18 LECTURES TO SCIENCE TEACHERS. 



of temperature between the two vessels and double the 

 thickness at the same time, the same quantity of heat 

 passes through, and that is the point which we wish to 

 arrive at. We see, then, the thicker the wall is the 

 greater is the resistance to the flux of heat, and the greater 

 the difference of temperature between the two faces of the 

 wall the greater amount of heat is allowed to pass, and 

 consequently the flux of heat is also proportional to the 

 difference in temperature, which I may call 6 1 9 . The 

 difference in temperature between the first and second wall 

 is thus universally proportional to the thickness of the 

 wall, and therefore, if the thickness of the wall be called D, 

 in the result the quantity of heat which passes through the 

 wall will depend on the area of the wall, consequently, if 

 we call A the area of the wall, you see that the flux of 

 heat will be proportional to A. Hence, altogether, the 

 flux of heat through the wall varies directly with the time, 

 directly with the difference in temperature between the two 

 faces, directly as the area of the surface through which the 

 heat is passing, and inversely as the thickness of the wall. 

 Since F varies proportionally to this, we are justified in 

 saying that the flux of heat is equal to this quantity multi- 

 plied by a constant, which I call K. If, then, in any 

 experiment we are able to measure the flux of heat, if we 

 can measure the difference of temperature in the two faces 

 and the area through which that heat is allowed to pass, the 

 thickness of the wall and the time during which that heat 

 is passing through, then we know all these constant quan- 

 tities except one, and we may state the result thus : 



f} A 



F = K t-^-T -A. All we have to do, then, is to determine 



K in this formula, which is called the conductivity of the 

 substance. The greater K is, the greater is the flux of 

 heat. K is the quantity which must be determined experi- 

 mentally in order that we may apply our knowledge of the 

 conductivity of different substances to practical or theoreti- 

 cal purposes. We find in the end that the conductivity is 



F. d 



equal to the flux K=r- 7TT-A- That is the value of 



t x (0 1 2 ) 



the conductivity in any experiment that we make. 



Now, to define the conductivity more simply, let us take 

 particular values of some of these quantities. Let us make 



