rial thermometer, and if
Joule's value 774.1 be increased by 1/200 of itself in order to reduce
it from the equivalent of the degree on the mercurial thermometer to
that on the air thermometer, we get 778 foot pounds, nearly. Rowland
found from his experiments that when reduced to the air thermometer
and to the latitude of Baltimore, the equivalent was nearly 783,
subject to small residual errors.

Nearly all writers upon this subject--except Rankine--have considered
that the mechanical equivalent of heat, in British units, was the
energy necessary to raise the temperature of one pound of water from
32 deg. F. to 33 deg. F., but Rankine defines it as the heat necessary to
increase the temperature of one pound of water one degree Fahrenheit
from that of maximum density, or from 39 deg. F. to 40 deg. F. For ordinary
practice it is immaterial which of these definitions is used, for the
errors resulting therefrom are much less than those resulting from
ordinary observations. But when the value is to be determined by
direct experiment at the standard temperature, Rankine's limits are
much to be preferred; for it is so very difficult to determine exact
values by observation when the substance is near the state bordering
on a change of state of aggregation, as that of changing from water to
ice. Observations made at about 60 deg. F. were reduced by means of
Regnault's law for the specific heat of water, as has been stated,
which is expressed by the formula

4 9
c = 1 + ------ t + ------ t^{2}
10^{5} + 10^{7}

in which t denotes the temperature according to the Centigrade scale.
According to this law, the mechanical equivalent would not be 0.2 of a
foot pound greater at 5 deg. C. (41 deg. F.) than at 0 deg. C. (32 deg. F.); hence, if
this law were correct, it would make no practical difference whether
the temperature were at 0 deg. C. or 5 deg. C. This law makes the _computed_
value at 32 deg. F. about 0.95 of a foot pound less than that determined
by experiment at 60 deg. F.; whereas Rowland's experiments make it
_greater_ at 40 deg. F. by more than four foot pounds, for the air
thermometer. In determining a _fixed_ value to be used for scientific
purposes, it is necessary to fix the place, the thermometer, and the
particular degree on the thermometer. The place may be known by its
latitude if reduced to the level of the sea. The air thermometer
agrees most nearly with that of the ideall