Let heat dH in dynamical measure be given to the wire while the stress S is maintained constant, and let the extension increase from s to s + ds. The stress S will do work ASds _on the wire_, and the work ratio will be -ASds⧸dH. Now let the stress be increased to S + dS while the extension is kept constant, and the absolute temperature raised from T to T + dT. The stress ratio (as we may call it) is dS⧸S and the temperature ratio dT⧸T. Thus we obtain (p. 134 above) －(dS⧸dT) = (1⧸TA) (dH⧸ds) In his Heat article Thomson used the alteration e of strain under constant stress (that is ds⧸l, where l is the length of the wire) corresponding to an amount of heat sufficient to raise the temperature under constant stress by 1°. Hence if K be the specific heat under constant stress, and le be put for ds in the sense just stated, we have dT = －(TedS⧸Kρ) ... (F) where ρ is the density, since dH = KρlA. The ratio of dH to the increase ds of the extension is positive or negative, that is, the substance absorbs or evolves heat, when strained under the condition of constant stress, according as dS⧸dT is negative or positive. Or we may put the same thing in another way which is frequently useful. If a wire subjected to constant stress has heat given to it, ds is negative or positive, in other words the wire shortens or lengthens, according as dS⧸dT is positive or negative, that is, according as the stress for a given strain is increased or diminished by increase of temperature. It is known from experiment that a metal wire expands under constant stress when heat is given to it, and thus we learn from the equation (F) that the stress required for a given strain is diminished when the temperature of the wire is raised. Again, a strip of india-rubber stretched by a weight is shortened if its temperature is raised, consequently the stress required for a given strain is increased by rise of temperature. These results, from a qualitative point of view, are self-evident. But from what has been set forth it will be obvious that an equation exactly similar to (F) holds whether the change ds of s is taken as before under constant stress, or at uniform temperature, or whether the change dS of S is effected adiabatically or at constant strain. In all these cases the same equation dT = －T (edS⧸Kρ) ... (G) applies, with the change of meaning of dT involved.