30& LECTURE XXV. 



opposed to it, may in general be found, with tolerable accuracy, in pounds, by 

 dividing the square of the velocity in a second, expressed in feet, by 500. 

 Thus, if the velocity were 100 feet in a second, the pressure on each square 

 foot would be 20 pounds ; if 1000 feet, 2000 pounds. For a sphere of a foot 

 in diameter, we may divide the square of the velocity by 1600. We may 

 also find, in a similar manner, the utmost velocity that a given body can 

 acquire or retain in falling through the air; for the velocity at which the re- 

 sistance is equal to the weight must be its limit. Thus, if a sphere one foot 

 in diameter weighed 100 pounds, the square of its utmost velocity would be 

 160000, and the velocity itself 400 feet in a second; if a stone of such di- 

 mensions entered the atmosphere with a greater velocity, its motion would 

 'very soon be reduced to this limit; and a lighter or a smaller body would move 

 still more slowly. The weight of Mr. Garnerin's parachute, with its whole 

 load, was about a quarter of a pound for each square foot, the square of its 

 greatest velocity must, therefore, have been about 1 25, and the velocity 1 1 feet in a 

 second, which is no greater than that with which a person would descend, in leap- 

 ing from a height of two feet, without stooping. Mr. Garnerin found the velo- 

 city even less than this, and it is not improbable that^the concave form of the 

 parachute might considerably increase the resistance. Thus, Mr. Edgeworth 

 found that a plate 9 inches long, when bent into an arc of which the chord 

 was 7-^, had the resistance increased more than one seventh. The diminution 

 of the resistance of the air by the obliquity of the surface is still less than 

 that of the resistance of water: thus, the resistance on the oblique surfaces 

 of a wedge is not quite so much less than the resistance on its base, as its 

 breadth is less than the length of those surfaces. 



When the velocity of a body moving through an elastic fluid is very great, 

 the resistance is increased in a much greater proportion than the square of 

 the velocity: thus, the retardation of a cannon ball moving with a velocity of 

 1000 feet in a second, or a little more, becomes suddenly much greater than 

 the calculation indicates. The reason of this change appears to be, that the 

 condensation of the air before the ball is necessarily confined to a smaller por- 

 tion, which is very intensely compressed, because the effect of the impulse can 

 only spread through the air with a certain velocity, which is not much greater 

 than that of the ball; and this smaller portion of air must necessarily be much 

 more condensed than a larger portion would have been. Thus, when a cannon 



