Note 23 — Chapter VII · MOLECULES AND ATOMS. THE LAWS OF GAY-LUSSAC AND AVOGADRO-GERHARDT

This formula (which is given in my work on ‘The Tension of Gases,’ and in a somewhat modified form in the ‘Comptes Rendus,’ Feb. 1876) is deduced in the following manner. According to the law of Avogadro-Gerhardt, M = 2D for all gases, where M is the molecular weight and D the density referred to hydrogen. But it is equal to the weight s0 of a cubic centimetre of a gas in grams at 0° and 76 cm. pressure, divided by 0·0000898, for this is the weight in grams of a cubic centimetre of hydrogen. But the weight s of a cubic centimetre of a gas at a temperature t and under a pressure p (in centimetres) is equal to s0p/76(1 + at). Therefore, s0 = s.76(1 + at)/p; hence D = 76.s(1 + at)/0·0000898p, whence M = 152s(1 + at)/0·0000898p, which gives the above expression, because 1/a = 273, and 152 multiplied by 273 and divided by 0·0000898 is nearly 6200. In place of s, m/v may be taken, where m is the weight and v the volume of a vapour.