1882.] 



Liquid Ellipsoid about an Axis. 



221 



figure 3, the curve which is the locus of (x, y) for Jacobi's or 

 Dedekind's ellipsoid, in which 



Fig. 3. 



a^A-c'C VB-<?C 



and 



*~a*' y "oJ 



Then the conditions lead to 



f °° ^~ (a 2 b 2 - b 2 c 2 - cV- c'X) = 0, 



and therefore the required curve must lie below the hyperbola 



x — y — xy — 0. 



Having plotted out the curve by means of points from x = to 

 x = 1, the points from x = 1 to x = oo can be drawn by putting - 



V 



for x, and - for y ; so that if 



CO 



y=f( x ) 



is the equation of the curve from x = to x = 1 ; then 

 is the equation of the curve from x = 1 to # = oo . 



