AS DETERMINED BY FIVE PLATINUM-RESISTANCE THERMOMETERS. 
257 
Similarly, for the half-yearly wave, we find 
Thermometer. P U 9. 
o 
5 . . . 2-GO 
4 . . . 3-01 
3 . . . 3-09 
2 . . . 2-97 
2’92 = amplitude of half-yearly wave at surface. 
Putting these values in the first of equations (f) we can determine the value of x, 
corresponding to a given value of P„, or the depth at which the amplitude of the 
wave is reduced to any given value, on the hypothesis that the conditions prevailing 
above 10 feet remain unchanged at greater depths. 
Although theoretically there is no invariable layer so long as equations ( f) are 
applicable, still we may consider that an annual variation of 0 r- 02 F. is less than can 
be certainly detected. The stratum, therefore, at which the amplitude of the annual 
wave is reduced to 0°'01 may to all intents and purposes be considered as invariable. 
For this depth we have M log P! = — 2 (M being the modulus of common 
logarithms), and therefore 
X = (2 + log P m )/M v / 7 r / k. 
Thus we find as the depth at which the amplitude of the annual wave is reduced 
to 0°-01, 
x l = GD21 French feet - 66 - 0 English feet, 
and similarly for the half-yearly wave, 
x 2 = 33’78 French feet = 36‘0 English feet. 
The depths at which the annual and half-yearly waves are reduced to an 
amplitude of 0 C, 1 F. are found in a similar way to be 45*3 and 2P4 English feet 
respectively. 
This paper deals with the observations of a single year, and the results accordingly 
exhibit discrepancies between theory and observations which, although they are less 
than might have been a priori expected, are greater than one would like to see- 
These discrepancies are due partly to the fact that the temperature variations are 
not strictly of a periodic character as the theory supposes, and as such they might 
he expected to be diminished in the mean of a number of years, and partly to 
irregularities, physical and formal, in the surface. 
The other source of irregularity considered by Lord Kelvin in his paper, referred 
to above, namely, thermometric errors arising from the uncertainty as to the tem¬ 
perature of the liquid in the long stems of the thermometers used in Professor 
VOL. cxcv.— a. 2 L 
