FIGURE OF EQUILIBRIUM OF A ROTATING MASS OF LIQUID. 
299 
Multiplying these last two expressions together, we have the moment of 
momentum of the j^ear ; it is 
2irp\ 
[1 + •068854t'2]. 
It follows that, whilst the angular velocity of the pear is less than that of the 
critical Jacobian, the moment of momentum is greater. This result would afford a 
rigorous proof of the stability of the pear if the numbers were based on a complete 
solution of the problem. But as we have not determined an infinite series of new 
harmonic terms, it becomes necessary to consider how the result might differ if the 
hitherto uncomputed terms were added. 
If € denotes the uncomputed portion of the infinite series N | [i, s\ + j’ 
A denotes the addition to be made on that account to any of the results as already 
computed, we have 
ec^ 
8«2\_ 
' 47rp/ '023332 ’ 
•023332 X -142 ’ 
Whence 
Since 
1 /8&>“ \ 2ec“ 
and 
A [\/((y^ “b [301 ■8346€e^]. 
CO" 
jy Scoc C BJ „ ti 
= ?r A 
3(0” 
Uj 4:7rp 
= — 10 
3 1263984 
A/o2= - ” A 
C/p iirp 
Then 
A (Aj — Ar) — 7 
3 Jr~a fc ti ^ .3 
ZTrpkQ l_n ' a _ 
34/ha 
iTT 
[- 8337892 + 397472] ee^ 
34/hl 
27rpko 
(- 794-0420) ee2 
Therefore 
+ Sco") = 01 [1 — -062156862 + 301-8346e62] 
34/2a 
Aj - Ar = v-w [1 + -1310106862 — 794-0420ee2] 
^TTpIvQ 
By multiplication we find that the moment of momentum is 
34/2nai 
[1 + -0688539e2 — 492-2074e2e]. 
2 Q 2 
