100 



LORD RAYLEIGH ON THE ACOUSTIC SHADOW OF A SPHERE, 



APPENDIX. 

 By Professor A. LODGE. 



TABLE of Zonal Harmonics ; i.e., of the Coefficients of the Powers of x as far as P 20 in 

 the Expansion of (1 - 2x cos 6 + x~)-* in the form l+P,a;+P 3 a; 3 + . . . + P,X'+ 

 for 5 Intervals in the Values of from to 90. The Table is calculated to 

 7 decimal places, and the last figure is approximate. 





 5 



10 

 15 



20 

 25 

 30 



35 



40 



45 



50 

 55 

 GO 



65 

 70 



75 



80 

 85 

 90 





 5 



10 

 15 



20 

 25 

 30 



35 



40 

 45 



50 

 55 

 60 



65 

 70 

 75 



80 

 85 

 90 



PI (= costf). 



1-0000000 

 9961947 

 9848078 

 9659258 



9396926 

 9063078 

 8660254 



8191520 

 7660444 

 7071068 



6427876 

 5735764 

 5000000 



4226183 

 3420201 

 2588190 



1736482 



Po. 



1-0000000 

 9215975 

 7044712 

 3983060 



+ -0719030 



- -2039822 



- -3740235 



- -4114480 

 3235708 



- -1484376 



+ -0563782 

 2297230 

 3232421 



3138270 



2088770 



+ -0431002 



- -1321214 



- -2637801 



- -3125000 



1-0000000 

 9886059 

 9547695 

 8995191 



8245333 

 7320907 

 6250000 



5065151 

 3802362 

 2500000 



1197638 

 0065151 

 1250000 



- -2320907 



- -3245333 



- -3995191 



- -4547695 



PS- 



1 0000000 

 9772766 

 9105688 

 8041639 



6648847 

 5016273 

 3247595 



+ -1454201 



- -0252333 



- -1767767 



- -3002205 



- -3886125 



- - 4375000 



- -4452218 



- -4130083 

 3448846 



- -2473819 



1-0000000 

 9622718 

 8532094 

 6846954 



4749778 



2465322 



+ -0234375 



- -1714242 



- -3190044 



- -4062500 



- -4275344 

 3851868 



- -2890625 



- -1552100 

 0038000 



+ -1434296 



+ -2659016 



1-0000000 



8961595 



6164362 



+ -2455411 



- -1072262 



- -3440850 



- -4101780 



- -3095600 



- -1006016 

 + -1270581 



2854345 

 3190966 

 2231445 



+ -0422192 



- -1485259 



- -2730500 



- -2834799 



- -1778359 



Nil 



1-0000000 



8675072 



5218462 



+ -0961844 



- -2518395 

 4062285 



- -3387755 



- -1154393 

 + -1386270 



2983398 



2946824 

 + -1421667 



- -0736389 



- -2411439 



- -2780153 



- -1702200 



+ -0233080 

 2017462 

 2734376 



1-0000000 



8358030 



+ -4227908 



- -0427679 



- -3516966 



- -3895753 



- -1895752 



+ -0965467 

 -2900130 

 2855358 



+ -1040702 



- -1296151 



- -2678985 



- -2300283 



- -0475854 

 + -1594939 



2596272 



1912893 



Nil 



1-0000000 

 9436768 

 7839902 

 5471259 



2714918 

 + -0008795 



- -2232722 



- -3690967 



- -4196822 



- -3756505 



- -2544885 



- -0867913 

 + -0898437 



2381072 

 3280672 

 3427278 



2810175 



1-0000000 

 8012263 

 + -3214371 



- -1650562 



- -4012692 



- -3052371 



- -0070382 



+ -2541595 



2973452 



+ -1151123 



- -1381136 



- -2692039 



- -1882286 



+ -0323225 



+ -2192910 



2316302 



+ -0646821 



- -1498947 



- -2460938 



