178 Mr Pocklington, On the Gonfiguration of a pair [Feb. 26, 



For free currents ^o is zero, and (43), (44) must reduce to the 

 same equation. This wiil be so if 



R [10 



Qo 



= P' 



2SSp (4 



Qo'+-^Q)^ + '^f --^(Qo'+Q:) 



i.e. if - (PoQo' - Po'Qo) j^ = I P:Qo, 



whence the modukis of decay is 



R 



the corresponding current function being 



*^ = -^2S\(cr^)^sin7i^e':^'* 



= - ^ S {AP:+RQ:) (aey sin nd e^P^ 



= A't (Qo'P; - Po'Q:) (^Of sin ne e^^/ie^A'Qo', 



since AP^,' + BQ^,' = 0, A' being an arbitrary constant and the 

 summation extending from n = 1 to w = oo . 



(2) The Complete System of Quaternariants for any Degree. 

 By D. B. Mair, B.A., Christ's College. 



[Published in the Transactions.] 



(3) The Configuration of a pair of equal and opposite hollow 

 straight vortices, of finite cross-section, moving steadily through fluid. 

 By H. C. Pocklington, B.A., St John's College. 



The motion of a fluid that circulates about an annular hollow, 

 which itself has a motion of translation, has been worked out by 

 Dr Hicks in a paper in Phil. Trans. 1884. He there finds the 

 shape of the cross-section and the velocity of the hollow, together 

 with other circumstances of the motion. He, however, assumes 

 the ratio of the diameter of the cross-section of the hollow to that 

 of the ring to be a small quantity of which the higher powers may 

 be neglected. As his results are thus only approximate it may be 

 interesting to give an investigation of the two-dimensional case 

 to which his three-dimensional one is analogous. This investigation 



