232 LECTURE XXV. 



its surface, there will still be an elevation before and a depression behind it, 

 the less in height and the greater in extent, as the depth at which the body* 

 is situated is greater. Such an elevation appears to be in some measure 

 analogous to the effect of a low were thrown across a river, which raises its 

 surface, and produces a swell. 



If two or more bodies differently formed, the resistances to the motions 

 of which had been ascertained, were caused to move through a fluid in 

 contact with each other, it is obvious that the paths described by the 

 particles of the fluid in gliding by them, must be very materially altered 

 by their junction ; and it seems natural to expect that the joint disturbance 

 produced in the motions of the fluid, when the surfaces are so united as to 

 form a convex outline, would be somewhat less than if each surface were 

 considered separately. Accordingly, it is found that no calculation, de- 

 duced from experiments on the resistance opposed to oblique plane surfaces, 

 will determine with accuracy the resistance to a curved surface. It appears 

 from experiment that the resistance to the motion of a sphere is usually 

 about two fifths of the resistance to a flat circular substance of an equal 

 diameter. The resistance to the motion of a concave surface is greater 

 than to a plane, and it is easily understood, that since the direction in 

 which the particles of the fluid recede from the solid, must be materially 

 influenced by the form of the solid exposed to their action, their motion in 

 this case must be partly retrograde, when they glide along towards the 

 edges of the concave surface, and a greater portion of force must have 

 been employed, than when they escape with a smaller deviation from their 

 original direction. (Plate XXI. Fig. 276.) 



For some reason which is not well understood, the hydraulic pressure of 

 the air appears to be somewhat greater in proportion to its density, than 

 that of water. It has been found that the perpendicular impulse of the 

 air on a plane surface, is more than equivalent to the weight of a column 

 of air of a height corresponding to the velocity, and the excess is said by 

 some to amount to one third, by others to two thirds of that weight. The 

 resistance appears also to be a little greater for a large surface, than for a 

 number of smaller ones which are together of equal extent. 



The resistance or impulse of the air on each square foot of a surface 

 directly 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 resistance 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 160,000, and the velocity itself 400 feet in a 

 second ; if a stone of such dimensions 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. 



