ON THE MEASUREMENT OF MAGNETIC HYSTERESIS. 
37 
Of the many advantages of the ballistic method, two may be mentioned. Thus 
the induction can be measured simultaneously with the hysteresis far more simply 
than when an alternating current is used. Further, the ballistic method enables 
measurements to be made so quickly as to render experiments easy which would 
otherwise be practically imj^ossible on account of the very great time required fu’ 
the numerous determinations of hysteresis necessary in investigations on the eftects 
of stress or of temperature. 
It will appear from the paper that several of the eftects of physical changes upon 
hysteresis which we have studied presented themselves to us as we worked out the 
method. We found afterwards that some of these eftects had already been discovered 
by Ewing or others, or might have been deduced from their experiments. These 
cases we refer to in foot-notes. The eftects of the vaiious physical changes upon tlie 
induction have received so much attention from others that we have not thoim-ht it 
O 
necessary to point out how much of that part of our work has consisted merely in 
going over old ground. 
A'jyproximate Theory of the Method. 
§ 4. Let an iron ring of section A sq. centim. and mean circumference I centim. be 
wound with N turns of primary windings per centim., so that the total number of 
turns is N/. The current C, which passes through the })rimary and magnetises the 
iron, producing the magnetic force H = 47rNC, passes also round the fixed coils of a 
sensitive electro-dynamometer. A secondary coil of n turns is wound over the iron, 
and is connected in series with the suspended coil of the dynamometer, and with an 
earth inductor, the total resistance of the secondary circuit being S. In ftnding the 
total induction through the secondary circuit, w'e must remember that tlie secondary 
will not generally be closely wound upon the iron. A certain number of lines 
of induction will in consequence pass through the secondary circuit due to the 
magnetic force H produced by the primary current. The total numljcr of lirdvages 
of lines of induction with the secondary circuit is thus AnB + MC where M is some 
constant. 
Let the primary current C change gradually (1) from -j- Cg to — Cq and back 
again to -f- Cq, so as to conqftete a cycle, or (2) from + to — making a semi¬ 
cycle. During the change the voltage AoidMidt -f MdC/d^ is set rq) in tlie 
secondary circuit. If the “ time constant ” of the secondary circuit be very small 
compared with the “time constant” of the primary circuit, the effect of the self- 
induction of the secondary circuit may be neglected, and the current in the secondary 
circuit may be taken to lie 
_ r/E M (If 
^ dt 8 dt 
