Note 23 — Chapter II · THE COMPOSITION OF WATER, HYDROGEN

The density of hydrogen in relation to the air has been repeatedly determined by accurate experiments. The first determination, made by Lavoisier, was not very exact; taking the density of air as unity, he obtained 0·0769 for that of hydrogen—that is, hydrogen as thirteen times lighter than air. More accurate determinations are due to Thomsen, who obtained the figure 0·0693; Berzelius and Dulong, who obtained 0·0688; and Dumas and Boussingault, who obtained 0·06945. Regnault, and more recently Le Duc (1892), took two spheres of considerable capacity, which contained equal volumes of air (thus avoiding the necessity of any correction for weighing them in air). Both spheres were attached to the scale pans of a balance. One was sealed up, and the other first weighed empty and then full of hydrogen. Thus, knowing the weight of the hydrogen filling the sphere, and the capacity of the sphere, it was easy to find the weight of a litre of hydrogen; and, knowing the weight of a litre of air at the same temperature and pressure, it was easy to calculate the density of hydrogen. Regnault, by these experiments, found the average density of hydrogen to be 0·06926 in relation to air; Le Duc, 0·06948 (with a possible error of ±0·00001), and this latter figure must now be looked upon as near to the truth.

In this work I shall always refer the densities of all gases to hydrogen, and not to air; I will therefore give, for the sake of clearness, the weight of a litre of dry pure hydrogen in grams at a temperature t° and under a pressure H (measured in millimetres of mercury at 0°, in lat. 45°). The weight of a litre of hydrogen

= 0·08986 × H / 760 × 1 / 1 + 0·00367t gram.

For aëronauts it is very useful to know, besides this, the weight of the air at different heights, and I therefore insert the adjoining table, constructed on the basis of Glaisher's data, for the temperature and moisture of the atmospheric strata in clear weather. All the figures are given in the metrical system—1,000 millimetres = 39·37 inches, 1,000 kilograms = 2204·3375 lbs., 1,000 cubic metres = 35,316·6 cubic feet. The starting temperature at the earth's surface is taken as = 15° C., its moisture 60 p.c., pressure 760 millimetres. The pressures are taken as indicated by an aneroid barometer, assumed to be corrected at the sea level and at lat. 45° C. If the height above the level of the sea equal z kilometres, then the weight of 1 cubic metre of air may be approximately taken as 1·222 - 0·12z + 0·00377z² kilogram.

Pressure Temperature Moisture Height Weight of the air

760 mm. 15° C. 60 p.c. 0 metres 1222 kilos. 1,000 cubic metres

700 „ 11·0° „ 64 „ 690 „ 1141 „

650 „ 7·6° „ 64 „ 1200 „ 1073 „

600 „ 4·3° „ 63 „ 1960 „ 1003 „

550 „ - 1·0° „ 62 „ 2660 „ 931 „

500 „ - 2·4° „ 58 „ 3420 „ 857 „

450 „ - 5·8° „ 52 „ 4250 „ 781 „

400 „ - 9·1° „ 44 „ 5170 „ 703 „

350 „ -12·5° „ 36 „ 6190 „ 624 „

300 „ -15·9° „ 27 „ 7360 „ 542 „

250 „ -19·2° „ 18 „ 8720 „ 457 „

Although the figures in this table are calculated with every possible care from average data, yet they can only be taken approximately, for in every separate case the conditions, both at the earth's surface and in the atmosphere, will differ from those here taken. In calculating the height to which a balloon can ascend, it is evident that the density of gas in relation to air must be known. This density for ordinary coal gas is from 0·6 to 0·35, and for hydrogen with its ordinary contents of moisture and air from 0·1 to 0·15.

Hence, for instance, it may be calculated that a balloon of 1,000 cubic metres capacity filled with pure hydrogen, and weighing (the envelope, tackle, people, and ballast) 727 kilograms, will only ascend to a height of about 4,250 metres.