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 ideally perfect gas thermometer, while the mercurial thermometer differs very much from it in some cases. Thus, Regnault found that when the air thermometer indicated 630 deg. F. above the melting point of ice (or 662 deg. F.), the mercurial thermometer indicated 651.9 deg. above the same point (683.9 deg. F.), a difference of 22 deg. F. It is apparent that the air thermometer furnishes the best standard. As for the particular degree on the scale to be used for the standard, it is apparent, from the observations above made, that the temperature corresponding to that at or near the