311 
of Edinburgh, Session 1870-71. 
perimenting 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 accu- 
racy the air-thermometer in the measurement of very high tempera- 
tures, and where very exact results are not required. 
In fact, if the formula above be correct, we have for two circuits 
with their junctions immersed in the same vessels 
E =«(<-<,) («„ - ) 
E' = a' (t -«,)(<'„ - 
so that if the resistances in the circuits be made as a to a' their 
resultant effect on the differential galvanometer will be proportional 
to 
(fa ~ t'o) (f ~ Q • 
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. On a 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 approxi- 
mately 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 indica- 
tions of two such arrangements at very high temperatures will 
give the means of determining whether the quantities called h 
above are really constants. 
3. Note on Linear Differential Equations in Quaternions. 
By Professor Tait. 
The generally non-commutative character of quaternion multi- 
plication introduces into the solution even of linear differential 
equations with constant (quaternion) coefficients, difficulties of a 
somewhat novel character. To some of these which have presented 
themselves to me in many investigations, I wish to draw attention 
in the following note, but want of leisure prevents my attempting 
at present either to classify the numerous curious forms which may 
be met with in physical inquiries, even when these lead to mere 
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