But later experimental researches have shown that the simple assumption of constant coefficients of conductivity and emissivity, on which the mathematical theory is based, is in many respects inadequate, and the special mathematical methods developed by J.
This he called the external conductivity, but the term emissivity is more convenient.
Taking Newton's law of cooling that the rate of loss of heat is simply proportional to the excess of temperature, the emissivity would be independent of the temperature.
The emissivity really depends on every variety of condition, such as the size, shape and position of the surface, as well as on its nature; it varies with the rate of cooling, as well as with the temperature excess, and it is generally so difficult to calculate, or to treat in any simple manner, that it forms the greatest source of uncertainty in all experimental investigations in which it occurs.
It is the most convenient method, in the case of good conductors, on account of the great facilities which it permits for the measurement of the temperature gradient at different points; but it has the disadvantage that the results depend almost entirely on a knowledge of the external heat loss or emissivity, or, in comparative experiments, on the assumption that it is the same in different cases.
The emissivity was reduced to one-quarter by lagging the bar like a steam-pipe to a thickness of i in.
The rate of diminution of amplitude expressed by the coefficient a in the index of the exponential is here greater than the coefficient b expressing the retardation of phase by a small term depending on the emissivity h.
The heat generated by the current C at a point x where the temperature-excess is 0 is equal per unit length and time (t) to that lost by conduction -d(gkdo/dx)/dx, and by radiation hpo (emissivity h, perimeter p), together with that employed in raising the temperature gcdo/dt, and absorbed by the Thomson effect sCdo/dx.