322 Mr J. Brill, Note on a Viscous Fluid. [May 27, 



and similarly ndx - Idz = k(^d\—^d/Jb], 



and Idy - mdx = k i^ d\ — ^ djjA . 



Thus equation (20) becomes 



Comparing this with the equation 



d(}) + -^dX + :^ d/ji=0, 



wehave M (^ ^-^ + m'|+..' |) =| . 



and M ( r ^ +m' :^ +n' ~) = - ^ . 



\ ox dy Gzi Ofjb 



An expression for h can be readily calculated in the case of any 

 particular pair of congruences. The quantity ^ is to a certain 

 extent analogous to the quantity m of the preceding investigations. 

 In addition to the above equations we have 



9 {k, \, fx) _ dl dm dn 

 d(x, y, z) dx dy dz ' 



(3) On a certain automorphic function. By Mr H. F. Baker, 

 Fellow of St John's College. 



On an infinite plane, and lying entirely in the finite part of the 

 plane, are drawn 2p circles, each outside all the others. They are 

 divided into p pairs of associated circles, G/, Ci denoting a pair. 

 The limiting points of the pair 0/, C,: being represented, by 

 complex variables in the ordinary way, by the symbols Ai, Bi, the 

 transformation 



^'-Bi _ ^-Bj 



connects the complex variable of a point ^, on 0/, with the complex 

 variable ^' of a point on Gi. We suppose Ai within C/ and Bi 



