116 Astronomical and Nautical Collections. 



tional to the magnitude of that displacement : so that the law 

 of their motion must be the same as that of the motion of the 

 pendulum, and of all small oscillations in general. This 

 hypothesis, which is suggested by the analogy with other 

 natural phenomena, and which is the simplest that can be 

 formed respecting the vibrations of the luminous particles, 

 may be considered as experimentally confirmed by the obser- 

 vation, that the optical properties of light are all indepen- 

 dent of any circumstances which cause the greatest difference 

 in the intensity of the vibrations : so that the law of their 

 motion must be presumed to be the same for the greatest as 

 for the smallest. 



It follows from this hypothesis respecting the small oscil- 

 lations, that the velocity of the vibrating particle at each 

 instant is proportional to the sine of an arc, represent- 

 ing the time elapsed from the beginning of the motion, 

 taking the circumference for the whole time required for 

 the return of the particle to the same point, that is, 

 the time occupied by two oscillations, the one forwards 

 and the other backwards. Such is the law according to 

 which I have calculated the formulas which serve to deter- 

 mine the effect of any number of systems of waves of which 

 the intensities and the relative positions are given. These 

 formulas will be found in the Annals of Chemistry, vol. xi., 

 page 254 : [they may be applied with security to the pheno- 

 mena there considered, though the perfect accuracy of the 

 hypothesis in all possible cases may be questioned, upon the 

 grounds of the microscopical observations on the motions of 

 vibrating chords, published by Dr. Young in the Philosophi- 

 cal Transactions for 1800. Tr.] Without entering into the 

 details of the calculations, I think it necessary to show in what 

 manner the nature of the undulation depends on the kind of 

 motion of the vibrating particles. 



^Let us suppose, in the fluid, a little solid plane which is 

 removed from its primitive position, towards which it is urged 

 by a force proportional to the distance. At the beginning of 

 its motion, the accelerative force produces in it an infinitely- 

 small velocity only ; but its action continuing, the effects 

 become accumulated, and the velocity of the solid plane goes 

 on continually to increase, until the moment of its arrival at 



