considered as the Results of Vibratory Motion. 345 



tive force when the distance varies. Finally, these two forces 

 may be considered as one, the mathematical expression of 

 which should contain two terms with contrary signs, each cor- 

 responding to one of the forces in question. 



Now, it is clear that if we admit the phenomena of heat to 

 be produced by vibrations, it is a contrndition to attribute to 

 heat the repulsive force of the atoms requisite to enable them 

 to vibrate. 



In order to form a clear idea of the manner in which heat 

 is propagated according to the several laws, 1st, when it moves 

 within the substance of a body, and 2ndly, when it exists 

 in the state of radiant heat, it is necessary to observe at start- 

 ing that in the latter case it cannot be distinguished from 

 light, for light is nothing else than radiant heat having be- 

 come capable of parsing through the humours of the eye, be- 

 cause the frequency and intensity of the vibrations which con- 

 stitute it are then sufficiently powerful to be transmitted 

 through these humours*. It will next be necessary to com- 

 pare these two sorts of propagations to the two modes in which 

 sound is propagated. As a preliminary we will describe these 

 two modes of propagation. 



Suppose a diapason set in vibration, and endeavour to de- 

 fine, first, what we ought to understand by the vis viva of its 

 vibratory motion. We obtain this vis viva by the summation 

 of the products of the masses of all its molecules by the squares 

 of their velocities at a given moment, adding double the in- 

 tegral of the sum of the products of the forces multiplied by 

 the differentials of the spaces described, in the direction of 

 these forces, by each molecule; this integral, which depends 

 only on the relative position of the molecules, being taken in 

 such a manner as to be null in the position of equilibrium 

 around which the vibration takes place f. 



* Experience proves that radiant heat, up to the temperature which 

 causes the bodies from which it proceeds to be visible in the dark, cannot 

 pass through water, either in a fluid or a solid state, and that, on the con- 

 trary, as soon as it attains the temperature of incandescence, it acquires the 

 power of traversing that medium. To explain this coincidence of two 

 facts which appear independent of one another, I set out from the prin- 

 ciple that under a certain degree of intensity and frequency of the vi- 

 bratory motions which constitute radiant heat, these vibrations cannot be 

 propagated through water, and that above that degree they are propagated 

 through it to a greater or a smaller amount. It is clear in the first case that 

 there can be no sensation of light, because the vibrations cannot be propa- 

 gated through the humours of the eye, nor, consequently, reach the retina ; 

 and in the second, that the bodies must become visible in the dark by the 

 rays which have then the power to penetrate the same humours. 



f The integral taken in this manner is positive in all positions near 

 those of equilibrium ; and that is the character of stable equilibrium 

 around which alone vibratory motions can take place. From this it fol- 

 Third Series. Vol. 7. No. 41. Nov. 1835. 2 Y 



