ÖFVBRSIGT AF K. VETENSK.-AKAD. FÖRHANDLINGAR 1 900, N:0 9. 1.08 1 



pose to put !]„ = o, and tlie direction is thence determined by 

 the sign of t^'^,. We now easily become 



2wij'„ 



v' + 



dH2 

 da"- 



).. 



dHl 



The sign of j'- + ^-^ is positive for all the curves, and 



thence the orbits are described in the opposite direction — seen 

 from the corresponding centre of libration — to the direction of 

 the motion of m^ and m^ round their common centre of gravity. 

 With the help of (32) we can express the relation between 

 the Jaoobian constant and the initial coordinate |q for the 

 different points. We thus get: 



Tab. lY. 



Vallies of the Jacohian constant. 



Li . . . . 



fl 



= 1 



." " 



= 0.1 



M = 1 : 320000 



8.500 — 



286 ^^ 



4.0182 - 



-103.5 Ij 



3.0009264 — 36.22 |2 



L,.... 



7.412 — 



9.16 IJ 



3.8876- 



- 15.12 IJ 



3.0009227—34.16 1^ 







L,. . . . 



7.412 — 



9.16 i; 



3.4905- 



- ^-'^^l 



3.0000156— 1.00^^ 



L,. . . . 



6.000 





8.3000 





3.0000094 



For L,^ (and Z,) the values of C for diiferent values of 'E,^^ 

 is already given. 



For those curves that lie sufficiently near to the centres of 

 libration I get with this formulae a good agreemeut with the 

 results of Mr. Darwin. 



Seek for instance the periodic orbit of the family a cor- 

 responding to C = 4.0000. 



f— 0.0125 

 Tab. IV gives: lo = ± 0.0133; Mr. Darwin obtains S,^^ ={ 



» » T° = 138\3 



Tab. III 

 Tab. IV 



:t°= 138^0; 

 : 6= 0.0531; 



3/r 



0.0531. 



