50 HEJSTRY A. ROWLAND 



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 establishes the inclination of 

 the diameter; H is the line A 0; and D depends upon the line A 0. 

 The following equation, adapted to degrees and fractions of a degree, 

 is the equation from which the values of ^ were found, as given in 

 Table I: 



A = 81-100 sin 



The large curve in Plate III was also drawn from 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 approximations. We might indeed solve 

 with reference to Q ; but in this case some values of ^ as obtained from 

 experiment may be accidentally greater than A, and so give an imagi- 

 nary value to Q. 



By plotting any Table in this way and measuring the distance C, 

 we have the maximum of magnetism. 



I have given in the same Plate the curve drawn from the observations 

 on the nickel ring with Q on the same scale, but ^ on a scale four times 

 as large as the other. The curve of nickel satisfies the equation 



quite well, but not so exactly as in the case of iron. This ring, when 

 closely examined, was found to be slightly porous, which must have 

 changed the curve slightly, and perhaps made it depart from the 

 equation. 



In Table VIII, I have collected some of the values of the constants 

 in the formula when it is applied to the different rings and bars, and 

 have also given some columns showing the maximum of magnetism. 

 When any blank occurs, it is caused by the fact that for some reason 

 or other the observations were not sufficient to determine it. The 

 values of a, H, D, and the value of X, when Q = 0, can in most cases 

 only be considered approximate ; for as they all vary so much, I did not 

 think it necessary to calculate them exactly. For comparison, I have 

 plotted Dr. Stoletow's curve and deduced the results given in the Table, 

 of course reducing them to the same units as mine. 



It will be observed that the columns headed "maximum of mag- 

 netism " contain, besides the maximum magnetic field, two columns 



