122 Mr A. B. Basset, On the Application of Lagrange’s [Oct. 31, 
and that 28 = («) P? +2 («x,) PP, +... 
IK = (Ke) K+ 2 (KK,) KK, +... 
where the coefficients are functions of the coordinates alone. Also 
© is that portion of the original expression for 7 which does not 
contain the y’s. Equations (10) may be written 
dh od ood e oa REs 
Se Re MG = dk, Te, ee vececceces (11). 
Let © be the generalised component of momentum correspond- 
ing to 6, and let © be the value of © after the velocities 6 have 
been destroyed by means of proper impulses applied to the system. 
Then 
CHE d@ 
Bales 6 
_d& AS , 
Soot 3s 
whence @= (One ee ¥ + (Oy,) 5 Get ctl she shies onan (12). 
Let ay, = (Uy ae Jk, 
aL _ de dss 
OE (Oy 
then eo a + > (Oy) dP 
_ a dP d¥ 
Qo- >— =| 
— db : do &P 
dt = 
Se EG) hock cn ecostotat somes eeeceeeee lk 
dé +0 (13), 
qar a dy 0 
whence = eam at a tae 1 ads dence eRe (14). 
The momentum ® is evidently a function of the momenta « 
and the coordinates only. 
dl. dd  d& 
do do" d0” 
Now since @ enters into % through «, we have 
dt d&dk  d& dk, DT 
dO de dO‘ de, d0** dO’ 
where the symbol ¥/d@ operates on the coefficients and not on 
the momenta «. Differentiating (10) with respect to 0, we obtain 
Again 
