ÖPVERSIOT AF K. VETENSK.-AKAI). PÜRILANDLINGAR 1900, N:0 *X lOdl 



Let mj and m^ be the two bodies revolving in circles about 

 their centre of gravity G. The largest body 771^ is supposed to 

 be of iinit mäss, m^, has the mäss /.i. The quantity /.i. wliich is 

 consequently a proper fraction, may also be equal to unity. 



Let r^ and o^ be the distances of /n, and m^ from the 

 centre of gravity, and let the distance from m^ to «i., be equal 

 to unity. 

 It is then 



(1) 



rj + ?'2 = 1 



The unit of time is so determined, that the gravitational 

 constant is equal to unity. Hence the time T of a revolution 

 of ??2j or m^ round G is 



2^ 



(2) 



T = 



n + f,i 



and the angular velocity n in this motion is 



In the plane determined by the motion of m^ and di^ moves 

 a third body m of infinitesimal mäss. 



The coordinates a; and y of this body are referred to rect- 

 angular axes moving with uniform angular velocity w, and having 

 their origin in G and the .-j^-axis directed towards m^. 



The equations of motion may thence be written 



(3) } 



where 



dt^ dt dx 



d^y dx _ dQ 



dt- dt dy 



2fi = ,:+l + „(,^.l)..) 



^) This symmetrical form for the potential is given by Mr. Darwin. 



