
326 . C. G. KNOTT AND J. G. MACGREGOR ON THE 
and second powers of the latter. In general the agreement between our obser- 
vations and the results of the substitution of the corresponding values of the 
temperature in the formule will show that this cae Sines was not unwar- 
ranted. 
In the case of charcoal, however, we find that we cannot express the 
deflection in terms of the first and second powers of the temperature. Fora 
small range of temperature up to about 230° C. it is possible. From 30° or 40° 
up to that temperature the following formula (in which 6 stands for deflection, 
and ¢ for temperature) holds :— 
d= —8'29 + °6047 + -000385? 
The fourth column of Table I. gives the values of 6 as calculated from this for- 
mula. Up to 230° they agree well with the observed results. Above that, 
however, they do not, and, perhaps because of chemical changes produced by 
heat, charcoal seems to’ be an exception to the general law. When it forms 
part of a thermo-electric circuit the electromotive force is not capable of being 
represented as a parabolic function of the temperature, except for comparatively 
low temperatures. . 
The above formula and a graphic treatment of the olicoramee at higher 
temperatures enable us -to determine the position of the charcoal line on the — 
thermo-electric diagram.* 
Differentiating the equation given above, we find 
& —-604 + 000772, 
whence, if j= WOnCe “= 604 F 
: a dé 
and if t=200° C., = ee : 
Now the results of Table II. are capable of representation by the formula 
| $,=const. + 5307t, 
where 6, stands for the deflection of the M-N circuit when the junction was 
immersed in oil, ¢ for the corresponding temperature. 
dé, 
- Hence == = "5307 
for all values oft. 
Since the circuits had equal resistances we find, by dividing © by a the ratio 
of the “thermo-electric powers” of the N-C and of the M-N circuits at 0° and 
200°C. This ratio may be written =. 
1 
* “Trans, Roy. Soc. Edin.” 1872-8, p. 131. 

