79 
1912-13.] Magnetic Induction in Ferric Oxide. 
the needle as possible on account of the somewhat unmagnetic nature of 
the working material. 
It is impossible to test for coil effect during the course of a heat cycle ; 
it can be done only at the beginning and end of the cycle. When the coil 
effect was small, say 2 mms., it was distributed uniformly over the curve, 
and the curve was re-drawn. All curves shown are either devoid of coil 
effect or have been corrected as described. When the coil effect at the end 
of a test was large, the heat cycle was repeated. These repeated tests have 
shown that the coil effect does not take place at any particular instant, but 
appears gradually, and a curve vitiated by coil effect exhibits the same 
maxima and minima as one in which no coil effect has been noted. The 
difference between the two curves lies only in the absolute value of the 
deflections. 
(i b ) Shortening of the Specimen while under Test . — Observation showed 
that shortening took place at temperatures higher than 500°, and chiefly in 
bars which had been moulded by mixing the ferric oxide with alcohol ; one 
such bar shortened by about 20 per cent, of its original length. 
The effect of change of length of the bar on the deflection which the 
bar produces may be calculated as follows : — 
The force F, due to the bar at a point on its axis at distance r from its 
centre is given by 
F = 2M rjif-Vf (1) 
where M is the magnetic moment of the bar, and 21 its pole distance. 
Suppose that, by the action of heat or otherwise, the bar, of length 2L, 
undergoes a change of length — 2£L. Suppose also that the permeability 
of the bar does not change as a result of shortening alone, and that the 
pole strength remains the same. 
Taking logarithms of equation (1) and differentiating, or taking the 
variation of the equation so formed, we obtain 
8F 8M _ 8r rt 8r + 8Z n Sr-Sl /ox 
Y~W + 7~ 2 7+T~ r^T ' ' ' ' () 
Since M — 2ml, and, on the usual assumption, 1 = 4L/5, 
SM 8/ 8L /QX 
M “ l~ L 
and shortening implies that all three quantities are negative. By substitut- 
ing from (3) in (2), using negative signs for SI and oL, we get 
8F 8L Sr Sr — SI Sr + Sl 
T - ~ T + 7 -2 T+7 -2 
r—t 
( 4 ) 
