80 
Proceedings of the Royal Society of Edinburgh. [Sess. 
The limiting values of (4) could be obtained by putting 
8r=± SL. 
In the course of our research, however, no case was observed in which 
shortening took place from one end while the other end remained fixed. 
In work with solid hsematite bars, no shortening whatever was noted. In 
other cases in which ferric oxide was held in a copper tube, there was 
a change of volume without change of length. But with ferric oxide 
moulded by means of alcohol and held in a copper mould or boat, shrinking 
took place at both ends, to an equal extent so far as could be judged. 
Hence experiment points to the value 
Sr = 0, 
and equation (4) becomes 
sf sl m m /KX 
i=-rVrn (5) 
or, substituting for l and Sl, 
SF SL | 8L 8L [ 
F ” “ L 1 1 “ 5r + 4L + 5r - 4L J 
( 6 ) 
This equation expresses the proportional change of magnetic force at 
the needle due to the shortening <5L/L, ; and if we substitute for r and L 
their usual values in our experiments, viz. r = 33 5 cms., L = 4 cms., the 
equation becomes 
SF_ 
F ~ 
1-037 
SL 
( 7 ) 
If 6 is the angular deflection of the needle in the earth’s field H, 
F = H tan 0 = nearly, 
where d is the scale deflection and D the distance from needle to scale. 
Hence 
SF _Sd 
F ” d ’ 
and 
U 
d 
SL 
1,037 L 
(8) 
From (8) we see that the shortening of the bar in situ causes a reduction 
of the deflection, the amount of which may be determined, if <5L/L is 
known, and added to the observed deflection. 
In order to use this result properly, one would require to know the 
shortening of the bar at each stage of the heating — a matter of consider- 
able difficulty and not within the scope of the present experimental series. 
