DETERMINATION OF THE SPECIFIC HEAT OF WATER. 437 
Comparison of Thermometers. 
Having found the calibration correction of a thermometer, it remains to determine 
its range. The calibration of our calorimetric thermometer was carried out between 
the points marked 12° and 23° respectively, and in order to find the interval between 
those points according to some fixed scale, it would seem most natural to compare the 
thermometer near the extreme points of its range with a standard. This we attempted 
to do at first, but found that the results of different comparisons were not as con- 
cordant as we could have wished. Two thermometers, however, carefully calibrated, 
will show differences when compared with each other amounting to a few thousandths 
of a degree, and there seems little doubt that local irregularities, either in the width 
of the bore, or in the nature of the surface affecting the capillary constant, render the 
readings of a mercury thermometer uncertain to that extent. These irregularities are 
more likely to occur near the ends of the scale where the tube had to be blown out 
into a bulb or joined to the reservoir. We decided therefore to compare the Baudin 
and Tonnelot along the whole scale in order to obtain as accurate a value for the 
Baudin as possible. 
The comparisons were carried out in a horizontal bath with a slowly rising tempe- 
rature. It is unnecessary here to enter into the details of the construction of the 
apparatus and method of comparison, as these will be furnished in another communi- 
cation. Table V. shows the result. Column II. gives the reading T, of the Baudin 
thermometer, corrected for calibration and division errors and reduced to the vertical 
position. The third column gives the correction y which has to be applied to the 
Baudin thermometer in order to reduce it to the readings of the standard mercury 
thermometer made of French glass. The values of y are those obtained by experiment. 
Calling t, the reading of the Baudin thermometer, we require to express y as a linear 
function of the temperature in the form 
VY == a) + biies 
Reducing the observations by the method of least squares, we found 
a= + 0:0194 
b = — 0:00089 + 0:000047. 
Calling y’ the value of y calculated with the help of these data, y — y = A will 
express the difference between the calculated and observed corrections.to the Baudin 
thermometer. The fourth column of the table in which A is entered shows that the 
agreement is satisfactory. The residual differences are accounted for by errors of 
observation, by remaining errors of calibration of the two thermometers and by irre- 
gularities in the capillary phenomena. The probable error of a single comparison is 
found to be 9°-00096, that is about one thousandth of a degree, and the probable 
error of the interval is about one part in 20,000. 
