38 LFXTURE IV. 



tic slower when they are placed on the summits of very high mountains. On 

 the other hand, a body not specifically heavier thau water, gains more in 

 apparent weight on account of the diminished density of the atmosphere at 

 great elevations, than it loses by the increase of its distance from the earth, 

 liut both these differences ma}-, in all common calculations, be wholly disre- 

 garded. The direction of gravity is always exactly perpendicular to the ho- 

 rizon, that is, to the surface of the earth, which is somewhat curved, on ac- 

 count of the earth's spheroidical figure ; but any Small portion of this surface 

 may be practically considered as a plane, and the vertical lines perpendicular 

 to it, as parallel to each other. 



The oblique motion of a prqjectile may be the most easily understood by 

 resolving its velocity into two parts, the one in a horizontal, the other in a 

 vertical direction. It appears from the doctrine of tilie composition of motion, 

 that the horizontal velocity will not be aflPected by the force of gravitation 

 acting in a direction perpendicular to it, and that it will therefore continue 

 uniform ; and that the vertical motion will also be the same as if the body had 

 no horizontal motion. Thus if we let fall from the head of the mast of a ship a 

 weight, which partakes of its progressive motion, the weight will descend by 

 the side of the mast in the same manner, and with the same relative velocity, 

 as if neither the ship nor the weight had any horizontal motion. 



We may therefore always determine the greatest height to which a projectile 

 will rise, by finding the height from Avhich a body must fall, in order to gain 

 a velocity equal to its vertical velocity, or its velocity of ascent, that is, by 

 squaring one eighth of the number of feet that it would rise in the first second 

 if it were not retarded. For example, suppose a musket to be so elevated that 

 the muzzle is higher than the but-end by half of the length, that is, at an 

 angle of 30° ; and let the ball be discharged with a velocity of 1000 feet in a 

 second; then its vertical velocity will be half as great, or 500 feet in a second : 

 now the square of one eighth of 500 is 3906, consequently the height to which 

 the ball would rise, if unresisted by the air, is 3906" feet, or three quarters of a 

 mile. But in fact, a musket ball, actually shot upwards, with a velocity of 1670 

 feet in a second, which would rise six or seven miles in a vacuum, is so re- 

 tarded by the air, that it docs not attain the height of a single mile. 



