Density of Water with the Temperature. 109 



However well the results of Hirn's repeated experiments 

 may agree with .one another, still they must contain errors 

 which it is impossible to avoid, but which should not be lost 

 sight of. Thus, for instance, Hirn determined the expansion 

 of his copper vessel between 22° and 101'78°, using water 

 and the figures representing its variation in volume given by 

 Despretz (Table I.) . We know that these results, although 

 derived from one of the best determinations, are somewhat in 

 error, especially at about 20° (Table I.), and therefore, on 

 their basis, the true coefficient of expansion of the copper 

 vessel cannot be obtained *. According to Hirn 0*0000o024 

 was determined to be the coefficient of cubical expansion, and 

 this value was adopted in his calculation. But Fizeau gives for 

 copper 0-00005034 at 40° and 0-00005094 at 50°, showing a 

 rapid increase with the temperature. This also follows from 

 the determinations of Dulong and Petit, who demonstrated 

 that the linear expansion from 0° to 100° is 0-00001718 and 

 0-00001883 from 0° to 300°; whence it may be supposed that 

 if the. mean coefficient of cubical expansion of copper from 

 0° to 100° is 0-000051, then from 100° to 200° it will be 

 0*000056. In general the coefficient of expansion of copper 

 increases with the temperature. Hirn took this quantity as 

 constant, and thus introduced an error amounting to 0'000005, 

 which in temperatures ranging from 100° to 200° involves an 

 error of not less than 0"0005 in the volumes of water. Since, 

 then, the reduction from 15 atmospheres to 1 atmosphere was 

 made by us on the basis of extrapolation, and very probably 

 the true compressibility of water between 100° and 200° is 



* Water, however, is the most convenient liquid for determining the 

 coefficient of expansion of vessels ; and if the data for the expansion of 

 water be complete we may prefer it to all other liquids, especially for the 

 determination of the expansion of glass vessels at moderate temperatures, 

 because in this case water varies in volume very slightly. The following- 

 simple method, which I have practised for a long time, gives very rapid 

 and concordant results for the coefficient of expansion of glass at tem- 

 peratures near 0°. The vessel is filled with water at 0°, up to a mark, 

 and then carefully heated ; at first the level falls, but then at a certain 

 temperature t it again returns to the former level. The determination 

 of t gives k. Evidently the volume of the vessel at 0° and at t is equal 

 to the volume of water V and Yt at these temperatures ; and hence the 

 ratio 



V 



v o 



In this manner the expansion of vessels can be rapidly determined by 

 means of a corrected thermometer, and the relative results obtained are 

 very precise. This method may be of especial use in the stud} of areo- 

 meters. 



