19 



303 



The angle variables u;,, w., and ly.j will now, according to (8), be defined by 



<P\ f l/-x2/|/^4-2;f(2/i+/3)/f-f^ + 2x/M )y 2;, (272+73) 



I'] $ l/_x-^7^P-f-2;f( 2 /?-f'' + 2;fP j 5y l/:_;,2/2p_|_2;,(2/^-^/^)/^-^2' 

 J '"V-x«i^P+2;^(2/i+/3)/e-T-^ + 2/P)j ;7 2/(2/,^-/3)/;y-./-• 



2.i^ _ 

 dl, 2x1 



Writing 



x{21^ + Q I, L\ = M\ - ^ i X- P I, {I, + /g), ) 

 K=xI.J, (49) 



M, = X (27, 1-/3)/, U ^ — = 4 7- 7^(7, 4- 73), J 



and introducing (compare (19)) instead of ç and two new variables and ;^ by 

 means of the formulae 



= M, + Lj cos 0, ^ = -f L2 cos (50) 



it is easily seen that 



^ ^ /, dj^ ^ ^ . 



l/^':^PT2;f(27i+ 73)7f- ^ ' I/- 7« F + 27(272 + 7^)^ ZT^' ^ ' 



and that the equations (48) may be written in the form 



2r = (Lj sin 4' ^ L, sin ;|.) + ^ + tt, (a) 



2;f7- 



= i^,(L,sinçA + L,sin;.) + i^^^ 2 \ ) AI, cos ' ^M,^/.,cos^ 

 Introducing the notations 



2 ^ ) M, 7., cos d> ^ ]m.,- L, C( 



the e(jualions (51) (a> and (b) become 



2;r«;i <r, sin c'/ f- sin / {-7:, (52) 

 2 ;ru>g = (Tj sin ^ + sin / + / + tt. (53) 



