496 Dr. Lees and Mr. Chorlton on the Thermal 



material used, two short pegs of brass, one vertically above 

 the other, project from the disks, and their distance apart is 

 measured by means of a wire gauge or calipers, when the 

 disks are in contact and when the plate to be tested is between, 

 the difference is the thickness of the plate of the material 

 tested. The under surface of the lower disk may be kept 

 polished, or it may be painted, in order that the heat radiated 

 from it may remain constant during a series of experiments. 



When steam is passed through the upper cylinder the tem- 

 perature of the upper disk is raised to nearly 100° C. ; heat 

 flows through the plate of material experimented on to the 

 lower disk, the temperature of which is therefore raised above 

 that of the surrounding air. It begins in consequence to lose 

 heat by radiation and conduction to the air, and eventually a 

 stage is reached when this loss of heat is equal to the heat 

 received from the material experimented on. 



Hence if the amount of this loss is found by a separate 

 experiment, a determination of the temperature gradient in 

 the material experimented on at its surface of contact with 

 the lower plate, will enable the thermal conductivity of the 

 material to be found. 



Theory. 



If is the temperature at a point x above the under surface 

 of the lower plate, O the temperature of the air, k x the internal 

 conductivity, h { the external conductivity or " emissivity," 

 Newton's law being supposed to hold for the limits of tem- 

 perature used, p. the perimeter, q the area, of cross section of 

 the plate, the differential equation for the motion of heat in 

 the plate, the isothermals being assumed plane, is satisfied if 



6 - e^A, cosh y/tfc . x + B x sinh /y/gi . .*, 



where A x and B t are constants. 



The condition for continuity of flow at the under surface is 



k-i -r- —h\6 for m = 0, 



ax 



i. e. 



vg 



B^AA; 



— O =A 1 \ cosh 



^.^--^sinh^.,} 



1 V qh , 



