76 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



movements has ouly 0. 2314 that of the velocity u of the ship, therefore 



there results : 



JJ=0. 2314 n. m=1. 06925«. 



For the hydrogen balloon under the same assumptions the velocity 

 will be somewhat larger, since in this case we have to assume 



5114 



Hence, 



%=6.390 



Z7=0. 2314 .n .«=1. 4786m. 



which is nearly one and a half times the velocity hitherto attained in 

 naval steamers. This last velocity for a hydrogen balloon would suffice 

 to go slowly forwards against a fresh breeze. 



But it is to be remarked that these computations relate to colossal 

 balloons whose linear dimensions are three and a half times larger 

 than those of the immersed portion of a large man-of-war, and that 

 the inflammable gas balloon would weigh C0220 kilograms, while that 

 of Dupuy de Lome only weighed 3791) kilograms. In order to return 

 to dimensions that are attainable in actual practice, one must so 

 diminish q and n as that the ratio of the work to the weight shall re- 

 main unchanged, therefore, so that 



<e " ■ (!) - !- 



whence q = w 4 - 



In this way the velocity n will diminish as the cube root of the linear 

 dimensions or as the ninth root of the volume or the weight. This 

 reduction is relatively unimportant. If we pass, for example, from 

 our ideal balloon down to one of the weight of that of Dupuy, there 

 results a reduction of the velocity in the ratio of 1.36 to 1 ; this would 

 give a velocity of 14.15 feet per second, or 16.5 kilometres per hour. The 

 linear dimensions of the balloon would therefore exceed in the ratio 1.4 

 to 1 the dimensions of the ship that is compared with it. 



The ratio between work and load in Dupuy's experiments correspond 

 to the above assumptions very nearly. The eight men that worked for 

 him are, according to our previous estimate, to be put down at 800 kilo- 

 grams, which is rather more than one-flfth of the total weight. Since 

 however the experiment only lasted a short time, therefore these men 

 could work the whole time through with their whole energy, whereas 

 in our computation only the average value of eight hours of work is 

 assumed for the whole day. Therefore these eight men are equal to 

 twenty-four steady workers, whereby the difference is more than made 

 up. Dupuy gives, as having been attained independent of the wind, 



