658 MR JAMES RUSSELL ON 



when H, = 20"9, and the dash lines the induction curves at same positions when 

 H t =437 C.G.S. units (not tabulated). 



The addition of the normal B-H curves (see Table I. or fig. iv.) in dotted lines to 

 these figures facilitates comparisons being made between the induction curves obtained 

 under the TO conditions (fig. xxvui., shield A, fig. xxix., shield B) and those 

 obtained under the CTT conditions (fig. xxx,, shield A, fig. xxxi., shield B). The 

 differences of the induction curves under these two conditions of superimposed fields are 

 very apparent, and it is now proposed to determine what part of the induction is linked 

 with the transverse field and what part is circular and wholly completed in the iron 

 shields. 



§ 44. Let the four diagrams of fig. xxxrv. represent in section one of the iron 

 shields placed in a uniform transverse field (l) when H c is zero, (2) when H c produces 

 zero magnetisation at position n, (3) when H c just causes the induction at n to change 

 sign, and (4) when H c is increased sufficiently to produce w T holly circular induction. 

 Also let the following conventions hold, (a) that the transverse field, and consequently 

 the shielded field, be considered positive, and (b) that the induction in the sides of the 

 iron shield be considered positive if the magnetic lines are clockwise, and negative if 

 anti-clockwise, relative to the circular section of the shield. Further, the total magnetic 

 flux per cm. of length of the shield 



At position m = dB m 

 At position n = dB n 



Across the \ _ o /t?_^\ /tt\ 

 shielded space j ' '" ^ ) \ h> 



where cl and R are the thickness and outside radius of either of the two shields. Then 

 it follows that whether B 9l be negative (1) or zero (2) or positive (3 and 4) 



dB m +2(R-d)(H) w -dB n = K t 



where N f is the total number of magnetic lined linked or continuous with the transverse 

 field per cm. of length of the shield. 



It is also evident that when the flux at n has changed sign (thus becoming positive) 

 and is not less than the total flux across the shielded space (3 and 4), 



dB,-2(R-d)(K) H> = N„ 

 where N c is the total number of circular magnetic lines wholly completed in the iron 

 per cm. of length of the shield. 



The values of (H)„, given in Table XV. for shield A under the TC and CTT con- 

 ditions, H f being equal to 20 '9, are now multiplied by 2(R — d), which for shield A = 2*82 

 (see § 5), and the total magnetic flux across the shielded space thus obtained, plotted 

 (dot and dash line curves) against the corresponding values of the circular field, to an 

 ordinate scale on the right of figs, xxvui. and xxx. respectively. In like manner, the 

 values of (H) w given in Table XVI. for shield B under the TC and CTT conditions, H e 

 being equal to 20*9, are multiplied by 2(R — d), which for shield B= 2*84 (see § 5), and 



