HELMHOLTZ ON THE CONSERVATION OF FORCE. 12? 



III. The application of the principle in Mechanical Theorems. 

 We will now turn to the special application of the law of the 

 constancy of force. In the first place, we will briefly notice those 

 cases in which the principle of the conservation of vis viva has 

 been heretofore recognized and made use of. 



1. All motions which proceed under the influence of the general 

 force of gravitation ; hence those of the heavenly and the pon- 

 derable terrestrial bodies. In the former case the law pronounces 

 itself in the increase of velocity which takes place when the 

 paths of the planets approach the central body, in the unchange- 

 ableness of the greater axes of their orbits, their time of rotation 

 and orbital revolution. In the latter case, by the known law 

 that the terminal velocity depends only upon the perpendicular 

 height fallen through, and that this velocity, when it is not 

 destroyed by friction or by unelastic concussion, is exactly suf- 

 ficient to carry the body to the same height as that from which 

 it has fallen ; that the height of ascent of a certain weight is 

 used as the unit of measure in our machines has been already 

 mentioned. 



2. The transmission of motion through the incompressibly 

 solid and fluid bodies, where neither friction nor concussion 

 takes place. Our general principle finds for this case expres- 

 sion in the known fact, that a motion transmitted and altered 

 by mechanical powers, diminishes in force as it increases 

 in velocity. Let us suppose that by means of any machine 

 whatever, to which mechanical force is uniformly applied, 

 the weight m is raised with the velocity c, by another mecha- 

 nical arrangement the weight nm may be raised, but only 



c 

 with the velocity -, so that in both cases the quantity of tension 



developed by the machine in the unit of time is expressed by 

 mgc, where g represents the intensity of gravity. 



3. The motions of perfectly elastic, solid, and fluid bodies. As 

 condition of complete elasticity, we must to the ordinary definition, 

 that the body which has been changed in form or volume com- 

 pletely regains its primitive condition, add, that no friction takes 

 place between the particles in the interior. In the laws of these 

 motions our principle was first recognised and most frequently 

 made use of. Among the most common cases of its application 

 to solids may be mentioned the collision of elastic bodies, the 



