625 
of Edinburgh, Session 1874-75. 
Making use of Fourier’s theorem, in the form, — 
o 9_ 
y = A 0 + A, cos ~t + A 2 cos 
+ B, sin ~t + B 2 sin 2 
values of A and B were obtained from the expressions 
= 2/0V2+2/1 - y-i - 2/4V2 - 2/0 +2/7 
4 x/SBj = y l + y. 2 J2 + y 3 - y s - y, V 2 - y , , 
where y 0 , y 15 &c., are the measured values of the ordinates of the 
curve, taken at intervals of J of a period, the axis of t being a 
tangent to two of the vertices, or a line parallel to it. From these 
values of A 1 and B 1? a and (3 were calculated, so as to fulfil the con- 
ditions 
a = VA* + B a 2 ' ; p = tan - 1 ( - • 
These having been calculated for the curves representing the oscil- 
latory state of temperature at two of the junctions, the value of the 
conductivity (K) was obtained from the equation 
K = _77 1 
cp T lo g e 03-/3'), 
where cp is the water equivalent, T the periodic time, and r the 
distance between the two junctions. Care must be taken that log — , 
is the Naperian logarithm, and that (3 - (3' is measured in radians.* 
The unit employed in measuring y is of no importance, but r and 
T must be measured in the units in which the answer is required. 
In the following calculations the units employed are millimetres 
and seconds. 
The substances experimented on in these preliminary investiga- 
tions were, Siemens’ gutta-percha, the same as is used by Messrs 
Siemens Brothers in the manufacture of their cable core, and 
Hooper’s india-rubber, which is the insulating material used by the 
* The unit angle has been named by Prof. J. Thomson a Radian. As there 
is no surface conduction in these experiments, the two quantities referred to 
ought to be equal. Their more or less close agreement may be taken as a 
test of the accuracy of each experiment. 
