34-6 Note by M. Ampere on Heat and Light 



Let us see then what takes place in the diapason in the fol- 

 lowing cases. 



1 . It* the diapason be in vacuo, the vibratory motion is in- 

 definitely continued, and the sum of the vires vivce, whether 

 implicit or explicit, remains constant. 



2. If the diapason be in a fluid the density of which is 

 less than its own, every entire vibration of the diapason, that 

 is to say, its motion within the compass of two complete re- 

 turns to the same position with velocities in the same direction, 

 will produce in the fluid an undulation of a determined thick- 

 ness, which traverses it, according to the known laws of the 

 propagation of sound, leaving at rest the part it has traversed, 

 excepting the motion which the following wave will produce 

 if the diapason continues vibrating. At every vibration, the 

 vis viva of the diapason will have lost all the vis viva which 

 passes into the wave, so that the different successive losses 

 which the diapason will sustain will gradually diminish with 

 the intensity of the waves which it produces. 



3. If the diapason be in a fluid of the same density and 

 elasticity with itself, it will be deprived of all motion at the 

 first vibration, and the whole of its vis viva will pass into the 

 only wave which it will propagate around itself. 



4-. Iftherebein an indefinite medium any number what- 

 ever of diapasons in unison, of which a single diapason or a 

 group of neighbouring diapasons are in vibration, the waves 

 produced in the medium, which we suppose to be of a density 

 much inferior to that of the diapasons, in meeting those of the 

 diapasons which were at rest, will gradually communicate to 

 them motions so much the less the greater their distance is 

 from the vibrating group, the vis viva of that part of the waves 

 which meets no diapason being lost to the system. But in 

 proportion as the diapasons which first were at rest are set in 

 motion, they will produce new waves, a part of the vis viva of 

 which will return to the first group, returning to it a smaller 

 amount of vis viva than it receives, as by virtue of these mu- 

 tual exchanges the vis viva of their vibrations cannot increase 

 but in proportion as it becomes inferior to that of the group 



lows that, the vis viva being the same, the sum of the products of the masses 

 by the squares of the velocities would become a maximum in the case in 

 which all the molecules would pass at once through the position of equili- 

 brium; for it would be when the other part, always positive, of what we 

 have called vis viva, is 0. I term the first part of the vis viva resulting 

 from the masses multiplied by the squares of their velocities explicit vis 

 viva (force vive explicite), and the double of the integral designated above 

 implicit vis viva. In a system which is retained at rest out of the position 

 of equilibrium theie is a positive implicit force equal to double the value of 

 that integral in the position in which the body is retained. 



