4 
1-3 
1-26 
{z — Z )la 
0 
1-06 
2-3 
X 
