OONVERSIONS OF MOTION AND FALLING-FOECE. 345 



from cosmical elevations, and also the general laws of central 

 motions, can be developed without its being needful to employ 

 equations of more than the second degree. 



Having now become acquainted with two species of force 

 motion and falling-force we can arrive at a conception of " a 

 force " in general, according to the well-known rule, by col- 

 lecting together the common characteristics of the two spe- 

 cies. To this end, we must consider the properties of these 

 objects somewhat more closely. Their most important prop- 

 erty depends on their mutual relation. Whenever a given 

 quantity of falling force disappears, motion is produced ; and 

 by the expenditure of this latter, the falling-force can be re- 

 produced in its original amount. 



This constant proportion which exists between falling- 

 force and motion, and is known in the higher mechanics un- 

 der the name of " the principle of the conservation of vis 

 viva" may be shortly and fitly denoted by the term " trans- 

 formation " ( Umwandlung) . For instance, we may say that 

 a planet, in passing from its aphelion to its perihelion, trans- 

 forms a part of its falling-force into motion, and, as it moves 

 away from the sun again, changes a part of its motion into 

 falling-force. In using the word " transform" in this sense, 

 nothing else can or is intended to be expressed but a constant 

 numerical ratio. 



But it follows from the axiom mentioned at page 326, that 

 the production of a definite quantity of motion from a given 

 quantity of falling-force, and vice versd, implies that neither 

 falling-force nor motion can be annihilated either totally or in 

 part. We thus obtain the following definition : 



Forces are transformable, indestructible, and (in contradis- 



be taken as the starting-point for the calculation of real velocities, mathe- 

 matical artifices become necessary which are inadmissible in the elementary 

 branches of science. 



15* 



