1822.] Difference in the Specific Gravity of Bodies, 409 



second is to g, so is the square of t or i"- to h ; that is, by multi- 

 plying means and extremes, we have h z= g t^. By taking the 

 same course with the velocity, which for one second (from what 

 has been observed above) will be 2 gy we have as the square of 

 2 g or 4 0-2 is to g, so is v- to //. 



This gives 4g', h ■= g v% and v* = 4 g //. 



From the first expression, f^ = - and t = \ / - = -^ ; from 



the second expression v = 2 g , and h = '^. These for- 

 mulae, as has beeia observed, are true only when bodies fall in 

 vacuo. In the atmosphere, or any other medium, the velocity 

 acquired by falling through a given space will be less than the 

 above in the inverse ratio of the difference between the specific 

 gravity of the body and the medium in which it falls. The dif- 

 ference of specific gravity in this case is precisely the same in 

 effect with the difference of the absolute gravity of two unequal 

 weights at each end of a cord, and hanging over a pulley. If the 

 weights are equal, it is plain that no motion will take place, since 

 the only moving force is the difference of the weights, and the 

 matter to be moved equal to the sum of these weights. Hence 

 if //. (as above) be the height which the heavy weight would fall 

 through, we shall have the following formula for the velocity, 



viz. V = 2 g^ If X ~ — -f W and to being the weights. It will 



be evident that v/hen W = w, v equals nothing, and when w 

 equals nothing, v will be the same as the first formula would 

 give. The motion of bodies in different media is affected in the 

 same way by the difference of specific gravity, and the theorem 

 is the same, with the exception of the denominator being the 

 greater specific gravity, and not the sum of the two as with the 

 motion of the unequal weights. 



Let S — the specific gravity of a body greater than the 

 medium in which it falls, and C = the specific gravity of the 

 medium ; then we shtdl have, agreeably to the above theorem, 



V — 2 g}r h^ X ^—^ . To make this more familiar, let S = 9, 



being the specific gravity of copper nearly, and c = I, being the 

 specific gravity of water; and let// = four feet. Then v = 2 x 



V It) X \/4 X — ^ = 14-1, being I ^ feet less than if the body 



had fallen through the same space in vacuo which would be 16 

 feet. 



When the difference of specific gravity is very small, the effect 

 of the medium is more conspicuous, as is well known in the ex- 

 periment of the feather and the guinea. When bodies fall in 

 vacuo, the velocity is accelerated during the whole time of falling, 

 whatever may be the space to fall through ; but in falling through 



