61 
of Edinburgh, Session 1872-73. 
The thermometers were read once a minute when the periodic 
state was arrived at, the corresponding curves were traced ; and 
from the curves so drawn, eight values of the temperature were 
deduced for successive intervals of three and three-quarter minutes. 
It was easy from these to calculate the coefficients of the harmonic 
terms up to the fourth inclusive, in the following expression — 
v = A 0 + A x cos ^ t + cos 2 ~ t + . . . 
+ B x sin t + B 2 sin 2 ^ t + . . . . 
From these again were calculated sets of values of a and (3 by the 
formulae 
a = J A 2 + B 2 , tan /3 = • 
In the preceding tables the dashes refer to the position on the bar, 
the suffixes to the order of the harmonic. It will he seen that the 
co-efficients of the even harmonics are too small to give any trust- 
worthy results. 
As the thermometers were read successively by one observer, the 
whole process occupying twenty seconds or g 1 ^ of a period, the 
values of the phase must be diminished by 0°, 1°, 2°, 3°, respectively, 
i.e., the differences of phase must each be diminished by 1°. 
