PKOFESSOK G. H. DARWIX OX THE PEAR-SHAPED FIGURE 
O 
o 
0(5 
These o’ive 
o 
y~ 
- I ---2 
cos" A|r ^ 1 - ^ ' 
0 • o 
c- sill- 7 
sin-i/r 
At the surface xfj = y, and we have 
cos- 7 
+ 
r 
1 — K~ sill- 7 
0 
= 
In tlie formulas for the third harmonics, in every case but one, and in two out of 
the five harmonics of the second degree, there occurs a factor of the form (w — con¬ 
stant) ; in each such case I write that constant in the form q~/K~, and (/~ — 1 — r/h 
'flius q will have a difterent value for eacli harmonic. 
It has lieen already remarked tliat for most purposes it is immaterial by what 
constants tlie several functions are multiplied. Although it would be easy to 
determine the constant in each case so as to make the function aoree with its value as 
O 
defined in “ Harmonics,” yet I shall not take that course, and shall omit factors as 
being in most cases redundant. 
For the sake of completeness I will give the first and second liarmonics in the new 
notation, as well as the third. 
Since the harmonics of the first degree are expressed by 
it is clear that in the new notation 
(^) = Pi' H = f*c>t xp, 
(/x) = sin 0, (^) = (1 — K' sin- Oy, 
Cf(ff)) = (f — K - COS- cf)}', (fp) = cos (f), 
Pi' (-) 
(1 — /c- sin- yp)- 
sin yjr ' 
Pi' (h) = ^. 
{(p) = sin cp 
\\ 
It appears from § 12 of “ Harmonics” that 
Po (^) = + w Pa" {^) = F- + ^-7, 
JJ -2 7 ' B + 2 
here 
7 
In accordance with the notation suggested above, let 
, and 71- = 1 -f .3/3-. 
o 
'£ 
K- 
2 + B 
• (1 - 
