48 
Proceedings of the Koyal Society of Edinburgh. [Sess. 
evidence, while the final reversible effect is distinctly greater than at the 
same positive value of magnetisation. If this want of symmetry be con- 
tinued at lower values, a point must be reached where at some positive value 
of residual magnetisation the final reversible effect of loading and unloading 
will be nil. The next pair of curves shows that such a point is reached 
between the values B=+200 and B=+140, which constitutes a Yillari 
critical point for cyclic residual magnetisation. Thereafter, until zero 
magnetisation is reached, loading and unloading produce increase and 
decrease of residual magnetisation respectively, as shown in fig. V., when 
B = +140. 
These results therefore in zero field, with cyclic residual magnetisation, 
do not differ essentially from those obtained in cyclic fields. The absence 
of the initial irreversible effects at a comparatively large value of residual 
magnetisation constitutes a vibrational neutral point, and corresponds to 
that which occurs in the first (and third) quadrants with cyclic fields where 
the effects of loading and unloading assume their final values at once. The 
absence of the final reversible effects (after the irreversible effects are over) 
at a smaller value of residual magnetisation constitutes a Villari critical 
point, and corresponds to that which occurs in the second (and fourth) 
quadrants with cyclic fields where the final reversible effects of loading and 
unloading are nil. The asymptotic nature of the curves are equally well 
marked in both cases (figs. V. and Ill.a). 
Fields increasing from Zero. 
ExjJerimental Data. — Figs. VI. and VII. show the induction changes 
(ordinates) due to the first superposition of loads of 3, 11, and 20 ozs., 
corresponding to 0T4, 05, and 0'9 kilos per sq. mm. of sectional area, for 
values of induction (abscissae) increasing from zero without and with 
permanently acting vibrations respectively. Figs. VIII. and IX. show the 
effects of cyclic load (abscissae) without and with vibrations respectively. 
In both cases the same value of field supports an induction of B = 650 
before the superposition of load. A total load of 14 ozs. (0‘64 kilos per 
sq. mm.) is put “on” in steps of 3, 3, 2, 2, and 2 ozs., and “off” in inverse 
order. The first two complete load cycles, and a practically closed loop 
obtained after ten such cycles have been performed, are shown without 
(fig. VIII.) and with (fig. IX.) permanently acting vibrations. 
When load is superposed under the A conditions many distinct curves 
may be obtained, showing the irreversible effects of the first, second, etc. 
“ ons ” and “ offs.” The effects of the first “ on ” have been shown in figs. 
