1904-5.] Magnetic Quality in Molecular Assemblages. 1033 
Assemblage . — As stated in § 2, the assemblage of magnets con- 
sidered is that having centres at the centres of spheres in the 
single homogeneous closest packed arrangement. The distance r 
between a pair of such centres is given by the formula 
A 2 + p 2 + v 2 , 
where p is the least distance between centres, and A, g, v, are 
positive or negative whole numbers ; for the homogeneous arrange- 
ment under consideration is the same as that of points situated at 
the centres, and the mid-points of the edges, of homogeneously 
arranged, closest packed, cubes filling all space. 
If we put r 2 /p 2 =p, we see that p must be an integer; for either 
one or all of A, g, v must be even integers. 
If we consider the origin of co-ordinates to be at the centre of 
one of the magnets, while the axes of co-ordinates are parallel to 
edges of the cubic arrangement ; and if we take a, /3, y, as the 
common direction cosines of the axes of the infinite system of 
magnets regarded as constituting a homogeneously magnetised 
body ; the expressions at the end of § 6 give the components of 
force at the origin, provided that we put 
cos 6 = (aA + (3g + yv)/'(2p) 1/2 , 
and sum for all possible values of A, g, v. But the force which we 
require is not that at the origin. It is the force at the pole of the 
magnet whose centre is at the origin. If we consider the north 
pole, it is therefore the force at the point + aa > P^ + r 
P\/2 + Q ^ ’ S ° we h ave to toke 
cos v = 
aA + /3g + y v + Jo, - 
P 
A + V 2a p) 2 + (p- + \/ 2 /? 
— ja 
P 
Developing the quantity (3 cos 2 6 - 1) in the value of F cos (0 + <£),. 
neglecting powers of a/p greater than the second, and summing 
