302 PEOFESSOE G. H. DAEWIN ON THE STABILITY OF THE PEAE-SHAPED 
In order to give this expression a clear meaning, it is well to define the several S’s. 
sin^ 6 — (f sin 6 ) {(/'^ — k'^ cos" ( f )) ^/(l — k cos" <^), 
where = "923128, = "574647 
k'" = "076872, q'-^ = "425353. 
For the other harmonics we have 
>S/ = [a —b cos^ d + c cos^ 6 —d cos® 0 . . .) {a/ -\-h' sin" (f) -f c' sin^ (f)-\-d' sin® . . .), 
where the values of a, h, &c., a' , h', &c. are as given in the following table :— 
?. s. 
a. 
h. 
cl. 
e. 
2 0 
•GO.3.374 
-923128 
0 0 
- -039203 
-923128 
4 0 
1 
5 - 4.50 
4-901 
4 2 
-1-7988 
36 - 006 
44 - 805 
4 4 
-0839 
-7-975 
95-574 
6 0 
1 
12-6 
29-984 
18-834 
6 2 
-8-4 
121-8 
439-425 
320-523 
6 4 
3-78 
-338-312 
3680 - 303 
4482-844 
8 0 
1 
18 
74-25 
107-25 
50-273 
i. s. 
ft'. 
h'. 
c. 
d'. 
e'. 
2 0 
2 2 
-603374 
- -039203 
-076872 
-076872 
4 0 
4 2 
4 4 
-8036 
- 1-0666 
1-0136 
-3718 
1-8135 
-8-0266 
-0280 
-1865 
8- 
6 0 
6 2 
6 4 
-5989 
-1-1408 
1-0305 
-6888 
1-5349 
-7-704 
-1512 
-4404 
6-944 
-0000 
-0264 
704 
8 0 
1 
0 
0 
0 
0 
The surface of the pear is determined by measuring a certain length along the arc 
of curves orthogonal to the surface of the ellipsoid. By equation (22) it appears 
that that length measured in the direction of the positive normal is 
