Page:Cathode Rays.pdf/22

no longer holds: thus 6 magnets do not arrange themselves at the corners of a hexagon, but divide into two systems, consisting of 1 in the middle surrounded by 5 at the corners of a pentagon. For 8 we have two in the inside and 6 outside; this arrangement in two systems, an inner and an outer, lasts up to 18 magnets. After this we have three systems: an inner, a middle, and an outer; for a still larger number of magnets we have four systems, and so on.

Mayer found the arrangement of magnets was as follows:—

000$1\cdot$	000$2\cdot$	000$3\cdot$	000$4\cdot$	000$5\cdot$
${\begin{cases}1\cdot 5\\1\cdot 6\\1\cdot 7\end{cases}}$	${\begin{cases}2\cdot 6\\2\cdot 7\end{cases}}$	${\begin{cases}3\cdot 7\\3\cdot 8\end{cases}}$	${\begin{cases}4\cdot 8\\4\cdot 9\end{cases}}$	00$5\cdot 9$
${\begin{cases}1\cdot 5\cdot 9\\1\cdot 6\cdot 9\\1\cdot 6\cdot 10\\1\cdot 6\cdot 11\end{cases}}$	${\begin{cases}2\cdot 7\cdot 10\\2\cdot 8\cdot 10\\2\cdot 7\cdot 11\end{cases}}$	${\begin{cases}3\cdot 7\cdot 10\\3\cdot 7\cdot 11\\3\cdot 8\cdot 10\\3\cdot 8\cdot 11\\3\cdot 8\cdot 12\\3\cdot 8\cdot 13\end{cases}}$	${\begin{cases}4\cdot 8\cdot 12\\4\cdot 8\cdot 13\\4\cdot 9\cdot 12\\4\cdot 9\cdot 13\end{cases}}$	${\begin{cases}5\cdot 9\cdot 12\\5\cdot 9\cdot 13\end{cases}}$
${\begin{cases}1\cdot 5\cdot 9\cdot 12\\1\cdot 5\cdot 9\cdot 13\\1\cdot 6\cdot 9\cdot 12\\1\cdot 6\cdot 10\cdot 12\\1\cdot 6\cdot 10\cdot 13\\1\cdot 6\cdot 11\cdot 12\\1\cdot 6\cdot 11\cdot 13\\1\cdot 6\cdot 11\cdot 14\\1\cdot 6\cdot 11\cdot 15\\1\cdot 7\cdot 12\cdot 14\end{cases}}$	${\begin{cases}2\cdot 7\cdot 10\cdot 15\\2\cdot 7\cdot 12\cdot 14\end{cases}}$	${\begin{cases}3\cdot 7\cdot 12\cdot 13\\3\cdot 7\cdot 12\cdot 14\\3\cdot 7\cdot 13\cdot 14\\3\cdot 7\cdot 13\cdot 15\end{cases}}$	${\begin{cases}4\cdot 9\cdot 13\cdot 14\\4\cdot 9\cdot 13\cdot 15\\4\cdot 9\cdot 14\cdot 15\end{cases}}$

where, for example, $1\cdot 6\cdot 10\cdot 12$ means an arrangement with one magnet in the middle, then a ring of six, then a ring of ten, and a ring of twelve outside.

Now suppose that a certain property is associated with two magnets forming a group by themselves; we should have this property with 2 magnets, again with 8 and 9, again with 19 and 20, and again with 34, 35, and so on. If we regard the system of magnets as a model of an atom, the number of magnets being proportional to the atomic weight, we should have this property occurring in elements of atomic weight 2, (8,9), 19, 20, (34, 35). Again, any property conferred by three magnets forming a system by themselves would occur with atomic weights 3, 10, and 11; 20, 21, 22, 23, and 24; 35, 36, 37 and 39; in fact, we should have something quite analogous to the periodic law, the first series corresponding to the arrangement of the magnets in a single group, the second series to the arrangement in two groups, the third series in three groups, and so on.