LUEDEKIXG — ANOMALOUS DENSITIES OF FUSED BISMUTH. 295 



as is that of water. The actual amount of anomalous expansion 

 calculated from the data given is for : 



No. I. No. II. 



0.0000853 -(- O.COO0870 -\- 



The actual amount of anomalous expansion of water according 

 to Volkmann (VVied. Ann. 14, 260) is 0.000122. 



The close coincidence of results for the two dilatometers makes 

 it quite probable that they are a close approach to the actual 

 magnitude. 



It was an easy matter to measure, in conjunction with these 

 observations of anomalous densities, the expansion of liquid bis- 

 muth itself in the range of temperature of the experiments. The 

 co-efficient of expansion of liquid bismuth between 270° and 303° 

 C. was determined by comparing the readings of the mercurial 

 and bismuth thermometers between those temperatures. The 

 value of the divisions of the bismuth thermometer was determined 

 by first filling it with mercury and observing the readings be- 

 tween the temperatures above mentioned. A direct comparison 

 with a mercurial thermometer was thus possible. It v/as ascer- 

 tained that the bi>muth column moved over only j\ of the dis- 

 tance of the mercury column between 270° and 303° C. Taking, 

 therefore, the mean co-tfficient of expansion of mercury, accord- 

 ing to Landolt and Bornstein, at 0.00016595, it follows that the 

 mean co-efficient of expansion of bismuth between these same 

 temperatures is 0.00004425. 



The mean co-efficient of cubical expansion of solid bismuth 

 between 0° and 100° is, also quoting Landolt and Bornstein, 

 0.000041 1. 



The expansion at the moment of solidification of liquid bismuth 

 is, according to Marx, about 3 p. ct. The expansion at the mo- 

 ment of solidification of water is about 9 p. ct., being three times 

 that of bismuth. We may on general grounds, supposing that 

 the mechanism of solidification is the same for bismuth as for 

 water, infer that the expansion from the point of maximum den- 

 sity of bismuth to the point of solidification is less for bismuth 

 than for water. Our experiments have proven this to be the case, 

 although the exact quantitative ratio, i.e. whether also the anom- 



