notion is slight. The correct raflnement of (2) is 



'a 



81 



(16) 



VJl _G /. N „ 2 £«= >3 G(a) G(amax) 



..e may treat the last two terms under the radical as small 

 compared with the remaining ones and so replace the integrand 

 by the first two terms of its expansion in pov/ors of these. 

 Setting W - G(agia;t) = ■i^'Pco^max we have, on making the 

 8a*-.ie substitutions as before. 





'-''CA D 



2 (r-1) yvw^ V i-y- 

 7 



where y s a /Sj^^^ . The first term in the brockets would 

 give the motion as previously calculated. Tho second can be 

 evaluated with sufficient accuracy for values of y near 1 by 

 setting 



-2Lli=L. = (>r-i)^X(Xrii (i-y^)^.... 

 1-y 2 



and then introducing the variable z defined by (5). The 

 details v;lll be omitted here, since we shall only need the 

 order of n^agnitude of the ratio of the second term of (17) to 

 the first when y is near 1. This ratio is asymptotically 

 y^ /2, which is small for the value of y^ {f\f 0.4) 

 v/hich characterizes the first pulsation. 



It should be remembered that -rr become's large almost 

 instantaneously after the detonation, so that the influence of 

 gas pressure does not increase the time taken by the first ex- 

 pansion in the way that it increases the time of the ensuing 

 contraction. 



