On* the Measure of Temperature. 
33 
whole of the thermometrical column immersed within the liquid, if the true indi- 
cations are required This precaution, though it may appear unnecessary f mi - 
nulieuse ) in lower temperatures, cannot he neglected in high ones ; for in this case 
the column of mercury contained in the stein undergoes a considerable increase. 
Thus, for example, we remarked that at the temperature of 300° there was fre- 
quently a difference of 12° between the indications of the same thermometer, 
according as the bulb only or stem also was immersed in the liquid. We might 
indeed estimate the error arising from any part of the stem being excluded, when 
we know the expansion of mercury, but the impossibility of saying what is the 
exact temperature of the stem, entailing on us errors the more to be deprecated as 
they would increase with the magnitude of the correction, it has always appeared 
preferable to us to place the thermometers horizontally. 
Although the experiments performed in the manner we have just described, 
have always shown a remarkable agreement in the results, we endeavoured to verify 
these results in another manner. 
In these other experiments, we made use of an air tube of much greater capacity 
than in the first set, placed in. the same manner, with the exception, that the small 
tube attached to it was he it on leaving the copper vessel, and continued downwards 
to a length of about five decimetres The heating process was conducted with the 
same care already described, and when a steady temperature was attained, and 
the height of the barometer noted, the lower end of the tube was made to dip 
into a capsule of dry mercury. The whole was then allowed to cool, till the oil was 
nearly of the temperature of the air ; during which process the mercury continued 
to rise in the vertical rube, until the internal air was completely cooled. The 
elasticity of the air became then, an equivalent to the external pressure of the at- 
mosphere, diminished by the height of the column of mercury that had been raised ; 
that of the heated air again, was equal to the barometric pressure observed at the 
moment when the temperature was stationary : we could thus calculate by the aid 
of Mariotte s law, what had been the expansion of the air, supposing it to have pre- 
served the same elasticity. 
To render this method perfectly exact, it became necessary to allow for the 
capillary depression of mercury, in the narrow tube into which it enters. We had 
determined beforehand the value of this depression, and took care to use a tube of 
uniform caliber, in order that this value should have little or no variation. 
A second point to he considered is, that the volume of air was not precisely the 
same. The portion contained in the small tube was forced of course into the large 
one as the mercury rose, and this portion suffered no change of temperature. We 
have calculated the amount of each of these errors, and have applied the necessary 
corrections. This correction, which depends on the ratio of the capacities of the 
tubes, is deduced by a calculation too simple to require any explanation here*. 
Not only have the experiments made in this way confirmed all the results with 
which the first set had furnished us, but they have also taught us that Mario tte’s 
* It will be sufficient merely to indicate the formula we have used in the reduc- 
tion of these new experiments. H represents the weight Of the batometer, which is 
the measure of the elastic force of the heated air,T the temperature of this air, indi- 
cated by the mercurial thermometer, T' that of the cold air, IF the height of the 
column supported after cooling, this height being corrected for the capillary depres- 
sion, A' the total height of the vertical tube,r the ratio between the capacity ofthis 
tube and of the large horizontal one, rfthe mean dilatation of glass between T and 
T'. V means a volume of air such as it would be when expanded to the tempera- 
ture T, without change of pressure, and supposing it \ at0°. Then 
H fl-H(T— T')) (1 + 0-00375 TQ 
(H_H')(l+r _£21' ) — t H 
we may also conclude that at any temperature T of the mercurial thermometer, 
the air thermometer corrected for the expansion of glass would indicate a number 
of degrees 
_ H (l+tf(T— TQ) (266.67+T) 
