80 



To = 1.829 ^'V^'-Brnax (14) 



s 3.66 f-p'J^^ean (14a) 



Tg o 3.07 ^p^^a, (15) 



Thus^ the coefficient of the meaai radius in the expression 

 for the period varies only slightly from infinitely large 

 to infinitely snail amplitudes. A numerical calculation 

 made by Professor Kennard c^ves the result that for "gr^a 1.4, 

 a^.^ s 5.9 amin « 2.07 a, , 



T :: 3.30 ^ p^^ a^g^n s 1.93 6 Pc 



nax 



Thus, for lar^e oraplitudos (14) c^^es a better approximation 

 to T than (14a), v;hile for small amplitudes the reverse is 

 the case. 



A calculation of the form of the a va. t curve 

 takin,^ account of c&s pressure could be made as follov/s. 

 For suall a an& reasonably large amplitudes, the second 

 ten.i of (1) could be nep;lected or treated as n saiall 

 correction; the integral for t could then be reduced to 

 an Incomplete beta function with indices involving ^ 

 For large values of a, the term G(a) could be regarded as 

 a small correction, and another tractable integral obtained. 

 It is hardly worth vjhile to carry out the calculations for 

 small a, however, since when the amplitude of motion is 

 large the a vb^ t curve in this region v/ill be Influenced 

 by dissipation (see Sections 4 and 7) . The calculations 

 for largo a v/ill be briefly sketched here, in order to show 

 that the effect of gas pressure en the outer parts of the 



