738 



whole mass of the star to expaiul coiiipletely iiniforml,y and what 



are the initial conditions required in this case? 



We must then have r zizz /'^/{t), where /' is independent of /•. 

 It follows that 



1 cip ^ £ dp^ ^,^^,^^ c/v ^ ^ rfy 



p dr 9o rfr/ r/^' " df} 



hence the equation of motion (1) becomes 



For / = this gives 



' /O 7 



The quantity /J' must be a constant; a special distribution of 

 density and pressure along the radius for ^ =: must therefore he 

 sought, in which 



1 dPo 



»'o Qo dr^ 



= A' (3) 



(The dimension of A is .7 -^) ; ƒ is then determined by 



f"^A\f-''h, ........ (4) 



By integration of this equation ƒ is found as a function of the 

 time 



df\ 5 



- -^ ^'/^"^ -f Const. 



dtj 6 -^ ^ 



The constant is determined bj the condition that for ^ =: and 

 f= 1, when the expansion begins, its velocity is 0, hence 



dt K 3 ■ 



-\/ 



5 l/l _ƒ-«/:, 



This form can be integrated by partial integration in the form 

 "of a series. Putting 



we have 



C 6 t 2 2.4 2 4.10 ) 



I x-''U{\—x)-'hd.xr^-x-%(\—x\h\ 1 X a?' '- x^—... \^- const, 



J ^ ' 5 1 1.7 1.7.13 r 



