DETERMINATION OF THE SPECIFIC HEAT OF WATER. 433 
looking through a telescope of small magnifying power, but without a micrometer. 
The observations with every thread were repeated more than once, often by different 
observers. The final result is given in Table IV., in which the second column gives 
the calibration correction in thousandth parts of one division. The reductions are 
easily made by the method of least squares in the manner indicated by THIESSEN. 
The probable error of a single observation®* was calculated to be ‘020 division, and the 
probable error in the final correction at each point is ‘008 division, or, as the thermo- 
meter was divided into fiftieths, the probable error in the calibration correction is 
0°00016. 



TABLE IV. 
A = F Calibration correction Calibration correction | 
a aee ebcetree deduced from observa- deduced from observa- | 
Ps totals atch beeen ere er 
sion = 0°-00002. ee ‘| measurements. 1894. | 
12 0 —— — 
13 77 88 75 
14 184 186 172 
15 22 30 15 | 
16 272 283 246 
17 253 265 257 
18 45 41 38 
19 83 82 122 
20 291 286 314 
21 75 86 50 
22 80 103 88 
23 0 — — | 





We conclude from this that it is extremely unlikely that our calibration is wrong 
by 0°:0008 at any point. In order to see how far the eye without micrometer may be 
trusted to carry out a calibration by means of one thread (Gay-Lussac’s method), we 
give in the third column of Table IV. the calibration corrections deduced from the 
observations of the thread of one degree. At the conclusion of our experiments it 
seemed more satisfactory to make certain that no appreciable change had taken place 
in the thermometer. The calibrations were, therefore, repeated, but this time only 
with one thread, according to Gay-Lussac’s method, and the readings were taken 
with a micrometer. The results are given in the fourth column. The greatest 
difference between the corrections found in 1892 and 1894 amounts to about ‘04 
division, or 0°:0008; the average difference amounts to less than half that value. 
The observations made at the conclusion of our experiments were only intended as 
a check, and we feel justified in concluding that no change has taken place in the 
* By a single observation here is meant the measurement of the mercury thread in one of its positions. 
Several measurements in the same position are taken, and their mean value counts in the reduction as 
one observation. 
MDCCCXCV.—A. omer 
