1907-8.] Magnetic Quality of Molecular Magnets. 
643 
XXXIX. — Magnetic Quality in the most open Cubic Arrangement 
of Molecular Magnets. By Professor W. Peddie. 
(Read in part July 6, 1908. MS. received July 21, 1908.) 
1. In a former paper ( Proc . R.S.E., 1905) an investigation was given of 
the magnetic properties of the closest packed homogeneous cubic arrange- 
ment of molecular magnets, and it was found that the results were in 
good agreement with the observed properties of crystals of magnetite. 
It was also suggested that a parallel investigation of other cubic arrange- 
ments might lead to a discrimination of molecular arrangement, so far as 
the magnetic constituents are concerned, in actual crystals. To settle 
this point, if possible, the present investigation was undertaken. 
2. The distances between pairs of centres of magnets in the most open 
arrangement are given by the values of r in the formula 
y 2 = p 2 ( A. 2 -4- p 2 -|- v 2 ), 
where p is the least distance between centres, and X, p, v are positive or 
negative whole numbers. 
The direction cosines of the axes of the magnets being a x /3, y, the 
component of the internal force, exerted by surrounding magnets on the 
pole of one, taken parallel to the common direction of the axes, is 
| + ^ + {■ -442.Np 
where M is the magnetic moment of a magnet, and a is the semi-axis, 
while p = X 2 + p? + v 2 , and N is the number of times of occurrence of given 
numerical values of X or p with a given p and y, and the summation extends 
from v — 0 to v = oo . The proof of the formula is exactly as in the previous 
paper. 
The transverse component of the internal force is 
245 Ma 2 
8p 5 L 
+ /3 6 + y 6 
( a 4 + £4 + 7 4)2 
i (xNk*p * 
with direction cosines a (a 4 +^ 4 + y 4 — a 2 )[a 6 +_p 6 + y 6 — (a 4 + /3 4 + y 4 ) 2 ]% etc. 
The requisite data for the evaluation of the sums are given in the appended 
tables. 
3. The transverse force is, in the neighbourhood of the quaternary 
