HIGHEST VELOCITY OF A FALLING BODY. 337 



before, and opposes a certain resistance to the reduction of 

 the compound ; but its power of performance (Leistungs- 

 fdhigkeit) is at an end as soon as there is no further available 

 falling-space. 



Whenever the attraction becomes indefinitely small, or 

 ceases altogether, space is no longer effective space ; and thus 

 it follows, from the diminution which gravity undergoes with 

 distance, that falling-space is limited in the centrifugal direc- 

 tion also, and hence that the cause of motion or " force " is, 

 under all circumstances, a finite magnitude which becomes 

 exhausted in producing its effect. 



This fundamental physical truth will be most easily per- 

 ceived when applied to a special case and reduced to figures. 

 "When a pound weight is lifted one foot from the ground, the 

 available force is, as every one knows, one foot-pound. If 

 the falling-height of this weight amounts to n feet, n not be- 

 ing a large number, the force may be taken as approximately 

 =n foot-pounds. But supposing n, or the original distance 

 of the weight from the earth, to be very considerable, or in- 

 deed infinite, the force (that is, the number of foot-pounds) 

 does not by any means thereby become infinite, but, according 

 to Newton's law of gravitation, it becomes at most =r foot- 

 pounds, where r is the number of feet contained in the earth's 

 semidiameter. Thus how great soever the distance through 

 which a weight falls against the earth, or the time occupied 

 by its fall may be, it can acquire no higher final velocity than 

 34,450 Paris feet per second. On the other hand, were the 

 mass of the earth four times as great as it is, its bulk remain- 

 ing the same, the force would likewise become four times as 

 great, and the maximum velocity would be 68,900 feet. 



It is one of the essentials of a good terminology that it 



should put fundamental facts of this kind in a clear light ; 



exactly the opposite, however, is done by the nomenclature at 



present in use. A few expressions, employed by a very meri- 



15 



