through the Atmosphere. 325 



be made to descend, at the same time adjusting the plane so 

 that it shall slant in the contrary direction to what it did during 

 the ascent. The balloon will now descend along the diagonal 

 of another square, and in the same plane as before. These al- 

 ternate ascents and descents are continued until the machine 

 roaches the required spot. 



The rate of the travelling of such a balloon may be estimated 

 by the application of the common laws for the resistance of the 

 air. On the supposition that the diameter of the balloon is 80 

 feet, the inclosed air will have a power of 8377 Ihs., two-thirds 

 of which may be allowed for the weight of the balloon, appa- 

 ratus, men, &c. The remaining 2792 lbs. would give the bal- 

 loon a velocity of 28 feet per second, or 19 miles an hour, which 

 would also be the horizontal velocity. If this should not be 

 sufficient for the object in view, it may be increased by using a 

 balloon and apparatus, the velocity being in the sub-dnplicate 

 ratio of the diameter*. If, however, the principle could be ap- 

 plied to a livdrogen-gas balloon, the diameter necessary to pro- 

 duce a velocity of 28 feet per second would be only 40 feet. 



It is o!>vion*s that the ahiolule motion gained by this plane 

 will only be equal to the excess of the balloon's relative velocity 

 in the air above the alwlide velocity of the wind. The most 

 serious objection, therefore,, to all schemes which have for their 

 object the direction of balloons, is this — that the velocity of the 

 wind is generaliv so very great as to destroy in a considerable 

 degree the relative motion of the balloon. This objection, how- 

 ever, derives its chief weight from an opinion entertained by 

 many persons, tliat a balloon always moves with the very same 

 velocity as the wind. This they attempt to prove by saying 

 that a balloon being in perfect equilibrio with the surrounding 

 air, becomes in effect a part of that fluid, and consequently moves 

 entirely with it. This reasoning I do not pretend to doubt; but 

 let it be observed that it does not at all apply to a balloon 

 which is not hi equilibrio. I am inclined to think that the 

 further a balloon is removed from a state of equilibrium, the less 

 is its motion with the wind, which opinion appears to be con- 

 firmed by the following easy experiment, which 1 have repeatedly 



* Wlieii tilt diameter of a liallooii is incro:iscd or dimiiiislied, tlie velo- 

 city R alVcctf'd l)y the alteration of tlie power and tlie surface. 



Let d be the diiinieter, p the power, 4 the surface, r the resistance, and 

 V tlie velocity. 



Now, hince p is as c/3, and v is as /^/p, it follows that v is as ^di, when 

 the alteration of pcmer only is considered. 



Again, ;• is as s or (/», and v; is inverseli/ as j^r: hence v is inverse!}/ a.& 

 j^/d*- or d, considering oidy the alteration of suiface. 



jjd^ ' d'i 



J'he actual velocity is therefore as . , or J—r- or ^d. 



X 3 performed. 



