VISCOSITY OF WATER BY THE EFFLUX METHOD. 114 
Navier’s equations (a) give for the flow in any cylinder—all 
motion being parallel to its axis, X say, 
If as before we put 
DRG Hee Se 
and write 
u=¢ oe lee ce all Pee er te (c) 
we shall have, for all points in the section, Laplace’s equation 
tS an at | 
the solution of which is 
= Plytez) + fly - 02) + €' (1) 
If there be no slipping, the boundary condition u = 0 is determined 
by (c); hence, if we assume that in (d) each function F, f is the 
Square,’ these two equations give for the boundary of the section 
M (y? — x?) - + Pee GC On. wens (e) 
in which VW and C’ are undetermined constants. If we further 
Suppose the boundary to be an ellipse whose semiaxes are B and C 
the remaining condition to be satisfied thereat is therefore 
£m 
BC 
and these two equations completely determine the values of I 
and C’, the solution giving 
ee Oh iy are 
ee ae Ld 2 B*+C? 
Substituting these values in (e) and writing w instead of 0 we 
obtain 
A BC? 2 22} 
ie. ey Ek ash, Le 17 
2 Pro} Cpe tos) 5 an 
The curves of equal velocity are homothetic ellipses, and the 
Velocities are the same for homologous points on the radii vectores. 
1 This 
7 sg 
is equivalent to supposing that ¢ = M yi +N s* +C': bot 
equation requires that N= —M, therefore 6 =M(y*-#*)+C’. 
