112 Proceedings of the Koyal Society of Edinburgh. [Sess. 
ment were set with a pitch {2a) of 4'52 cms. Their mean length from 
centre to centre of the balls was 3‘54 cms. : their true magnetic length 
between poles was more nearly 3'70, making i = V22. The row of magnets 
was so set as to bring its free end near the middle of the field of the 
Helmholtz coils. The curve AAA shows the current required to produce 
rupture for values of a ranging from 45°, which is the lowest for which 
instability could be clearly detected, up to 200°. The points of observa- 
tion are marked by small circles. The curve BBB, which is added for 
comparison, relates to a single pair of the same magnets with the same 
half-pitch a. On comparing the two curves it will be seen that there are 
interesting differences between the behaviour of the isolated pair and that 
of the end members of a long row. For the end member of a long row 
the maximum at a = 180° is much sharper as well as higher. With values 
of a between 110° and 170° the isolated pair required a stronger field to 
upset them than sufficed for the end member of a row. On the other 
hand, with values of a less than 110° the end member of a row is less 
easily upset than a single pair, and when a was less than 45° there was 
no instability, although with the single pair there was clear instability 
down to a = 32° or so. The minimum field was nearly the same in both 
cases, but it was found at a considerably larger value of a for the end 
member of a long row. 
1 9. These differences become accentuated when a straight-line group of 
three or four magnets is tested by itself, without any support at either end. 
Fig. 10 shows in the curve CCC the result of a test in which three of the 
same magnets as those of fig. 9, still with the same distance between the 
centres, formed an isolated group. Here again the curve BBB for a single 
pair is drawn to facilitate comparison. With three magnets the maximum 
at 180° becomes so remarkably sharp as to resemble a cusp, and the 
Tninimum is further shifted to the right, to about 120°. 
20. From the above calculations and observations it follows that a 
model consisting simply of rows of pivoted magnets fails quantitatively to 
represent what happens when a ferromagnetic substance is magnetised. 
This becomes apparent when a quantitative estimate is made of the field 
that would be required to break up rows of such magnets, assuming them 
to be so closely spaced as to comply with the essential condition laid down 
in § 2. Take, for example, the case of iron. From the form of the 
magnetisation curve, we know that in soft and fairly pure iron the 
elementary magnets show instability when the applied field reaches a value 
of the order of 1 c.g.s. unit. A much smaller field, of the order of yV c.g.s., 
will suffice to upset them in iron that has been electrolytically deposited 
