342 
Duno’deer, 
upper surface. 
Duno’deer, 
undersurface. 
Felspathic 
substance 
Knockfarrel. 
Silica 
46-80 
44-21 
78.45 
54*42 
Peroxide iron 
19-92 
19-24 
1-31 
15-19 
Alumina 
20*07 
23-26 
13 39 
19-72 
Lime 
7-81 
7 64 
1-48 
6-42 
Iron 
0-81 
0-31 
... 
Potash 
0-94 
0-95 
1-24 
0-61 
Soda 
3*44 
2.5 7 
490 
0-07 
Magnesia 
0-89 
2-34 
2-49 
99-98 
100-52 
100-77 
9892 
Specific gravity. . 
2-35 
2-54 
' 2-37 
2-85 
Oxygen ratio 
1 : 1 
1 : 1 
1 : 5 
1 : 2 
Oxygen quotient. 
076 
0-87 
0*20 
0-57 
3. On the Reduction of Observations of Underground Tempera- 
ture, with applications to Professor Forbes’ Edinburgh 
Observations and the continued Calton Hill Series. By 
Professor William Thomson, Glasgow. 
The principle followed in the reductions which form the subject 
of this communication may be briefly stated thus :■ — 
The varying temperature during a year, shown by any one of the 
underground thermometers on an average for a series of years, is 
expressed by the ordinary method in a trigonometrical series of 
terms representing simple harmonic variations*, — the first having 
a year for its period, the second a half year, the third a third part 
of a year, and so on. The yearly term of the series is dealt with 
separately for the thermometers at the different depths, the half 
yearly term also separately, and so on, each term being treated as if 
the simple periodic variation which it represents were the sole varia- 
tion experienced. The elements into which the whole variation is 
thus analysed are examined so as to test their agreement with the 
elementary formulae by which Fourier expressed the periodic varia- 
tions of temperature in a bar protected from lateral conduction, and 
experiencing a simple harmonic variation of temperature at one end, 
By a simple harmonic variation is meant a variation in proportion to the 
height of a point which moves uniformly in a vertical circle. 
