320 Mr J. Brill, Note on the Steady Motion [May 27, 



To do this we shall have to satisfy the equation 



+ „j«f_,^ + „(8|_|)| = (19). 



Now consider the congruence of curves given by the differential 

 equations 



doG _dy _dz 

 I m n ' 



Let A, and fi be the parameters of two families of surfaces 

 belonging to this congruence. Then we have 



9 {y> z) ' d{z, x)' d {x, y) ' 



Substituting these values for Z, m, n in equation (18) we have 



d(x, y, z) 

 or ^ a function of X and //,. We may write this result in the form 

 </> +/(^. H') — const., 



or ^+ F + |5^+/(\, /a) = const, 



r 

 Now equation (19) gives only one relation between the quan- 

 tities I, m, n, and we are therefore at liberty to assume another. 

 We see that the equation will be satisfied if we assume I, m, n to 

 be connected by the two equations 



I {wri — v^) + m, (u^ — w^) + n (v^ — ur]) = 0, 



\dy dz) \dz dxj 



+ «('^-'^l=o. 



\,dy dzj \dz dxJ \dx dy/ 



Thus the congruence of curves given by the differential equations 



dx 



<--"(3f-a^)-(<-'"«(|-a^ 



