﻿498 On tlie Electric Conductivity of Bismuth. 



10°, 30°, 50°, G5°, and 80°, deduced from the above temperature- 

 resistance curves represented in fig. 8, and forming cross curves 

 to them. 



The three variables — resistance, field-intensity, and tempe- 

 rature — could thus be made the three coordinates, and a 

 smooth regular surface obtained giving the value of any one 

 of the variables if the other two are known. PL XVI. fig. 8 

 represents sections of this surface perpendicular to the field 

 coordinate, fig. 9, sections perpendicular to that of tempera- 

 ture ; and in fig. 10 are represented sections perpendicular to 

 the resistance-coordinate, or equi-resistance lines of the sur- 

 face. It is evident that fig. 9 represents a family of curves 

 with a variable parameter, namely the temperature, and the 

 envelope of this family is interesting. It represents the 

 projection on the field-resistance plane of the locus of the 

 minimum points considered in fig. 8, or gives the connexion 

 between the field and resistance for which a minimum value 

 of the latter takes place ; or, to put it still another way, at 

 these values of the resistance and field the former is inde- 

 pendent of small increases or decreases of temperature. Thus 

 for each field there is a ceriain temperature at which increases 

 or decreases of temperature of one or two degrees have no 

 effect on the resistance. The projection of this locus on the 

 field-temperature plane would be represented in fig. 10 by a 

 curve through all the points where the tangents are parallel 

 to the temperature coordinate — that is, the points where the 

 field is a maximum. 



A few words have still to be added on the practical appli- 

 cation of Bi wire to the measurement of magnetic fields. 



We have seen that the phenomenon of alteration of resist- 

 ance of Bi wire in magnetic fields is greatly influenced by 

 temperature, and therefore for anything like exact determi- 

 nations the temperature must be known. A suitable combi- 

 nation of thermometer with the spiral would therefore remove 

 difficulties, and this can be most conveniently arranged by 

 winding a spiral of copper or platinum side by side with the 

 Bi spiral, and from its resistance determining the temperature. 



In closing, I desire to express my great indebtedness to 

 the late Prof. Kundt and Drs. du Bois and Rubens for 

 the help which they have given me by putting private 

 apparatus at my disposal, and for the advice which I have 

 received from them from time to time. 



Physical Institute, Berlin University, 

 July 20, 1894. 



