Applications of the Formulas 73 



M would be independent of C and e, that is to say of the material 

 of the body and of its thickness. This case may occur when the 

 value of e is very small relatively to that of C. 



Consider for example lead, the poorest conductor among the 

 metals, and for which C= 113; supposing the surfaces of the plate 

 to be dull, Q will equal approximately 1.25 and for thicknesses of 

 395"> -79" and 1.18" the values of zC-\-Qe would be 226+ .494, 

 226+ .988, 226+1.48, numbers which differ very slightly. The 

 differences would be even less for the other metals. If we imagine 

 a plate of woolen material, for which the lowest value of C is .323, 

 to have a thickness of .004", which is about that of a sheet of 

 paper, the value of zC-\-Qe would be equal to .646 + .005; the 

 second term being again small relative to the first may be neglected 

 and the value of M would be the same as in the preceding case. 

 Thus a sheet of paper transmits the same amount of heat as a 

 metal plate, of which the thickness may be varied through quite 

 a wide extent. 



The case of thin sheets of glass is similar. Since C for glass 

 equals 6.05; <2=.6o+.45 = i.o5 and 2C-\-Qe=i2.i-}-i.o5e and 

 for thicknessesof .04", .08" and .12", this last expression becomes, 



I2.I-j-.042, I2.I+.O84, I2.I + .I26. 



866. If we suppose C very small and the thickness e so large 

 that 2Ccan be neglected in comparison with Qe, the value of M 



C 



reduces to (T0), consequently it would be independent of the 



nature of the surface, and inversely proportional to the thickness 

 e; but it is necessary, even for the poorest conductors, that the 

 thickness be very great. For example for woolen cloth with^= 

 19.7" we would have 2C-\-Qe=. 646+ 1.23X19.7=. 646+ 24. 2. 



867. If we had two walls in immediate contact with one 

 another, admitting that there is no sudden change of temperature 

 in the passage of heat from the first to the second, which is con- 

 firmed by experiment, and designating by x the temperature of 

 the junction of the two walls, by e and e' their thicknesses, by C 

 and C their conductivities, we would have after the regime was 

 established: 



** M= C < x 7 t:) M=Q(T-t) 



