( 633 ) 
A parabola 
parabola , 
The points of intersection of the 1 parabola with the C t and C t 
parabolae lie again on the ellipse having RJi and 2 RJi as axes. The 
parabolae are confocal; the focus lies on the y-axis at the height 
of — ^RJi.f. In fig. 6 a , 6 6 , 6 C we find those parabolae (and 
also the osculating parabolae) corresponding to the cases q’" 1 and 
In fig. 7 we see how the limitation approaches more and more 
to a rectangle for increasing q’". 
The l x and u 3 parabolae coincide for maximal and minimal K. 
Arbitrary mechanism with 2 degrees of freedom 
for which S= 3. 
§ 13. Let q x and q 9 be the principal coordinates of the mechanism; 
they remain during the movement of order A and are zero in the 
position of equilibrium. 
The kinetic energy T and the potential energy U may be written: 
where 7\ and U s are expressions in whose terms h appears at least 
to the 3 rd degree. 
Let us write down the terms of order A* in T s : 
As far as and inclusive of the terms of order A s the equations 
of Lagrange now become: 
