ON THE MEASUREMENT OF MAGNETIC HYSTERESIS. 
47 
which is calculated from the throw of the dynamometer coil simply, without any 
regard to the corrections. 
If, further, we denote by Y the correction due to the finite conductivity of the 
secondary circuit, we can write (14) in the form 
W = U - (X + Y) = U - Z.(18), 
where Z = X + Y. 
Comparing (18) with (14), we see that we can put 
clG 
V U ('C 
. ( 19 ). 
where x and y depend only upon C, and not upon dCjdt. 
§ 14. The form of Y at once suggests the way to find Y. For if U, Y correspond 
to S, and XT', Y' to S', then since X and W are unaffected by the change in 
S, U — U' = Y — Y', But SY = SY', and hence 
Y = (U - U') S'/(S' - S).(20). 
Thus, by observing the values of U found in two experiments with two values for S, 
the values of Y and Y' can be determined. 
In this determination it is not necessary to find the throw for the earth inductor 
for each value of S. If there were no damping we should have = S<^/S', so 
that (j)' could be calculated if (f) were known for the one resistance S. But the 
logarithmic decrement depends upon S, being of the form X = u v/S. where 
V is proportional to the current C', and hence each throw must be corrected for 
damping before it is used in the calculations. The easiest way of making the 
correction is to add to each throw a quarter of the difference between it and the next 
elongation on the same side when the dynamometer coil is allowed to continue in 
vibration. Since the throws are of very different magnitudes, it is necessary to 
correct each one for the difference between ^tan 26 and 6, if accuracy be desired. 
§ 15. The correction X is of great importance when the section of the specimen is 
of considerable area. In this case the secondary coil will generally be wound so 
closely upon the iron that L and M will be negligible in comparison with the 
quantities to which they are added in (14). Under these conditions the value of X/Y 
can be calculated, for now by (16) X/Y = QS//n~o-, and hence, when X + Y is known, 
X can be calculated ; for iron, a = 10“® ohm per centimetre cube approximately. It 
is not jDracticable to calculate X from the value of Y found by varying S, for an 
examination of the numerical magnitudes shows that X/Y is noy^ a large numeric— 
in Mr. Wills’s research something like 1000—while experiment shows that Y is so 
small as to elude observation. 
To determine X -h Y or Z, when the section of the specimen is considerable, we 
must vary dCjdt in a known manner. This could be done in the following way :— 
