THERMAL CONDUCTIVITIES OF SOME ELECTRICAL INSULATOBa 447 



which the temperature spirals were wound, and it is necessary to determine whether 

 this will have an appreciable effect on the result. 



For this purpose we may assume the cylinder of material to be infinitely long. 



The source at C, fig. 6, is surrounded by a narrow glass cylinder, whose effect is 

 merely to decrease or increase the temperature of all points external to it by a 

 constant amount depending on the thermal conductivities of the glass and the 

 material surrounding it. It produces therefore no change in the difference of 

 temperature l>etween two points in the material tested. If the narrow glass tube 

 round C? were absent, the temperature at a point P within the 

 material would be that due to the source at C, and since the 

 circle AA' is at a constant temperature, an equal sink at C, \^ J*/ 

 the image of Ci, where OC, = OA'/OC. We may therefore put Fig. 6. 



it =-^-log7^, where 7 is the strength of the source and k the thermal con- 



ductivity of the medium. The presence of the glass tube at C" makes it necessary to 

 add to this expression terms representing a source and an equal sink whose strengths 

 depend on the relative conductivities of the material and glass, and whose positions 

 are O w and C",, the images of C and C, respectively, with respect to the circle 

 representing the section of the glass. The complete expression for the temperature 



c P <i r (y P 



at P will therefore l)e -^ log -~ + -^y log -^ . But the mean value of the tempera- 



ture along the circumference of a circle of radius p enclosing a source of strength <f 

 is equal to &* log . - , where k is the conductivity of the medium. Hence for any 



^TTnT P 



circle enclosing both source and sink at C 7 and C w , it is zero. Since the temperature 

 is determined by the resistance of a coil of wire wound round the glass tube, the 

 coil encloses both C' and C', and the tul* has no effect on the observed temperature 

 difference between that coil and the one wound round the source. 



The following table shows the values of the functions which enter into the 

 expression for k in terms of the difference of temperature observed : 



