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 = 
a(t - t L ] 
/ t + t i 
- 2 
E' = 
/, t + t x 
a' {i - Q 
>K-- 2 - 
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 
ft, - Q) (t - O • 
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 ma} r 
be met with in physical inquiries, even when these lead to mere 
2 s 
VOL. VII. 
