508 Dr. J. R-. Mayer on the Mechanical Equivalent of Heat. 



necessary condition of every falling motion is that the centre of 

 gravity of the two masses concerned in it (that is, of the earth 

 and of the falling weight) should approach each other. But in 

 the case of the falling together of the two masses, the approach 

 of their centres of gravity reaches its natural limit, and hence 

 the production of a falling movement is thus bound up with an 

 expenditure, namely, with the exhaustion of the given falling- 

 space, and thereby also of the product of that space into the 

 attraction. The falling down of a weight upon the earth is a 

 process of mechanical combination ; and just as in combustion 

 the capacity of performance (that is, the condition of the deve- 

 lopment of heat) ceases when the act of combination comes to an 

 end, so also the production of motion ceases when the weight 

 has fallen to its lowest position. The weight, when lying on the 

 solid ground, is, like the carbonic acid formed in combustion, 

 nothing but a caput mortuum. The affinity, whether mechanical 

 or chemical, is still there after the union just as much as before, 

 and opposes a certain resistance to the reduction of the compound; 

 but its power of performance (Leistungsfahigkeit) 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 direction 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 perceived 

 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, = 1 foot-pound. If the falling-height of 

 this weight amounts to n feet, n not being a large number, the 

 force may be taken as approximately =n foot-pounds. But sup- 

 posing n, or the original distance of the weight from the earth, to 

 be very considerable, or indeed infinite, the force (that is, the num- 

 ber of foot-pounds) does not by any means thereby become infi- 

 nite, 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 velo- 

 city 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 

 remaining 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 



