128 PROFESSOR TAIT ON A FIRST APPROXIMATION 
correction of the indication of the thermometers for the long column of mercury 
not immersed in the hot oil round the junction. 
“ To settle the question rigorously, I have been for some time experimenting 
with an arrangement sometimes of double metallic arcs, sometimes of two’ 
separate thermo-electric circuits acting on a differential galvanometer—a second 
object being to obtain, if it be possible, an arrangement capable of replacing 
with sufficient accuracy the air-thermometer in the measurement of very high 
temperatures, and where very exact results are not required. 
“Tn fact, if the formula above be correct, we have for two circuits with 
their Junctions immersed in the same vessels 
E = a(t—4)(, —*3*), i= a (t—14)(t, ae) ; 
so that if the resistances in the circuits be made as a to @’, their resultant effect 
on the differential galvanometer will be proportional to 
(, 7% ANG < t,). 
“It is obvious that so far as these factors are concerned, the most sensitive 
arrangements will be such as have their neutral points farthest apart. Ona 
future occasion I hope to lay the results of my new experiments before the 
Society. They appear to promise to be of great use in furnishing an easily 
working and approximately accurate substitute for the air-thermometer in an 
inquiry on which I am engaged respecting specific heats and melting points of 
various igneous rocks, &c., while the comparison of the indications of two such 
arrangements at very high temperatures will give the means of determining 
whether the quantities called 4 above are really constants.”* 
A year later (Dec. 18th, 1871) the following communication, giving rough 
materials for the construction of a thermo-electric diagram, was made to the 
Society, and appeared in the Proceedings :— 
“ For some time back I have been endeavouring to prove, by experiment, 
through great ranges of temperature, the result announced by me in December 
last, viz., that the electro-motive force of a thermo-electric circuit is in general, 
unless the temperature be very high, a parabolic function of the absolute tem- 
perature of either junction, that of the other being maintained constant. 
“For moderate ranges of temperature the experiment presents little diffi- 
culty; but when mercurial thermometers cannot be employed, a modification 
of the experimental method must be made. I have employed in succession 
several such modifications, of which the following are the chief :— 
“The simplest of all is to dispense altogether with thermometers, and to 
* In Pogg. Ann. 1873, Heft 7, which has just reached this country, there is another paper on 
this subject by Avenartus, in which he altogether deserts his earlier assumptions and line of reason- 
ing, and comes to conclusions somewhat resembling those just quoted from my paper of 1870. 

