118 Astronomical and Nautical Collections. 



minate distance from the centre of agitation. This time is the 

 shorter, as the fluid is less dense, and more elastic ; that is, 

 composed of particles which possess a greater repulsive force. 

 This being granted, let us assume, in order to facilitate the 

 explanation, the moment when the moveable plane is returned 

 to the initial situation, after having performed two complete 

 oscillations in opposite directions : at this moment, the nascent 

 velocity, which it had at first, is transmitted to a stratum of 

 the fluid removed from the centre of agitation by a distance 

 which we may represent by d. Immediately afterwards, the 

 velocity of the moveable plane, which has a little augmented, 

 has been communicated to the stratum in contact with it : 

 ** hence it has passed successively through all the following 

 strata ;" and at the moment when the first agitation arrives 

 at the stratum of which the distance is d, the second has 

 arrived at the stratum immediately before it. Continuing 

 thus to divide, in our imagination, the duration of the two 

 oscillations of the moveable plane into an infinity of small 

 intervals of time, and the fluid comprehended in the length d, 

 into an equal number of infinitely thin strata, it is easy to 

 perceive, by the same reasoning, that the different velocities 

 of the moveable plane, at each of these instants, are now dis- 

 tributed among the corresponding strata ; and that thus, for 

 example, the velocity which the plane possessed at the middle 

 of the first oscillations in the direction of the motion, must 

 have arrived, at the instant in question, at the distance | d : 

 so that it is the stratum at this distance which possesses at 

 the moment the greatest direct velocity ; and in the same 

 manner when the plane arrived at the limit of its first direct 

 oscillation, its velocity was extinguished, and the same absence 

 of motion will be found at the distance J d. 



It is always supposed, that the oscillations of the plane are 

 so minute in comparison with the length d, that their extent 

 may be neglected in this calculation : and this hypothesis is 

 actually consistent with the fact, since there is every reason 

 to suppose that the excursions of the incandescent particles 

 are very small in comparison with the extent of an undula- 

 tion, which, though an extremely minute space, is still an ap- 

 preciable quantity, and may be actually measured. Besides, 



