( 755°) 
other coordinates than q,, q,, and q,, and they appear only in 
the equations of motion which refer more in particular to these 
coordinates. So it is clear that to determine the disturbing terms of 
the second kind we can restrict ourselves to a mechanism with three 
degrees of freedom. 
In the equations there are no disturbing terms among the terms 
of order #4; terms of a higher order than 4’ are not inserted. Hence 
we can write the potential function and the kinetic energy as follows: 
q 
| 
tol 
M! 
Ay Gi = HE, (7, NER) Qs): 
We i = Ge a 4 = (Ps Ge + 2] rs Qrqs)s 
== ill 
where //, represents a homogeneous function of degree 4, and 
Pis = 4 GrsQy + 3 Ores” dr 3 Orsa” H Orsa + frs,a + PrsQa9s « 
If e.g. we write the equation of motion for q,, then for the 
relations (A) and (B) the following terms 
Ya Ins Jeans Ae I> Ao In AMT 9,9500 > 
are to be regarded as disturbing. 
Let us replace in these terms g, by — 7,°q., dab n ge we 
by --7,q,", and 29s by 739.93: 
Let us omit all non-disturbing terms of order 4’ and let us make 
use in the disturbing terms of the relation n, + 2n, = n,—=0 (which 
is permissible, as ¢ is of order /*); we then find that the first equation 
can be written as follows: 
ia ny", = (= nn,h,, =} nn, bis zeik hen IE NgN slo — p) Ia Ys AE 
disturbing terms of the first kind (p being the coefficient of a terni 
14°, in U). 
Of the += and + signs the top one must be taken in the case of 
the relation (A), the bottom one in the case of the relation (B). 
When determining the disturbing terms of the second kind in the 
equations g, and g,, and when reducing these terms according to 
the method given just now, we find as result that the disturbing 
terms are the derivatives of one and the same function, namely of 
! 2 
P 41%: Ja: 
where 
| ew ee F ll) 27 pen 
PSP En nh Ft Oi ae fe Has 
This part of the function of disturbance can be again expressed 
in the same manner in the «'s and the 2’s. 
As disturbing terms of the first kind we have but to take the 
