434 OK. CHARLES H. LEES ON THE EFFECT OF TEMPERATURE ON THE 



different pressures and at different temperatures, and the present paper gives an 

 account of the first steps taken to this end. 



It deals with the effect of temperature on the thermal conductivities of some 

 electrical insulators which could readily be obtained in a pure state and were fairly 

 representative substances. 



The temperature interval used has been small, the actual temperature of the test 

 has been ol>served, and the mathematical work has been made to follow the experi- 

 mental conditions very closely. 



Consideration of a Suitable Method. 



A form of apparatus which lends itself readily to mathematical treatment is one in 

 which the isothermal surfaces are concentric spheres, but the mechanical difficulties 

 in the construction and use of such an apparatus render it unsuitable. 



The mechanical difficulties disappear if cylindrical isothermal surfaces are 

 substituted for spherical, and the mathematical treatment of such cases is com- 

 paratively simple if the cylinders are long enough to enable the effects of the ends to 

 be neglected at points near the middle of the length. 



If through an infinitely long, straight thin wire, embedded in an electrical insulator 

 extending on all sides to infinity, an electric current is sent which, on account of the 

 resistance of the wire, generates in each centimetre length of it an amount H of heat 

 per second, the temperature v at a point whose perpendicular distance from the axis 



TT 



of the wire is r, is given by the equation v = A =- log r, where A is a constant 



and k is the thermal conductivity of the medium surrounding the wire. 

 If the temperatures v arid r, are determined at two points r and r lt then 



H 



Hence if r and r, are observed, the thermal conductivity k of the medium 

 surrounding the wire may be found. 



It is, however, not possible to carry out the experiment in this simple form. The 

 medium must in the first place be confined within a cylindrical surface of limited 

 radius, and the effect of this boundary on the difference between ?> and i\ must be 

 calculated. 



For reasons which will be explained later, it is not advisable to have the axis of 

 this cylinder coincident with that of the wire in which the heat is generated, but to 

 have it midway between the points at which the temperatures are measured. The 

 heating wire and two points at which temperatures are measured lie in a diametral 

 plane of the cylinder, with the heating wire further from the axis than the two points 

 at which temperatures are measured. 



The conditions to which the surface of this cylinder is subjected influence the 



