ON THE MEASUREMENT OF MAGNETIC HYSTERESIS. 
;R) 
Since it is only the ratio of the angles 6 and ff) wliich appears in the formula 
for l/47r . I Hc/B, we may take for the ratio 6/(f) the ratio of the two “ throws ” of the 
spot of light along the scale, provided that the “ throws ” are not so large that 
tan 20 differs appreciably from 20. 
The effect of damping has so far been neglected. If X he the logarithmic 
decrement, we must Avrite (5) 
where 0 is now the ohserved “ throw.” The “ throw ” <[) must l)e treated in the same 
way, and hence the ratio 0/(f) is unaffected and the expression (8) remains true. 
§ 5. If, instead of making the primary current go through a complete cycle, we 
make it go through a semi-cycle from + Cq to — or vice versa, Ave can A'ery 
coiiA'eniently combine the measurement of the hysteresis by the dynamometer Avith 
the measurement of the magnetic induction by a ballistic galAmnometer. F(Ar if a 
ballistic galA'anometer be connected in series AA’ith a second secondary coil Avound 
upon the specimen, the throAv of tlie galA’-anometer gh^es the A-alue of — Ik, AAdiere 
B^ and B,, are the algebraical A^alues of B corresponding to + Cq and — In the 
ideal case Bo = — B^, and then B^ = (Bj — Bo). 
Whether this ideal state obtain or not, AA^e shall denote ^(B^ —Bo) by B,j, 
calling it the mean maximum induction. When the specimen takes the form of a 
ling, the ballistic galA’anometer only enables us to find Bq ; it giA^es no information 
as to B^ or Bo. This knoAAdedge could, hoAA^eA'er, be obtained in the case of a long 
straight specimen by slijijiing the secondary coil off the specimen. 
Wlien, as in our case, there are tAvo obserA'ers, the oliservations for W and B^ can 
he made simultaneously. 
§ 6. To take the specimen through a complete cycle, Ave must make the curi'ent go 
through the semi-cycle -h to — and then from —Cq to -f- Cq. If the iron has 
reached a cyclic state the throAvs of the galA^anometer Avill be the same in magnitude, 
though opposite in direction for the two reA^ersals of the current. But it aauII often 
lia])pen that, on account of the preA'ious treatment of the iron, Bj differs consider¬ 
ably fi’om — Bo, and in this case the throAvs of the dynamo¬ 
meter differ in magnitude for the tAAm reversals, though 
tliey are in the same direction. 
A little consideration aviH sIioaa^ us Iioaa' to proceed in 
this case. Let ahca'Uca (fig. 1) he a B—H curA*e, and let 
ad, a'd! be draAAui parallel to OH. By reversal of the cur¬ 
rent, let the iron 1)e caused to go thi'ough the clianges 
represented liy the curA^e abca'. From a to h H is positive 
and c/B is negative, Avhile from h to a' lioth H and c/B 
are negative. Hence the value of | HdB for the semi-cycle 
+ Qj to — C^j is giA-en liy (area Ijca'd') — (area ahd). Simi- 
