814 
ME. W. HOPKINS’S EXPEEBIENTAL EESEAECHES 
The cases (2) and (4) are those in which the junction was doubtless rendered most com- 
plete, by means of plaster of Paris in the first case (applied in a moist state and allowed 
to dry), and in the latter case, by means of moistened clay, applied under considerable 
pressure. These cases, it will be obseiwed, correspond to the largest values of and. 
therefore, to the most rapid transmission of heat through the siuTace of junction for any 
given difference of temperature on each side of it. 
8. The influence of this kind of discontinuity in the conducting mass is manifestly of 
great importance in the conduction of terrestrial heat from the interior of the earth to 
its surface through a series of different strata. If we have several superimposed strata, 
each having the same conductivity, but separated by planes of discontinuity, as in the 
preceding experiments, it may be convenient to know what must be the conductive 
power of a continuous mass of equal thickness, in order that the temperatm'es of the 
upper surfaces of the continuous and discontinuous masses may be the same, the tempera- 
tures of their lower surfaces being equal, as well as the radiating powers of their upper 
surfaces. The quantities of heat transmitted in the two cases tvfill then be the same. 
Let us suppose the conducting mass to have the same conductirity throughout, but to 
be divided into n-\-\ portions by n planes of discontinuity, /q, /q, .../q being their 
respective thicknesses. Let us also suppose the coefficient q to be the same for each 
discontinuity. Instead of the equations (a) (art. 6), we shall have the following 
system : — 
t, — 
^1 ^2 
L ^1 
&c. 
t? -ifp =f(r— 
r=|(r-rXA+/<, +/!,+.. 
and adding, 
= &c. 
