( 743 ) 
Here P and Q are homogeneous quadratic functions of ]/a. and 
I /a t ; and 1 
• = T < 3 V ~ V)«. + W - 3/, 
(The terms - 3/ in « and -l in / originate from the term 
l <P<h appearing in U 4 ). 
In the terms of higher order we may substitute 3n, for n in the 
coefficients. We then find: 
-si (- 
We may now write the equations of motion: 
9i + 
~*9t 
r ^-~2 Ph ' q '' + ~ + T ^» 4 * 
So they get the same form as for the simple mechanism so that 
m case S = 4 also the horizontal projection of the point moving 
over the surface may be regarded as representative point for an 
arbitrary mechanism with 2 degrees of freedom. 
S= 2 . 
§ 20. So we suppose that the relation exists: 
— is of order 
the ( 
we have already seen 
■ 3 and S = 4 in which way such a residue of relation 
may be taken into account by inserting in the function R a term 
with qo 2 , we restrict ourselves here to the case that the residue of 
relation is zero, therefore: 
Proceedings Royal Acad. 
VoL X1L 
50 
