74 THE MECHANICS OF THE EARTH'S ATMOSPHERE, 



and the increase of volume is 



( 



^ ") =42.61 

 n 



The work in this case is very slight, namely, 



The ship, including the crew and the load, must weigh as much as 

 the volume of water displaced by it. The balloon, filled with hydro- 

 gen, in order to carry an equal weight with the ship, must have a vol- 

 ume 837 times as great. If it is tilled with illuminating gas of a specific 

 gravity 0.65 relative to that of the air, it must have a volume 2,208.5 

 times as great as the ship. Thus, the weight that the balloon must 

 have for the given dimension is now determined. The weight for the 



42.6 1 

 hydrogen balloon would be ^777^=?Tr7T that of the shii) ; that of the 



•^ *' 66 1 19.6 '- ■ 



42.6 1 



illuminating gas balloon would be -o.,;vv^ = rT^ that of the ship. 



The work that is necessary under such circumstances to propel the 

 balloon, as the above number for the value o£ qhir shows, would, how- 

 ever, for the adopted small velocity, be reduced in much greater propor- 

 tion thauthatofthe weightof the balloon to the weight of the ship, so that 

 the work here required for the given weight is easy to accomplish in the 

 balloon. For even when we so choose the ship that its load in excess of that 

 of the driving machine (or in excess of the men who act as the machine) 

 is negligible, then the weight of the illuminating-gas balloon need 



be only ^ part of the weight of this driving machine, but the machine 



thus carried by it would also have to do only the one ^,-, , of the work 



•^ 5114 



of the ship's machine, it would, therefore, need to have a less weight in 



about this latter ratio. Especially would this latter be the case when 



we utilize men as the driving machine, whose work and weight both 



increase proportionally to the number. 



So far we can therefore apply the transference from ship to balloon 

 with complete consideration of the peculiarities of air and water. As 

 a maximum velocity for fast ships (large naval steamers), "The Engi- 

 neer's Pocket Book," published by the society " Die HUttc,''^ gives 18 feet 

 per second, or 2.7 German miles, or 21 kilometers per hour. Similarly 

 built balloons, with relatively very feeble or small propelling machin- 

 ery, can attain about one-fourth of this velocity. 



Ships of the above-given dimensions find the limit of their efBciency 

 bounded by the limits of the power of the machinery (including the 

 fuel) that they can carry. However, the practical experience thus far 

 attained allows us to neglect the influence of viscosity for large, swift 



