Manchester Memoirs, Vol. xhi. (1898;, No. 8. 5 



{p-\-iy)e^^ in place of x-{-iy and to stipulate that the 

 imaginary part oi f{x-\-iy) shall, in consequence, become 

 constant. 



The corresponding condition affecting the velocity 

 may be dealt with in the same manner, when that is pre- 

 ferable to dealing with i//. 



Other modes of orienting the system. 



Hitherto, the orientation of the system in space has 

 been effected by orienting the axes by means of y 

 relative to the vertical, and the system relative to the axes 

 by j3's. This is, of course, an arbitrary arrangement, but 

 it is perhaps the least arbitrary among such arrangements, 

 and it has secured a formal unity in the expressions 

 without interfering with the generality of the results. 



In any particular case, however, the horizontal and 

 vertical will probably be taken as axes, and all that is 

 then necessary is to orient the system in the most con- 

 venient method with reference to the axes, and this may 

 sometimes best be done by using some line specially con- 

 venient for the purpose which need not be the vertical. 



In illustration of this, we may take the general case 

 of transverse motion of a fluid within a space bounded by 

 two intersecting lines. 



Most symmetrically, the system may be oriented by 

 the position of the bisector of the angle between these 

 lines, and the shape of the space containing the fluid 

 determined by the semi-angle at the apex. 



It would also be convenient to take the origin at the 

 apex. We should then replace 7 by (/32 + j3i)/2, and get in 

 the first place 



-cp-ixP =/ { (x+ iy)e-^{^i + ^2)/2} 

 with the boundary conditions that the imaginary parts of 



may be constant. 



