OF THE MAGNETIC PERMEABILITY OF MAGNETITE. 573 



Thus the curve may be plotted exhibiting graphically the relation between k and k'. 

 The two branches of the curve are shown in figure 4. 



Now it is clear, from the physical conditions of the case, that k and k' are of the 



same sign, and, from (3), that when k is infinite k becomes -^-. Hence we see that if 



in fig. 4, k be measured along OK and k' along OK', it is only the part OPQ of the 

 curve which expresses the actual relation between k and k'. 



19. k' and N required. — But before this curve can be of any service, one must 

 know the relative scale of the curve (vi.) whose ordinates are proportional to the values 

 of k' for the specimen, and the curve in fig. 4 which exhibits the relation between k 

 and k' in terms of the constant N. It thus became necessary to determine k at some 

 one temperature and to estimate N. An independent absolute measurement of k at 

 ordinary temperatures with a larger piece of magnetite seemed desirable also, both for 

 its own sake and as a stepping-stone to the foregoing. These ends were accomplished 

 by the following methods — 



VI. Absolute Values op True Susceptibility. 



20. Absolute Value of k. — For determining the absolute value of k, for the longer 

 specimen of magnetite, the electrical connections shown in fig. 1 were again employed. 

 The specimen now used was still so short that its reaction on the original magnetic field 

 could not be neglected. It was therefore matched, magnetically, by a preparation 

 containing finely-divided iron and occupying exactly the same volume and position in 

 the coils P and S, fig. 1, as did the specimen of rock. A cylinder of the same composi- 

 tion and about 100 diameters long was then used. For the very slight effect of 

 its ends a correction was applied on the supposition that it was equivalent to an ellip- 

 soid. In matching the mixtures against the actual specimen of magnetite, the second- 

 aries S and S' were arranged so as to exactly neutralise one another's effects. In 

 getting the value of k from the long cylinder of the mixture, this balance was disturbed. 

 The cylinder was first introduced in S and readings for the kick taken, then the 

 cylinder was placed in S' and readings for the kick again taken. Hence two equations 

 are obtained. Between these two equations the entire constant for the galvanometer 

 and the total resistance of the secondary circuit can be at once eliminated and k obtained 

 in terms of known quantities. 



21. Theory — Thus, referring to fig. 1, 



Let p denote the number of turns per cm. of length in the primary coils P and P' 

 (they were the same). 

 a and a' the cross-sectional areas of P and P'. 



s and s' the total number of turns in the secondaries S and S', after the balance has been 

 disturbed. 

 A the cross-sectional area of the long cylinder of mixture. 

 C the primary current in electro-magnetic units. 



