340 Dr. E. van AubeFs Researches on 



To sum up, all these bismuths contained lead in variable 

 amounts, Classen II. and Latest Brommsdorff containing the 

 least. 



But in the case of the bismuth obtained by electrolysis, no 

 impurity was discovered by spectrum analysis. 



This very minute spectrum analysis of products, prepared 

 with the greatest care by such a distinguished chemist as 

 Prof. Classen, warrants us in saying that pure bismuth cannot 

 be obtained with certainty by precipitation. The electrolyzed 

 metal can alone be considered as chemically pure. 



In the successive precipitations the traces of lead are 

 drawn down mechanically. 



In electrolyzing the solutions of bismuth, in which the 

 spectrum analysis had revealed traces of lead, a very thin but 

 perfectly visible coating of peroxide of lead was found at the 

 positive pole. 



Calculation of the Absolute Values of the Electrical Resistances. 



The mode of measuring the electrical resistance has been 

 described in the preliminary communication. 



In order to determine the absolute value of the electrical 

 resistances at 0° of the tempered rods, it was necessary to 

 calculate the mean section of these rods from their weight, 

 density, and length. 



No sensible error is committed in taking 9"82 as the density 

 of bismuth or of the alloys which we have studied, as the lead 

 and tin contained in the latter were only present in very 

 small quantities. Besides, a much greater cause of error is 

 the exact determination of the length of the rods of bismuth 

 between the -two solderings. 



In the case of the slowly cooled rods the difficulty is greater, 

 because the bismuth adheres very closely to the glass tubes in 

 which it is contained *, and because these tubes cannot be con- 

 sidered as cylindrical. In spite of every precaution it is impos- 

 sible to break the glass, so that the whole of the metal may be got 

 out clear without breaking the rod of bismuth. So I measured 

 with a spherometer the diameters of the bismuth rod at the 

 two extremities and in the middle ; and I considered the rod 

 as formed of two truncated cones joined together at the small 

 end. It was then easy to calculate the electrical conductivity 

 at 0°; for example, either using the formula given by Siemens 

 (Annalen der Physik, vol. ex. 1860, p. 3, or F. Kohlrausch, 

 Guide de Physique pratique, edition franchise, p. 223), or 

 calculating the section of a cylinder whose height is the length 

 of the rod of bismuth, and whose volume is that of the two 



* Righi, Journal de Physique, 2nd series, vol. iii. 1884, p. lo2, 



