( 493 ) 
the centre of gravity and of the oscillation centre of the rotating 
spherical space. 
Case k=1. The centre of gravity of volume and surface of 
the spherical space Sp,—1(”) lying in the centre, we find 
VES cra, Goa ite en Sh Er TN 
Case k}=2. The radii of inertia of volume and surface of a 
5) 
5 y 5 il 
spherical space Spp—s (r) with respect to the centre are 7 pe 
1 
Ge 
and 7, those with respect to a diametral space S,—3 are thus 7 == 
nr 
1 
and 7 4 . So we find 
n—2 
1 1 
V= Ar (« dn open? , Suda? + - a ) «Sg 78, 
n n—2 
If instead of a whole spherical space Prik (7) we allow only 
. vs (a) 2 > 8 
half of it to rotate around a space Sj in its space S,—; parallel 
to its base at a distance a, then the limits (—7,7) of the two 
integrals (1) change into (0,7) or (—r,0) according to the half 
spherical space Spy (7) turning its base or its spherical boundary 
. ‚(a) 7 
to the axial space Sj. We shall occupy ourselves another moment 
with the former of these cases, namely for k—=1 and #=—=2. 
Case (0,7), k=1. We find immediately 
2 Un. 9 . Zie OE 
2 ; ea yeas , n—2 5 
nf adr }. Op? ‚SUR Ar. Sn 0-2, 
Un) n—2 Sn—1 
Case (0,7), k=2. We determine the moments of inertia of 
Y= 
volume and surface first with respect to the base Sa and then 
: : : (2 
suecessively with respect to the parallel space Shae through the centre 
: ; : : Sl . 
of gravity and with respect to the axial space S,“’5. Thus we 
finally find the formulae 
r 2 Un—2 3 2 Un—2 3 
Vl See — er Hf — +: ra » U_—9 1—2, 
n (0, Basil 1D Brea 
„3 a 2 29 N 2 
7 2 Sn—2 a Spn—2 
Su = 27 — —— r}] Hf —— or a 8 n—8 
= . =D 
n—2 NA Snel N—2 Sn sy wi : 
or 
4 Un—2 r? 
VS 27 | a? = art — » Un—2 72, 
n Un—1 n 
4 89 je 
Su= 2 f a a ar Fats) yn—3, 
n—2 Bp) | n—2 
Which pass for « =O appropriately into volume and surface of the 
spherical space Sp, (7). 
