in which t is the temperature of the thermometer, and t0 that of the
enclosure, a is a constant having the value 1.0075, and the coefficient
A depends on the form of the bulb and the nature of its surface. For the
ranges of temperature they employed, this formula gives much better
results than Newton's, but it must be remembered that the temperatures
were expressed on the arbitrary scale of the mercury thermometer, and
were not corrected for the large and uncertain errors of stem-exposure
(see THERMOMETRY). Moreover, although the effects of cooling by
convection currents are practically eliminated by exhausting to 3 or 4
mm. (since the density of the gas is reduced to 1/200th while its
viscosity is not appreciably affected), the rate of cooling by
conduction is not materially diminished, since the conductivity, like
the viscosity, is nearly independent of pressure. It has since been
shown by Sir William Crookes (_Proc. Roy. Soc._, 1881, 21, p. 239) that
the rate of cooling of a mercury thermometer in a vacuum suffers a very
great diminution when the pressure is reduced from 1 mm. to .001 mm., at
which pressure the effect of conduction by the residual gas has
practically disappeared.
Dulong and Petit also observed the rate of cooling under the same
conditions with the enclosure filled with various gases. They found that
the cooling effect of the gas could be represented by adding to the term
already given as representing radiation, an expression of the form