108 Prof. T. R. Lyle on the Variations of 



Dividing D by the volume lot of iron we get for quotient 

 the space average throughout the ring of the iron loss per 

 cubic centimetre per cycle. In the sequel this quantity will 

 be represented by I. 



I can also be obtained from the harmonic expressions for 

 H and B in § 6. 



For as 



H/ = 47rn 1 0, B« = F, 



hence 



4ttJ 



HdB, 



and it is easy to show that if 



H = Hj [sin cot + h B sin 3(cot — qf> 3 ) + h& sin 5(g>£ — 5 ) + &c] 



B = B x [sin (cot — 6{) + b z sin 3(cot — 3 ) + b 5 sin 5 (at — 5 ) -f &c] , 



then 



~ {RdB = 5^i J sin 6 X + 3/^3 sin 3 (6> 3 -0 3 ) + 5 V> 5 sin 5 (<9 5 - fc) + &c. | 



Applying this formula to the expressions for H and B in § 6 

 we find, for the experiment being discussed, that 



1 = 1346. 



8. For the two rings used what has been called the static 

 hysteresis (U, say) was determined for various induction 

 densities by Ewing and Klaasen's method. It was found 

 that the Steinmetz coefficients cr, where 



1*6 

 Max. 



for them were not constant but varied with the induction, 

 and that the variation was quite as great for the narrow 

 ring as for the broad one. 



In fig. 2 the Steinmetz coefficients a for these two rings 

 are plotted against maximum induction (B say). It will be 

 seen that cr tends to be very small in weak fields, possibly 

 vanishing with B , that it increases rapidly to a maximum, 

 then diminishes to a minimum^ and then steadily increases. 

 It is possible that the maximum a point, which is very marked, 

 may give the induction at which some definite physical 

 change due to magnetization begins to take place in the iron, 

 perhaps that at which magnetization begins to produce 

 lengthening. 



