34 Mr Forbes's description of a New Anemometer. 



resistance of the air, of which, therefore, it becomes a measure. 

 Now, for the sake of conciseness, let R be the resistance op- 

 posed to a velocity expressed by 1, while r is the resistance to 

 the terminal velocity u. Since the resistance varies with the 

 square of the velocity, r = R x ^^ which is also — W, the 

 weight of the body, since it is able to counteract the accele- 



W /W 



rating force of gravity ; hence u"^ — -^ and u=z^ -rr-- Now 



the common theorems of motion give the space through which 



a body must fall to acquire the velocity u in vacuo = a =r — , 



where g expresses the usual unit of the force of gravity. But 

 the time corresponding to a is of course by the same theorems 



= -, which call e ; whence - = - and eu = 2a, which is ob- 

 g e 2 ' 



viously the space described uniformly with the velocity u in 

 the time e, which is equivalent to the time of the extinction of 

 the acceleration of gravity opposed by the uniform action of 

 the resistance r ; for r is assumed = g^ and e is the time during 

 which a body would ascend, uniformly resisted by gravity. 

 Since r extinguishes the velocity in the time e, R, which is w^ 

 times smaller, will do it in vr e, and will extinguish the velo- 

 city 1 (being u times less than u) in the time we, that is, in 

 the time 2a, and the space described being uniformly resisted, 

 will of course be half of that through which it would have 

 moved with a constant velocity, and will be = a ; and this 

 result is quite general for any velocity v or V. 



To find r, u, or o, is the next object, since any one of these 

 being discovered, the others may be .deduced. Newton, by an 

 extended process of investigation in the second book of the 

 Principia, has arrived at this theoretical conclusion of the 

 value of r, (which, however mathematicians have doubted 

 the accuracy of the method in this ** res difficillima,"" as 

 Newton himself has called it, the result has been generally ac- 

 quiesced in ;) that the resistance of air to a sphere moving 

 with any velocity is equal to half the weight of a column of 

 air of equal section, and whose altitude is the weight produ- 

 cing the velocity. 



Hence let a he the height producing the velocity (in feet), 

 d — diameter of the ball (in inches) -^r^: 3.1416, &c. ; 62.5 

 lbs. being the weight of a cubic foot of water, and jj^ the 



