Table of Zonal Spherical Harmonics. 

 Table (continued). 



517 



9. 



Pr 



P,. 



P 3 . 



P 4 - 



Po- 



Pe- 



P 7 - 



o 



55 



•5736 



-•0065 



- -3886 



-•3852 



-•0868 



+•2297 i 



3191 



56 



•5592 



-•0310 



-•4016 



-•3698 



-•0510 



+•2559 1 



•3095 



57 



•5446 



-•0551 



-4131 



- -3524 



-•0150 



+•2787 i 



•2949 



58 



•5299 



-'0788 



-•4229 



-3331 



•0206 



+•2976 ! 



2752 



59 



•5150 



-•1021 



-•4310 



-•3119 



•0557 



+•3125 



2511 



60 



•5000 



-•1250 



-•4375 



-•2891 



•0898 



+•3232 



2231 



61 



•4848 



-•1474 



-•4423 



-•2647 



•1229 



+•3298 



•1916 



62 



•4695 



-•1694 



-•4455 



-•2390 



•1545 



+ •3321 



1571 



63 



•4540 



-•1908 



-•4471 



-2121 



•1844 



+•3302 



1203 



64 



•4384 



-•2117 



-•4470 



-•1841 



•2123 



+•3240 



0818 



65 



•4226 



—•2321 



-•4452 



-•1552 



■2381 



+•3138 ; 



0422 



66 



•4067 



-•2518 



-•4419 



-•1256 



•2615 



+•2996 



0021 



67 



•3907 



-•2710 



-•4370 



-•0955 



•2824 



+•2819 



0375 



68 



•3746 



-•2896 



-•4305 



-•0650 



•3005 



+•2605 - 



0763 



69 



•3584 



-•3074 



-•4225 



-•0344 



•3158 



+ •2361 - 



1135 



70 



•3420 



-•3245 



-•4130 



•0038 



•3281 



+•2089 



1485 



71 



•3256 



-•3410 



-•4021 



•0267 



•3373 



+ •1786 - 



1811 



72 



•3090 



-•3568 



-•3898 



•0568 



•3434 



+•1472 



2099 



73 



•2924 



-•3718 



-•3761 



•0864 



•3463 



+•1144 



2347 



74 



•2756 



-•3860 



-•3611 



•1153 



•3461 



+•0795 



2559 



75 



•2588 



-•3995 



-•3449 



•1434 



•3427 



+ •0431 



2730 



76 



•2419 



-•4112 



-•3275 



•1705 



•3362 



+ ■0076 



2848 



77 



•2250 



-•4241 



-•3090 



•1964 



•3267 



-•0284 - 



2919 



78 



•2079 



- -4352 



-•2894 



•2211 



•3143 



-•0644 



2943 



79 



•1908 



-•4454 



-•2688 



•2443 



•2990 



-•0989 



2913 



80 



•1736 



-•4548 



-•2474 



•2659 



•2810 



-•1321 - 



2835 



81 



•1564 



-•4633 



-•2251 



•2859 



•2606 



-•1635 



2709 



82 



•1392 



-•4709 



-•2020 



•3040 



•2378 



-•1926 



2536 



83 



•1219 



-•4777 



-•1783 



•3203 



•2129 



-•2193 - 



2321 



84 



•1045 



-•4836 



-•1539 



•3345 



•1861 



-•2431 



2067 



85 



•0872 



-•4886 



-•1291 



•3468 



•1577 



-•2638 



1779 



86 



•0698 



-•4927 



-•1038 



•3569 



•1278 



-•2811 



1460 



87 



•0523 



-•4959 



-•0781 



•3648 



•0969 



-•2947 



1117 



88 



•0349 



-•4982 



-0522 



•3704 



" -0651 



-•3045 



0735 



89 



•0175 



-•4995 



-•0262 



•3739 



•0327 



-•3105 



0381 



90 



•oooo 



- -5000 



-•oooo 



•3750 



•oooo 



-•3125 



0000 



KB.— To find P>, if lies between 90° and 180°, look up 



the 



angle 18O°-0, 



and change the 



sign if i be 



the value for 

 odd. 



When P 1? P 2 , &c. are plotted as radial heights and depths 

 above and below a quadrant, the resulting curves, especially 

 if coloured, are exceedingly interesting. A student can draw 

 them to a useful scale in about one hour. 





Example I. 



The density a of attracting matter on a spherical shell 

 1 centim. in radius is proportional to the square of the 



