482 
one nucleus at the centre with a double charge, hence for it a = 0) 
Normal angular velocity: w. 
Distance of electron from centre of orbit: 7;== FR + 0; (measured 
parallel to the plane of the orbit). 
Deviation of an electron normally to the plane of the orbit: 2;. 
Angle of position: y;—= wt + 9;. 
Furthermore we put: 
WVR 
ate YEAat Pd dr 
BO — @, — “, Ts 
The quantities 9,, 0,,2,, 2,, 4, B, y, d, p are considered as infinite- 
simal, likewise o0,, etc. 
Between a, FR, w the relation exists: 
2e°R e 
mRw? = —— — —— (3) 
WwW? 4R 
which expresses the condition of equilibrium in the stationary state. 
The kinetic energy is found to be: 
fly zE pm (Ed) 3m Ree ai smb (9,?-+ 3,2) SF 
+ mito (9,9) + 2mRo (v,9,+0,9,) + Amo? (0, +0,°) + 
+ mRw’ (9, +0.) + mR?w’. 
Potential Energy : 
Bai te ED 2e Fe, +0.) (940) fre) 
Pati ie Ww? AR? 8R° 
Oe oats e (9 P2 2 2 2 2 2 2 2) 
RN ae [(2.R* —a*)(9,* H0,°) —(R?—2a*)(z,°+-2,")]4- 
eg 
Piom 
(In both expressions terms of the 3rd and higher orders in the 
quantities 9, etc. have been neglected). 
NN 
D'ArrMmBeERT’s principle gives the equations : 
d- (or OTN NA ; 
ef EE SEE Q, = 0. 
dt Òg» 0g. Ogu 
(the Q, are the auxiliary forces mentioned above). 
Hence we get: 
2 ‘ e | 4R’0,—2a70, 0,+09, 
0,—2hwd,— WW 0, SS ae | ae = d EE AR? | . (4) 
: e*( 4h*9,—2a70, 0,+0, 
SO) — 2 er, Di — ——_ nd mm md Ë, 5 
Q, kod, ® 0, al ws 4R ( ) 
5 : eq Q: 
RY, + 200, = he ea ee de woe aante katate (OO) 
— 8mR? ' mR 
