Thermal Conductivities. I9 



If 



V = excess of temp, at point x over that of air. 



q = area of section of bar. 



p = perimeter of section of bar. 



p = density. 



c = specific heat 



k = internal Conductivity 



k = external conductivity supposed to follow Newton's law. 



the equation to the motion of heat in the bar, the isothermal 

 surfaces being supposed plane, is 



[•supposed constant. 



the steady periodic solution of which is : — 



V = (l>{x) + lA„e ~ ^^cos2 wtt f^ - £ + «„ j (2) 



where T= period. A, ju, X are constants and 







(3) 



From these equations it is evident that observations of 

 temperatures at two points of one bar give X„ and ju„ and 

 thence the internal and external conductivities of the bar, and 

 observations at two points on opposite sides of the crystal 

 plate and as close as possible to it, give similarly the conduc- 

 tivities of the crystal. 



Temperatures were determined by three thermo-electric 

 couples of iron and German silver wire soldered into the bars 

 near the crystal, and in circuit with a galvanometer. By 

 taking two additional thermo-junctions in the metal bar, the 

 solution (2) was tested, and found not to represent the varia- 

 tion of temperature throughout the bar. I have since shown 

 that this is to a great extent due to the great increasebf ^ with 



