26 Mr M¢Connel, On Lagrange’s Equations of Motion. [Oct. 25, 
Multiply both sides by p, and differentiate with regard to t, 
remembering that a =e &e., 
d (dT p.)= (mat turin dy ae ee) 
aia, Ht Yay, ay) 
+ 3 (mba + myB + my). 
Now p, is perfectly arbitrary so we shall suppose it not to change 
with the time, so that the increment of yr, is zero, but aBy are 
bound by the connections of the system and therefore vary with 
the time; gis the change of # produced by w, being changed to 
wr, + p,, while w,, wr, -.. as well as W,, yy, ... are unchanged, 
dé dy PNG 
io (Ss dap, Ps and B= Fy Po 1 dap, Pv 
ad =| dT 
dt db, Py day, Ps 
dx 
== (mis Fy +mi Gh + me) p, ieee (4). 
Thus g (—) uly CT is obtained from the rates of change of 
dt\dy/ dr, 
momentum of the particles by the same process as in the previous 
cases, and might be called the generalised component of rate of 
change of momentum. 
It differs from the rate of change of the generalised component 
of momentum by the term — And this term is entirely due 
avy 
to the circumstance that the coefficient 22 
1 
1 
time. 
To complete the proof we need merely remark that by the 
second law of motion 
Nein, Wein Ate, 
so that by (2) and (4) 
See 
dt Gaal ae 
Clerk Maxwell gives a proof of Lagrange’s equations in his 
Electricity and Magnetism, in which no direct reference is made to 
