VARIABLE STARS 
189 
/ 
3£i + £o£i' — 0 and will probably fall within the boundary; the wave is 
thus a little too short to fit the star. We lengthen it by diminishing oj 2 . 
On trying a> 2 = ‘055 we see that we have greatly overshot the mark; 
£i" is (as far as we trace it) increasing more and more rapidly and the 
wave is quite out of control. Taking co 2 = -065 we find that the wave is 
much too short and there will be a node well within the star. The results 
show that the solution is very sensitive to small changes of oj 2 so that the 
true solution cannot be far from to 2 = -060. 
Table 26. 
Trial Solutions for a Pulsating Star (a = 0-2). 
oj 2 = -055 
co 2 = -069 
w 2 = , 065 
= 0 
Si 
Si 
£i" 
ii 
& 
Si" 
Si 
Si 
Si" 
0 
1 
0 
•0423 
1 
0 
•0413 
1 
0 
•0403 
1 
1-0218 
•0443 
•0504 
10212 
•0431 
•0476 
1-0206 
•0420 
•0448 
li 
1-0345 
•0573 
•0538 
1-0335 
•0554 
•0506 
1-0325 
•0535 
•0474 
H 
1-0505 
•0713 
•0585 
1-0489 
•0685 
•0541 
1-0474 
•0657 
•0497 
ii 
1-0702 
•0867 
•0644 
1-0678 
•0825 
•0584 
1-0654 
•0784 
•0524 
2 
1-0940 
•1037 
•0718 
1-0903 
•0977 
•0634 
1-0867 
•0919 
•0550 
2J 
1-1223 
•1227 
•0806 
1-1168 
•1142 
•0688 
11114 
•1059 
•0570 
H 
1-1556 
•1441 
•0912 
1-1475 
•1320 
•0744 
1T396 
•1202 
•0577 
2| 
1-1946 
•1685 
•1041 
1-1829 
•1514 
•0804 
1T715 
•1346 
•0568 
3 
1-2401 
•1965 
•1203 
1-2234 
•1723 
•0862 
1-2069 
•1484 
•0529 
3i 
1-2932 
•2290 
•1407 
1-2692 
•1945 
•0917 
1-2456 
•1606 
•0440 
H 
1-3551 
•2672 
•1676 
1-3208 
•2181 
•0968 
1-2870 
•1697 
•0276 
H 
1-4272 
•3135 
•2045 
1-3784 
•2427 
•0999 
1-3300 
•1735 
-•0014 
4 
1-5122 
•3707 
•2571 
1-4422 
•2678 
•0994 
— 
— 
— 
4i 
1-6131 
•4442 
•3361 
1-5122 
•2919 
•0927 
— 
— 
— 
4* 
1-7349 
•5427 
•4621 
1-5879 
•3130 
•0735 
— 
— 
— 
4£ 
— 
— 
— 
1-6680 
•3266 
•0289 
— 
— 
— 
5 
— 
— 
— 
1-7497 
•3233 
-•0680 
— 
— 
— 
It will be shown later that the adiabatic approximation breaks down 
near the boundary so that it would not be possible to introduce exact 
boundary conditions. But this does not much matter. So long as the node 
falls well inside the star (where the approximation is valid) we have to go 
on lengthening the wave; and when we have lengthened it a little too 
much the solution changes in such a way that no node can possibly occur. 
It is found that the value of oj 2 for the fundamental oscillation is 
roughly proportional to a. The following results have been found: 
a -- 0*1, 
CU 2 = ‘0315 
a = 0-2, 
oj 2 = -060, 
ZO 
© 
II 
to 2 = -156.