( 392 ) 
plane, proves to be impossible for a > /. For a ■< l it can however 
be realised, for values of % and s (as far as e ]> |), determined by 
the equations 
15 = ~ + and 24g>5’ (1—e) = (8+(*'), ! 
3+f* s 3-hp 2 
where S and p may be the coordinates of a point inside the region 
ABC out of fig. 2,. In this figure the equation of AB is: 1 -f = 2g* 
Fig. 2. 
9. The fourth case was treated only for parallelepipeda with 
square section, where three vertices of the pentagonal level section 
were supposed to lie on the unequal edges 2 1. Only such positions 
that the level section is normal to one of the two diagonal planes 
passing through the unequal edges, proved to be possible. Such 
positions appear, in as far as e >$, for values of I and s deter¬ 
mined by 
1 _ w 4 —2s 4 j 
| “ 2(a) s —2s 3 ) + ~ 2{w~s)\w 3 —2 s') J 
^-2**_ 6(1—e) 
(wsY ~ § ! 
where w and s are the coordinates of a point situated inside the 
region OQP in fig. 3. 
The equations of the curves out of tig. 3 are: 
Of PQ : (to— s) s (w 4 — 4ws 8 -}-2s 4 ) = w*— 2r<? 8 s-|-2s 4 , 
Of OP : to = 2s 
Of OQ: 3(w— s)(w a —2s 2 i(w 8 —2s 3 ) — 
(»' - +8wV - 6m> 9 s 4 -f 4s 8 ) (w—sy + (2 w* — 6w 4 s* — 2w*s 3 -f 1 -4s 6 )- 
10. The fifth .case finally proved very unfit to be treated. Only 
for the floating cube could it be investigated a little more closely- 
