PAPER BY PROF. HELMHOLTZ. 75 



ships, and therefore to arbitrarily assume the coustant 5, as also n 

 (when we can neglect the movements at the surface). If we assume 

 that q increases proportionally to n, then the dimensions remain un- 

 changed, the velocities increase as w, the resistance as w^, the work done 

 as n\ If therefore we were able to build a marine engine of the same 

 weight as the present ones, but of greater efficiency, we would then be 

 able also to attain greater velocities. 



We must compare the balloon with such a ship, although the latter 

 has not yet been constructed, in order to attain complete utilization of 

 the propelling machine that goes up with it. But for this case also 

 and for unchanged dimensions, when the velocity increases as n the 

 work must increase as n^. 



Now the ratio between weight and work done by the men who are 

 carried by a balloon can only, for balloons of very large dimensions, be 

 perhaps more favorable than for a war shi[) and its machinery. For 

 the latter I compute from the technical data that to attain a velocity of 

 18 feet requires an expenditure of one horsepower to 4636.1 kilo- 

 grams weight.* On the other hand, a man weighing 200 poumls, 

 who under favoiable circumstances can do 75 foot-pounds of work }Hr 

 second during eight hours daily, gives on the average for the day 

 one horse-power per 1,920 kilograms. When therefore the balloon 

 weighs one and a half times as much as the laboring men whom it 

 carries, then the ratio is the same as for the ship. Dupuy de Lome 

 has carried out his experiments under somewhat less favorable circum- 

 stances ; in his balloon were a crew of 14 men whose weight was one- 

 fourth of the whole, and of whom only eight worked. Under these 

 circumstances it is a relatively A'ery favorable assumption when for the 

 balloon we assume the ratio between the weight and the work to be 

 the same as for a war steamer. We can therefore for the illuminating 



gas balloon increase the ratio -4 — ^-between work and weight bv in- 

 •t, oll4rr 



creasing n so that the ratio shall equal unity; that is to say, equal to the 



value for ships. lu this case we must have 



w=4. 6208. 



Since now the velocity U of the balloon which we have before com- 

 puted under the assumption of a perfect geometrical similarity in the 



*The special data ou which the computation is based are as follows : 



L = length of the ship over all = 230 Prussian feet. 



£= breadth of the ship over all = 54 " " 



fi"^ total height of the ship = 24 feet. 



T— depth under water = H— ^ B 



V= volume of water displacement = 0. 46 L. B. T. 



Weight of one cubic foot of sea water ^63. 343 lbs. 



A the area of the immersed principal section = 1000 sq. feet. 



The total work = C A V^ 



Where ^ — 0. 46. 



