348 ACROPHYSICS. 



body, it communicates to the latter a part, at least, of its own force. A 

 continuous force, is one which acts continually ; either increasing or 

 diminishing the velocity, if it acts on a free body, or changing the 

 direction of motion; or producing these effects conjointly. Gravity, 

 is a continuous force, which, near the earth's surface, produces equal 

 increments of velocity in equal times ; and hence it is called a con- 

 stant force; being the cause of bodies having weight, and of their 

 falling, when unsupported. 



A body falling freely, descends through 16 feet in one second ; at 

 the end of which time it is falling at the rate, or with the velocity of 

 32 feet per second. At the end of two seconds, it will have fallen 

 four times as far, and at the end of three seconds, nine times as far, 

 as in the first ; the space increasing as the square of the time. Call- 

 ing t the time in seconds ; v the velocity in feet ; s the space fallen 

 through ; and taking g 32 feet, as the measure of the force of 

 gravity ; we have v = g t = 32 t ; and s = g t* 1 6 t 2 ; and con- 

 sequently, v 2 = 2 gs = 64 s: for problems concerning bodies falling 

 vertically, or for their vertical descent, when falling obliquely. In 

 the case of a ball thrown obliquely upwards, if there were no 

 resistance of the air, its projectile curve would be a parabola ; and 

 calling x and y the horizontal and vertical coordinates of this curve, 

 a being the angle of elevation above the horizon, and v the initial 

 velocity, its equation would be y v 8 cos *a = x v* sin a cos a 3 gx z . 

 But the resistance of the air, which is proportional to the square of 

 the velocity, diminishes the random, or distance to which a cannon 

 ball can actually be thrown, from 15 or 20 to only 3 or 4 miles. 



A pendulum, is a rod, or thread, suspended at or near one end, 

 usually with a weight at the other end, and made to oscillate by the 

 force of gravity. When once set in motion, it would continue to 

 oscillate forever, were it not for the resistance of the air, and of fric- 

 tion, which require that it should be kept in motion by an extraneous 

 force, usually that of a descending weight. Calling a the length of 

 the pendulum, in feet; t the time, in seconds, of one oscillation; g 

 the measure of gravity, = 32 feet, as before ; and jt = 3.1416, the 

 circumference of a circle whose diameter is unity ; we have the equa- 

 tion t = 7t A , for finding the time of one oscillation, by means of 



the length of the pendulum ; it being proportional to the square root 

 of the length, while the force of gravity remains constant. 



3. In the division of Hydrics, so named from the Greek <i>cop, 

 water, we would include both Hy drostatics, and Hydrodynamics; or 

 the laws both of equilibrium and motion, in so far as they are peculiar 

 to liquids. All liquids, are, in theory, regarded as incompressible; 

 though they are found to admit of compression in a slight degree. 

 When enclosed, or confined, in vessels, so as to be acted on as single 

 masses, liquids are subject to the same laws of motion and rest, as 

 solids. But even in this case, their pressure against the sides of the 

 containing vessel, becomes a distinct problem of Hydrics ; and it is 

 found that the pressure produced by their weight, is the same, for 

 equal surfaces, at e"qual depths below the highest level of the liquid ; 



