112 Dr. 0. J. Lodge on a Method of measuring the 



flat faces, and to squeeze it between two copper or iron rods 

 (or any other metal whose conductivity is well known) of 

 exactly the same cross section as itself both in shape and size, 

 putting a pad of a few thicknesses of tinfoil between the sur- 

 faces, so as to make better contact, and then to observe the 

 curve of temperature down each rod when one end of one is 

 heated and the further end of the other is cooled, the whole 

 having been left long enough to attain a permanent state. 



Conduction through a cylinder inserted between a pair of metal 



rods. 

 3. Let the cylinder be of length z y 

 and conductivity %, 

 and let its surface have the radiation-coefficient h' . 

 Let the packing on each side be of thickness y, 



and conductivity k, 

 and let it be so thin that radiation from its edge is negligible. 



Fig. 1. 



Also let us take the atmospheric temperature as an artificial 

 zero ; so that by " temperature " we shall always mean excess 

 of temperature above that of the air. 



And let T and % be the temperatures of metal and cylinder 



on each side of first packing (see fig. 1), 



T' and W ditto on each side of second packing. 



Then the quantity of heat which leaves the first rod traverses 



the first packing and enters the cylinder, which is expressed 



analytically thus (k being the conductivity of the metal), 



7 dT ©-T d® 



and similarly for the quantity which crosses the second packing, 



7 dv T'-e' aw 



k ^= K -j~= x ^~ ' ' ' (2) 



four equations from which the unknown quantities, -, <£), and 



j 

 %' can be eliminated, and % be found. 



Now the curve of temperature down the cylinder is, from 



6= ® cosh qx — (© coth qz — %' cosech qz) sinh q,r, . (3) 



