536 
MR. T. GRAY ON THE MEASUREMENT OF 
eKdCjdt) — L, the coefficient of induction at any instant, can be obtained for different 
values of the magnetomotive force applied, or by comparison with the curve of total 
induction, for different degrees of magnetization. Similarly, if the curve of variation 
of current from maximum in one direction to maximum in the other direction, due to 
a reversal of the impressed E.M.F. be traced, the various changes of total induction, 
and of L through a complete cycle can be studied. The curve of total induction for 
the cycle forms generally, as is well known, a closed loop. The area of this loop is 
the difference of the values of JeC dt for the two halves of the cycle, and, consequentlv, 
is proportional to the energy dissipated in a cycle of magnetization. This area includes 
the dissipation due to magnetic retentiveness, and also that due to currents set up in 
the iron or in conducting currents surrounding the iron. It is interesting to study these 
curves, as is done for a few cases below, for different conditions of the magnetic circuit. 
This method of experiment applied to electrical transformers has the advantage 
of giving directly the total dissipation of energy in the iron, and also of furnishing 
data from which the magnetic quality of the iron can be studied. The electromagnetic 
arrangement used for the experiments quoted in this paper was, as has already been 
stated, of such a form that it could be used either for a simple electromagnet or for 
an open or closed circuit transformer. Diagrams are given illustrating the action in 
these different cases. It should perhaps be stated that these curves are copies on a 
reduced scale of the original curves from which the calculations were made, and may 
not be sufficiently accurate to bear exact comparison. The values of the dissipation 
of energy, total induction, &c., calculated from the original curves, are therefore 
marked on the diagrams. The method usually adopted in reducing the curves was to 
integrate by means of the cross-section paper the successive values of edt for succes¬ 
sive values of t, say, for one, two, three, &c., seconds, and plot a new curve with these 
areas as ordinates and the corresponding value of the current through the magnetizing 
coil as abscissse. When the proper scale is adopted this gives the magnetization curve 
with magnetomotive force as abscissse and density of magnetic induction as ordinates. 
From this curve, by a repetition of the integration of areas, the dissipation of energy 
was deduced. The values of L used in the curves for coefficients of induction were 
obtained by drawing tangents to the current curve at a sufficient number of points, 
and from these tangents reading the values of dCjdt. The corresponding value of e, 
for example, ah in fig. 3, was then divided by dCjdt, and the quotients used as ordi¬ 
nates in curves ha,vir)g current through the coil, that is, with proper change of scale, 
magnetomotive forces, as abscissae. Curves of permeability can, of course, be also 
obtained by taking the ratio of the ordinates to the abscissae of the induction or 
magnetization curves, that is LcZC^y'^lTruC as ordinates, and the corresponding values 
of IttuC as abscissae. These curves have not been drawn, as the curves on the diagrams 
seem to be already sufficiently numerous, and should the permeability be wanted at 
any time it can be readily obtained from those already given. The lines of impressed 
