. The Edinburgh new philosophical journal . On the common scale of an air-thermometer, let the straight CI/* —. From B draw BCD at right angles to line AB = 1 -f ai AB, making BC to BD as the specific her* of air under a constant volume is to its specific heat under a constant pressure, or as 1 to k. Through C and D describe two rectangular hyperbolas having A for their centre, and AB for an asymptote. Let T — r, the temperature of a mass of air, be increased r degrees, or from B to E : Then AE = -^—^. Draw EG pa-- rallel to BD, and meeting the curves in F and G ; hence EF : EG : : 1 : A-, and
. The Edinburgh new philosophical journal . On the common scale of an air-thermometer, let the straight CI/* —. From B draw BCD at right angles to line AB = 1 -f ai AB, making BC to BD as the specific her* of air under a constant volume is to its specific heat under a constant pressure, or as 1 to k. Through C and D describe two rectangular hyperbolas having A for their centre, and AB for an asymptote. Let T — r, the temperature of a mass of air, be increased r degrees, or from B to E : Then AE = -^—^. Draw EG pa-- rallel to BD, and meeting the curves in F and G ; hence EF : EG : : 1 : A-, and so of every such parallel. If this in- crease of temperature take place under a constant volume, the additional heat may be represented by the area BCFE, but if under a constant pressure, by area BDGE. For in the hyper- bola, as is well known, the variations of tiie area are as those of the logarithms of the abscissa.'. Sup[X)se the temperature to have increased under a constant pressure, and then let the vo- lume of air be instantly reduced to its former magnitude, the temperature by tiiis operation will be farther augmented i de- grees, or from E to H, making area HIFE = CDGF. For the heat at first added now brings the tcmjK'rature to the same pitch, as if it had been added to tlic original volume all the while invariable. By the property of the hyperbola, the area BCFE represents log —. Hence also area HIFE =r CDGF = (A: — 1) log '^^ , AH , , , AE*-' AH = log » """ therefore ^-rrr = -r--. ^ AE AB AE AB JULY OCTOBEU 182(>.
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