and the Maximum of Magnetism of Iron, Steel, and Nickel. 155 



and permanent magnetism ; but I will call attention to the fol- 

 lowing facts which the Tables seem to establish. 



1. Nearly or quite all the magnetism of a bar is ? with weak 

 magnetizing -forces } temporary ; and this is more apparent in steel 

 than in soft iron. 



2. The temporary magnetism increases continually with the 

 current, 



3. The permanent magnetism at first increases very fast with 

 the current, but afterwards diminishes as the current increases, 

 when the iron is near its maximum of magnetism. 



I have now described the methods of plotting the Tables 

 hitherto used ; and I will now describe the third, which is, I be- 

 lieve, new. This is by using the values of the magnetism of the 

 bar as abscissas, and those of the permeability as ordinates. In 

 this way we obtain a perfectly regular curve, which is of finite 

 dimensions, and from which the maximum of magnetism can be 

 readily obtained. Plate III. shows this method of plotting as 

 applied to Table I. If we draw straight lines across the curve 

 parallel to the axis of Q and mark their centres, we find that 

 they always fall very exactly upon a straight line, which is there- 

 fore a diameter of the curve. The curve of nickel shown upon 

 the same Plate has this property iu common with iron. I have 

 made several attempts to get a ring of cobalt; but the button 

 has always been too porous to use. However, I hope soon to 

 obtain one, and thus make the law general for all the magnetic 

 metals. There are two equations which may be used to express 

 the curve : one is the equation of an inclined parabola ; but this 

 fails for the two ends of the curve; the other is an equation of 

 the general form 



A sin 



( Q + aX-h H 



) • . • • (11) 



in which A, H, D, and a are constants depending upon the 

 kind and quality of the metal used. A is the maximum value 

 of X, and gives the height of the curve E D, Plate III. ; a esta- 

 blishes the inclination of the diameter ; H is the line A ; 

 and D depends upon the line A C. The following equation, 

 adapted to degrees and fractions of a degree, is the equation 

 from which the values of X were found, as given in Table I. : 



X=31-100sin( — j. 



The large curve in Plate III. was also drawn horn this, 

 and the dots added to show the coincidence with observation; 

 it is seen that this is almost perfect. As X enters both sides of 

 the equation, the calculation can only be made by successive ap- 



M3 



