gß Art. 3. — K. Hi raya ma: 



sis' p^xW _(§^)X10^ 3(^yxiœ (|_yxl0 3(|^,)xlO 



The variations of the constants, Cancl E, l:)econie rapid by 

 this increase of the eccentricity. 



42. The revolution of Type 2 will change to the revolution of 

 Type 8 sooner or later, since E decreases and C cannot become 

 neg-ative. It has been proved that 6' increases when E is less than 

 a certain positive value. Hence C begins to increase without 

 limit just as E decreases. 



43, The equation (10) may be integi'ated by expanding iu 

 series when 6 is small. Let us first take the integral 



I e{e- — e-yit 



where T is the period of the libration as before. Putting 



$=x—x '// = e—c 



2 

 we have e'-e^—2êr^ + y = ^$ 



and a;^ — 5' = 25=1^ + ^ '" = ^Pt (^ cos ^ — è cos d) 



Eliminating $ and making use of the relation 



s'ex=Pi cos 



we get 



whence, neglecting r/, ffi"', ffi"^ and higher powers, we obtain 



