where A, and 4,, represent constants. 
So we have shown that there is a function of which the disturbing 
terms in the equations are the derivatives. If we write it as function 
of the a's, 6’s and ¢ and afterwards leave out the terms containing 
t explicitly, we find: 
—R=~y,(a,,4,,.-.. a) + eha, + ma, Wa, cos 6n, (3,—8,). 
Here x, is a homogeneous quadratic function of the e's; the term 
o'h?a, is inserted in order to take in the wellknown way the residue 
of relation into account. 
The es and 8's must now be determined as functions of ¢ with 
the aid of the following system of equations : 
OR + OR 
C= a2, oe =— a, lr Iene AR 
We immediately notice that now also 
a, = — 0, 
Hence 
a, + a, = constant. 
From the absence of @,,8,...(3, in R it is evident that: 
i, —a,=. pis — ar — 0. 
Hence 
a, constant, @, = constant... aj = constant. 
Here a, and a, have the same form as for the mechanism with 
two degrees of freedom, 
The expressions for 8, and 3, contain both, besides the terms which 
they have for the mechanism with two degrees of freedom, one more 
linear function of @,, @,,....a@. On account of what was just found 
these functions can be reduced to constants of order 4*. Let m,h? 
be this constant term in the second member of the equation for g,, 
mh? the term in the second member of the equation for B. This 
is then the influence of these terms that the frequency of vibration n, 
must be increased by m,h’ and the residue of relation by 6n, (m,— m,)h’. 
Then e@,,@,,8, and 3, are determined out of the same equations 
as in the case of the mechanism with two degrees of freedom. The 
coordinates of q, and g, behave here too as if they were the only 
ones. The influence of the /:-—2 remaining degrees of freedom consists 
in a modilication of 7, and n,, which modification is of order 4? 
and dependent on the amplitudes of the remaining 4—2 vibrations. 
