95 



by (14) of Appendix 1. ITie quantity (B) represents the 



fractional change in f-Jrj produced by the dissipation, 



as coiapared with the ideal notion of Appendix 1. This 



chance is necliftible in the neichborhood of the maxinum 



radius, since for ifs 1.4, Poo s 1 atr.osphero, 



c = 1.5 X 10^ cn/sec, ti r i , (B) reduces to 



.4 4. ^nax 2 



3.4 X 10 ilf o 



(ill) For large amplitudes of motion we may i^nora p ©o 



in the neighborhood of the minimxira radius, and thus obtain 



from equation (1) of Appendix 1 



da - Yw - G , , 



whore G = W /^in ^ 



a 



Using this and (2), the right of (1) becomes 



12 IT rv^^ <i^ 



(10) 



dx (11) 



wher-e x = ^ — - . "vVe want to find out how much energy is 



^In 

 radiated av/ay dui'lng the entire portion of a cycle when 



the radius of the bubble Is small (we have seen that the 



radiation is negligible at other times). To do this let 



us take the limits of the Integral in (11) to be 1 and Oo 



(the exact value of the upper limit is unimportant) and 



multiply by two. The resulting integral con be expressed in 



terms of gaira~ia fimctlons, and dividing (11) by W v/e have 



finally 



