PROPAGATION OF MAGNETIZATION OF IRON. 97 
solving the differential equation connecting induction with time and radius in the iron 
with the true relation of induction and magnetizing force. But we may inversely from 
these curves attempt to obtain an approximation to the cyclic curve of induction of 
the iron. 
Let 7 be the mean length of lines of force in the magnet. Let n be the number of 
convolutions on the magnet, and let c be the current in amperes in the magnetizing 
coils at time ¢. Then at this epoch the force due to the magnetizing coils is 4mnc/10/. 
Call this H). 
Next consider only one centimetre length of the magnet in the part between the 
pole-pieces which is circular and has coils 1, 2, 3, wound within its mass, and coil 
4 wound outside. The area of each of the electromotive force curves of the coils 1, 2, 
3, 4, up to the ordinate corresponding to any time, is equal to the total change of the 
induction up to that time. , 
In fig. 2 let Aj, Ay, As, A, be the areas in sq. centims. of coil 1 and the ring-shaped 
areas included between the coils 1, 2, 3, 4 respectively. Then the induction at time ¢, 
as given by the integral of curve 1, divided by A, is the average induction per 
sq. centim. for this epoch over this area. Also, the induction at time ¢, as given by 
the integral of curve 2, minus the induction for the same time, as given by the 
integral of curve 1, divided by Aj, is the average induction per sq. centim. for this 
area. Similarly, average induction per sq. centim. for As, A, can be found for any epoch. 
Consider area A,. It is obvious that all currents induced within the mass 
considered external to this area, due to changes of induction, plus the current in 
the magnetizing coil per centim. linear, at any epoch, go to magnetize this area, and, 
further, the induced currents in the outside of the area A, itself go to magnetize the 
interior portion of this area. We know the electromotive forces at the radii 1, 2, 3, 
4, and the lengths in centims. of circles corresponding to these radii. From a know- 
ledge of the specific resistance of the iron we can find the resistance, in ohms, of rings 
of the iron corresponding to these radii, having a cross-sectional area of 1 sq. centim. 
Let these resistances be respectively 1), 72, 13,7, At time ¢, let e,, e, es, e, be the 
electromotive forces in volts at the radii 1, 2, 3, 4, then 2s 5 = ; ah, = are at this 
1 2 3 4 
epoch the amperes per sq. centim. at these radii. Let a curve be drawn for this epoch, 
having amperes per sq. centim. for ordinates and radii in centims. for abscissee. Then 
the area of this curve, from radius 1 to radius 4, gives approximately the amperes per 
centim. due to changes of induction, and (neglecting the currents within the area 
considered) the algebraic sum of this force (call it Hy), with the force due to the 
magnetizing coils (H,) at the epoch chosen, gives the resultant magnetizing force 
acting upon area A,. If H is this resultant force, we have H=H,+ H, Next 
draw a curve showing the relation between the induction per sq. centim. (B) and the 
resultant force (H) for different epochs. This curve should be an approximation to 
the cyclic curve of induction of the iron. 
MDCCCXCV.—A. O 
