x 
XXXVIII. HYDRAULIC ASPECT OF THE ARTESIAN PROBLEM. 
When a fifth sphere is placed on the four in Fig. 3, it will 
be seen that the interstitial volume is triangular in shape 
as in Fig. 2. 
Slichter shews that the porosity, that is the ratio of 
void to total volume occupied, viz. m to 1 is given by the 
expression, 
m=1- - ee (e 
6 (1—cos 8) /1+2 cos 6 
from which 6 may be found by solving the cubic equation— 
s? 0~3.cos* 6+ 1— 
2 cos 3.cos? 6+ 1 36 d—m)? 0 (5) 
and that the curved length / of a triangular pore is ex- 
pressed by 
J ___ Ah60s ) (1-195 -0-39 Gye 
h sin 6/1+2 cos 0 
in which h is the depth of the packed spheres. It is easily 
seen that the most open arrangement of spheres, viz. that 
when their centres are the points of cubes, gives voids the 
volume of which is r°(8—47/3); while when the closest 
arrangement is followed, viz. when the centres are the 
points of a regular rhombohedron (60°, 120°) the void-volume 
is r°(6—47/3). Hence the porosity m in one case is 1—7/6 
