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II. Researches in Vortex Motion .—Part III. On Sj^ircd or Gyrostatic Vortex 
Aggregates.'^ 
By W. M. Hicks, D.Sc., F.R.S., Professor of Physics in University College, 
Sheffield. 
Received January 12,—Read February 3, 1898. 
(Plates 1, 2.) 
Contents. 
Aet. Page. 
Introduction. 34 
Section i .—General Theorems. 
1. Analog’ue of spiral cylindric vortex. 36 
2. General nature of motion .. 36 
3. Spiral motion in general, with yy given. 37 
4. Application of cuiwilinear co-ordinate.s. 39 
5. Condition of steadiness impressed. Differential equation in . 42 
Section ii.— Non-Gxjrostatic Aggregates. 
6. Monad aggregates (Hill’s vortex). 43 
7. Dyad aggregates. 45 
8. Poly-ad aggregates. 48 
9. Equatorial axes. 51 
10. Energy. 52 
11. Comparison with ring aggregates. 53 
12. Spheroidal aggregates. 55 
13. Dyad spheroids. 58 
Section hi .—Gyrostatic Aggregates. 
14. Case i.—F uniform and/^cc yjr. Aggregate with solid oval nucleus. 69 
15. Case ii.—F unifoiun and/oc yj/. General form of . 61 
16. Stream-function for given sphere and parameter \ . 62 
17. The two cyclic constants. 64 
18. Moment of angular momentum. 66 
19. Energy. 66 
20. Velocity of translation. 68 
21. The stream and vortex spirals. 69 
22. Values of the V ^2 parameters. 73 
23. Position of equatorial axes. 75 
24. Forms and angular pitches of spirals. 78 
25. Graphical methods. 90 
26. The X .2 and \j aggregates of the first two orders. 92 
27. Poly-ad aggregates. Case of dyads. 95 
* Parts I. and II., ‘ Phil. Trans.,’ 1884 (I.), 1885 (II.) 
VOL. CXCII.—A. 
F 
10.12.98 
