( 682 ) 
§ 4. Discussion of the measurements. In $ 2 we have already 
remarked that the mean temperature of the platinum wire, wound 
round the portion BC of the rods, which is at the temperature 
of the bath, may, with sufficient accuracy, be put as 
equal to the mean temperature of that portion of the rod 
asf itself. Throughout this length, the differences of temperature 
or the length over which they are found, are on the whole 
small, so that only the mean temperature comes into 
account. Further consideration is however necessary in 
respect to the relation of the temperatures of the ends 
AB and CD and the resistances determined. 
Fig. 2. Let us suppose that the level of the liquid reaches to a 
position 4, fig. 2, and hence that the upper portion of AB is outside 
the liquid. We may suppose that, for the length 4, the rod has the 
temperature of the bath. The resistance of the wire between B and 2 
is then w, = w, (1 + pt + qi’) where ¢ is the temperature of the bath. 
Also we may suppose that at A, which was damp but just free 
from ice, the temperature was about 0° C. Further let us suppose that 
between 2 and £ the temperature gradient is linear, in other words 
that the external conduction may be neglected in comparison with the 
internal conduction of the glass. There is every reason to assume 
that this was true to the first approximation, since the glass rods were 
well enclosed in paper the conductivity of which is about */,,, of that 
of glass. Then, neglecting the conduction of the platinum wire, itself 
the resistance of an element of the wire between À and ZL is wdz, 
nlb 
where w= w, (L + pt, + giz’) and the whole resistance f dr. 
CI 
Further for « between O and 4, t‚=t,, between 4 and J, 
Om 
i= EE (@—a) and for c= lj t; = 0, so that 
k 8 A : 
Wan = Wap, 7 CEE (6) Sp 
a aie ek i) ENE 
es anes z } allt “u— ies 
a) (AB) > aie Er (a q =e v 
From this 2, the only unknown, can be obtained. One of the 
most unfavourable cases, that for the upper end of the Jena glass 
rod in N,O, shows when calculated that the linear form for the 
resistance can be employed in our measurements without difficulty, 
in place of the quadratic form. We found 2= 8.4 em. with the 
