12 
Proceedings of the Royal Society of Edinburgh. [Sess. 
the origin or the cyclic extremes according as the amplitude is sufficiently 
decreased (zero amplitude at the origin) or sufficiently increased (saturation 
values of induction at the extremes). The maximum range of possible 
shift, which may be extensive, occurs between these two extremes. Between 
the lower and higher limiting values of the range of shift, vibrations in- 
crease or decrease the induction according as the vibrations are sufficiently 
increased or sufficiently decreased. Below the lower limiting value vibra- 
tions of all intensities, however great, decrease the induction. Above the 
higher limiting value, vibrations of all intensities, however weak, increase 
the induction. 
In Section III. these results will be co-ordinated with the immediately 
preceding field change. 
Cyclic Residual Magnetisation. 
Experimental Data . — In fig. III. the series of nine trains of damped 
vibrations, increasing in intensity, are superposed in succession upon a 
sufficient number of values of cyclic residual magnetisation as already 
defined, between the limits of B= +9100 and —9100, the field being zero. 
The reference diagram shows these values as reached from the positive 
cyclic extreme, viz. H — 2 7, B = 10,400, just as the results for cyclic field 
have been represented as occurring with the decreasing positive field. The 
abscissm (fig. III.) represent (as in fig. I.) the intensity of the vibrations in- 
creasing from W xD°' 7 = 2 , 2 to 10*4 superposed upon eight values of cyclic 
residual magnetisation, viz. B = + 9100, +8700, +8020, +7500, +4570,0, 
— 3390 and — 9100 ; the ordinates, the summation of the induction changes 
following thereon. 
In fig. IV. the induction changes from the same experimental data are 
plotted, not against W x D 0 ' 7 for various values of cyclic residual magnetisa- 
tion, as in fig III., but against cyclic residual magnetisation as abscissae for 
the following values of vibrational intensity, viz. WxD 07 = 2'2, 4'8, 6*9, 
and 10*4. The curves for the other five values of vibrational intensities 
have been omitted, to avoid confusion. 
Obviously figs. III. and IV. for cyclic residual magnetisation correspond 
to figs. I. and II. respectively for decreasing cyclic field. 
Results . — When damped trains of mechanical vibrations are superposed at 
the extreme values of cyclic residual magnetisation, the resulting induction 
changes are, for reasons of symmetry, the same quantitatively, but of reversed 
sign — negative in reference to positive magnetisation, positive in reference 
to negative magnetisation. In other words, the residual magnetisation is for 
all values of vibrational intensity reduced. In fact, the extreme values of 
