48 
ME. W. SPOTTISWOODE ON THE CONTACT OE CUEVES. 
Similarly, for the first minors, 
o o oo 
.r-, 
X ,y , ^zx— j - 
, , BUjBU/BUBH 
^ ^ 1 dx dij ' 
„ _ „ Bupu/BUBH 
If, Z-, ^.zx, -Jf- 
dz I dx dij 
o o o o BU|BU/BUBH 
y, Z-, 2 .fy, -^- 
J I ? y-' dx y dx \ dx dy 
0 20 o BUJBU/BUBH 
.t-, 2 .Ty, 
0,0 o BU/BU/BUBH 
.-, %Tf -^■ 
JU — U, 
dz dy j I dy dxdz dz dxdy j y 
JU _3jj/^ B"U_BU 
dx dz J y dz dydx dx dydz J j ’ 
BH\_gH/^U B"U_BU B^U\) 
dy dx j ydx dzd;y dy dzdx J y 
^\_ 3 jj/^ B^U_BU B"U\ 
dx dz j \ dz dydx dx dydzj 
.W — U- 
dx j' \dx dzdy dy dzdx j j 
dx dz ) y dz dx'^ dx dxdzjy 
W 
[n — 1)^ ■ 
dy dx J 
dz dy j 
BU BH' 
• 3H 
X- 
dx \ 
^ dy 
dz 
dz 
1 dy ' 
dx 
dy ~ 
dy 
JBU 
BU 
I dz 
\ dy 
dz 
dz 
JBU 
^_ 
_^_u 
[ dz^ 
y dz 
dx 
dx 
JBU. 
BU 
1 dx \ 
V dy 
dz 
" dz 
yu/ 
^_ 
' dy \ 
dz 
dx 
dx 
dy) 
■3H 
■ 3H 
dxdy 
dy 
dx’^ ) J’ 
B®U 
BU 
B^uy 
dydz 
dz 
%VJ’ 
B^U 
BU 
B^^Un 
dzdy 
dy 
dzdx J 
B"U 
BU 
B^uy 
dxdz 
dz 
dxdy J f 
B'U 
BU 
B^uy 
dy^ 
■ dy 
dydx J J ’ 
B'U 
BU 
B'uy 
dz'^ 
dz 
dzdy) y 
B"U 
BU 
B"U\1 
dzdx 
dx 
dz^ ) y 
B^U 
BU 
B^u\ 
dxdz 
dz 
dxdy j 
B"U 
BU 
B^uy 
dydx 
dx 
dydz J 1 
\ 2 ’ 
I2\5 
9 .. 9 ,^ 2xy 
lyz, Z.ZX, Z.xy, ^ yy dz\dy dz 
2.. 2...2....=2Vr-ff^f. 
■ dz 
dy ) \\dy ) dz^ \ds ) dif J ’ 
^)- 3 H 
dx dz J 
^)- 3 H 
dy dz j 
BUyB^U_ /BU\^B"U 1 
dz J dx^ ydx J dz^ J ’ 
/BU\^B"U 1 
dx j dy^ ydy J dx^ J ‘ 
